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"abstract": "Psychophysical studies show motion cues inform about shape even with unknown reflectance. Recent works in computer vision have considered shape recovery for an object of unknown BRDF using light source or object motions. This paper proposes a theory that addresses the remaining problem of determining shape from the (small or differential) motion of the camera, for unknown isotropic BRDFs. Our theory derives a differential stereo relation that relates camera motion to surface depth, which generalizes traditional Lambertian assumptions. Under orthographic projection, we show differential stereo may not determine shape for general BRDFs, but suffices to yield an invariant for several restricted (still unknown) BRDFs exhibited by common materials. For the perspective case, we show that differential stereo yields the surface depth for unknown isotropic BRDF and unknown directional lighting, while additional constraints are obtained with restrictions on the BRDF or lighting. The limits imposed by our theory are intrinsic to the shape recovery problem and independent of choice of reconstruction method. We also illustrate trends shared by theories on shape from differential motion of light source, object or camera, to relate the hardness of surface reconstruction to the complexity of imaging setup.",
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"title": "The Information Available to a Moving Observer on Shape with Unknown, Isotropic BRDFs",
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"abstract": "Predicting specularities in images, given the camera pose and scene geometry from SLAM, forms a challenging and open problem. It is nonetheless essential in several applications such as retexturing. A recent geometric model called JOLIMAS partially answers this problem, under the assumptions that the specularities are elliptical and the scene is planar. JOLIMAS models a moving specularity as the image of a fixed 3D quadric. We propose dual JOLIMAS, a new model which raises the planarity assumption. It uses the fact that specularities remain elliptical on convex surfaces and that every surface can be divided in convex parts. The geometry of dual JOLIMAS then uses a 3D quadric per convex surface part and light source, and predicts the specularities by a means of virtual cameras, allowing it to cope with surface's unflatness. We assessed the efficiency and precision of dual JOLIMAS on multiple synthetic and real videos with various objects and lighting conditions. We give results of a retexturing application. Further results are presented as supplementary video material.",
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"content": "Predicting specularities in images, given the camera pose and scene geometry from SLAM, forms a challenging and open problem. It is nonetheless essential in several applications such as retexturing. A recent geometric model called JOLIMAS partially answers this problem, under the assumptions that the specularities are elliptical and the scene is planar. JOLIMAS models a moving specularity as the image of a fixed 3D quadric. We propose dual JOLIMAS, a new model which raises the planarity assumption. It uses the fact that specularities remain elliptical on convex surfaces and that every surface can be divided in convex parts. The geometry of dual JOLIMAS then uses a 3D quadric per convex surface part and light source, and predicts the specularities by a means of virtual cameras, allowing it to cope with surface's unflatness. We assessed the efficiency and precision of dual JOLIMAS on multiple synthetic and real videos with various objects and lighting conditions. We give results of a retexturing application. Further results are presented as supplementary video material.",
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"abstract": "The prevalence and monetary value of mobile devices, coupled with their compact and, indeed, mobile nature, lead to frequent theft due to a lack of proper anti-theft mechanisms. Currently, there only exist damage control efforts such as remote wiping the device's memory or GPS tracking, but nothing to notify users of theft while it takes place. We propose such a mechanism which utilizes the unique walking patterns inherent to humans and differentiate our work from other walking behavior studies by using it as first-order authentication and developing matching methods fast enough to act as an actual anti-theft system. We test our system with the aid of 45 volunteers and demonstrate detection of unauthorized movement within 10 to 20 steps with an accuracy of 96.4 to 98.4 percent, while simultaneously distinguishing owners as themselves with 97.8 percent accuracy.",
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"abstract": "As mobile devices play increasingly important roles in our daily lives, it is of great significance to protect personal mobile devices from being lost. Noticing the trend that one person normally carries more than one mobile device, we propose an innovative scheme, called <italic>CoSafe</italic>, to detect device loss by verifying the motion consistency between a pair of devices. The rationale is that the vibrations perceived on devices carried by the same person should be tightly coupled whereas a lost device would show distinct mobility characteristics from others. Specifically, CoSafe compares the mobility consistency between a pair of devices on three levels, where coarse features (i.e., the mobility state and motion periodicity) are first compared to give fast response and more complex comparison on subtle feature (i.e., the relative phase) is conducted only when needed. In this way, CoSafe can instantly respond and introduce very low computation and communication costs. We implement CoSafe on a Commercial-Off-The-Shelf Android smartphone and a smartwatch, and conduct both trace-driven simulations and real-world experiments to evaluate the performance of CoSafe. The results show that CoSafe achieves a mean false negative ratio and false positive ratio of 1.46 and 3.12 percent, respectively, even under sophisticated stealing attacks.",
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"abstract": "Object-sensitive pointer analysis (denoted <italic>k</italic><sc>obj</sc> under <inline-formula><tex-math notation=\"LaTeX\">Z_$k$_Z</tex-math></inline-formula>-limiting) for an object-oriented program can be accelerated if context-sensitivity can be selectively applied to only some precision-critical variables/objects in a program. Existing pre-analyses for making such selections, which are performed as whole-program analyses to a program, are developed based on two broad approaches. One approach preserves the precision of object-sensitive pointer analysis but achieves limited speedups by reasoning about all the possible value flows in the program conservatively, while the other approach achieves greater speedups but sacrifices precision (often unduly) by examining only some but not all the value flows in the program heuristically. In this paper, we introduce a new pre-analysis approach, <sc>Turner</sc><inline-formula><tex-math notation=\"LaTeX\">Z_$^{\\mathcal{m}}$_Z</tex-math></inline-formula> (where <inline-formula><tex-math notation=\"LaTeX\">Z_$\\mathcal {m}$_Z</tex-math></inline-formula> stands for modularity), that represents a sweet spot between these two existing ones, as it is designed to enable <italic>k</italic><sc>obj</sc> to run significantly faster than the former approach and achieve significantly better precision than the latter approach. <sc>Turner</sc><inline-formula><tex-math notation=\"LaTeX\">Z_$^{\\mathcal{m}}$_Z</tex-math></inline-formula> is simple, lightweight yet effective due to two novel aspects in its design. First, we exploit a key observation that some precision-uncritical objects in the program can be approximated based on the object-containment relationship pre-established (from Andersen's analysis). In practice, this approximation introduces only a small degree of imprecision into <italic>k</italic><sc>obj</sc>. Second, leveraging this initial approximation, we apply a novel object reachability analysis to the program by pre-analyzing its methods according to a reverse topological order of its call graph. When pre-analyzing each method, we make use of a simple DFA (Deterministic Finite Automaton) to reason about object reachability intra-procedurally from its entry to its exit along all the possible value flows established by its statements to identify its precision-critical variables/objects. In practice, this new modular object reachability analysis, which runs linearly in terms of the number of statements in the program, introduces again only a small loss of precision into <italic>k</italic><sc>obj</sc>. We have validated <sc>Turner</sc><inline-formula><tex-math notation=\"LaTeX\">Z_$^{\\mathcal{m}}$_Z</tex-math></inline-formula> with an open-source implementation in <sc>Soot</sc> (already publicly available) against the state of the art by using a set of 12 widely used Java benchmarks and applications.",
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"normalizedAbstract": "Point cloud registration (PCR) is an important and fundamental problem in 3D computer vision, whose goal is to seek an optimal rigid model to register a point cloud pair. Correspondence-based PCR techniques do not require initial guesses and gain more attentions. However, 3D keypoint techniques are much more difficult than their 2D counterparts, which results in extremely high outlier rates. Current robust techniques suffer from very high computational cost. In this paper, we propose a polynomial time (-, where - is the number of correspondences.) outlier removal method. Its basic idea is to reduce the input set into a smaller one with a lower outlier rate based on bound principle. To seek tight lower and upper bounds, we originally define two concepts, i.e., correspondence matrix (CM) and augmented correspondence matrix (ACM). We propose a cost function to minimize the determinant of CM or ACM, where the cost of CM rises to a tight lower bound and the cost of ACM leads to a tight upper bound. Then, we propose a scale-adaptive Cauchy estimator (SA-Cauchy) for further optimization. Extensive experiments on simulated and real PCR datasets demonstrate that the proposed method is robust at outlier rates above 99 percent and 1-2 orders faster than its competitors. The source code will be made publicly available in https://ljy-rs.github.io/web/.",
"title": "A Practical <inline-formula><tex-math notation=\"LaTeX\">Z_$O(N^2)$_Z</tex-math></inline-formula> Outlier Removal Method for Correspondence-Based Point Cloud Registration",
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"givenName": "Jiayuan",
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"fullName": "Jiayuan Li",
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"abstract": "Proximal operators are of particular interest in optimization problems dealing with non-smooth objectives because in many practical cases they lead to optimization algorithms whose updates can be computed in closed form or very efficiently. A well-known example is the proximal operator of the vector <inline-formula><tex-math notation=\"LaTeX\">Z_$\\ell _1$_Z</tex-math></inline-formula> norm, which is given by the soft-thresholding operator. In this paper we study the proximal operator of the mixed <inline-formula><tex-math notation=\"LaTeX\">Z_$\\ell _{1,\\infty }$_Z</tex-math></inline-formula> matrix norm and show that it can be computed in closed form by applying the well-known soft-thresholding operator to each column of the matrix. However, unlike the vector <inline-formula><tex-math notation=\"LaTeX\">Z_$\\ell _1$_Z</tex-math></inline-formula> norm case where the threshold is constant, in the mixed <inline-formula><tex-math notation=\"LaTeX\">Z_$\\ell _{1,\\infty }$_Z</tex-math></inline-formula> norm case each column of the matrix might require a different threshold and all thresholds depend on the given matrix. We propose a general iterative algorithm for computing these thresholds, as well as two efficient implementations that further exploit easy to compute lower bounds for the mixed norm of the optimal solution. Experiments on large-scale synthetic and real data indicate that the proposed methods can be orders of magnitude faster than state-of-the-art methods.",
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"content": "Proximal operators are of particular interest in optimization problems dealing with non-smooth objectives because in many practical cases they lead to optimization algorithms whose updates can be computed in closed form or very efficiently. A well-known example is the proximal operator of the vector <inline-formula><tex-math notation=\"LaTeX\">$\\ell _1$</tex-math><alternatives><mml:math><mml:msub><mml:mi>ℓ</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math><inline-graphic xlink:href=\"bejar-ieq2-3059301.gif\"/></alternatives></inline-formula> norm, which is given by the soft-thresholding operator. In this paper we study the proximal operator of the mixed <inline-formula><tex-math notation=\"LaTeX\">$\\ell _{1,\\infty }$</tex-math><alternatives><mml:math><mml:msub><mml:mi>ℓ</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>∞</mml:mi></mml:mrow></mml:msub></mml:math><inline-graphic xlink:href=\"bejar-ieq3-3059301.gif\"/></alternatives></inline-formula> matrix norm and show that it can be computed in closed form by applying the well-known soft-thresholding operator to each column of the matrix. However, unlike the vector <inline-formula><tex-math notation=\"LaTeX\">$\\ell _1$</tex-math><alternatives><mml:math><mml:msub><mml:mi>ℓ</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math><inline-graphic xlink:href=\"bejar-ieq4-3059301.gif\"/></alternatives></inline-formula> norm case where the threshold is constant, in the mixed <inline-formula><tex-math notation=\"LaTeX\">$\\ell _{1,\\infty }$</tex-math><alternatives><mml:math><mml:msub><mml:mi>ℓ</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mi>∞</mml:mi></mml:mrow></mml:msub></mml:math><inline-graphic xlink:href=\"bejar-ieq5-3059301.gif\"/></alternatives></inline-formula> norm case each column of the matrix might require a different threshold and all thresholds depend on the given matrix. We propose a general iterative algorithm for computing these thresholds, as well as two efficient implementations that further exploit easy to compute lower bounds for the mixed norm of the optimal solution. Experiments on large-scale synthetic and real data indicate that the proposed methods can be orders of magnitude faster than state-of-the-art methods.",
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"title": "The Fastest <inline-formula><tex-math notation=\"LaTeX\">Z_$\\ell _{1,\\infty }$_Z</tex-math></inline-formula> Prox in the West",
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"givenName": "Benjamín",
"surname": "Béjar",
"fullName": "Benjamín Béjar",
"affiliation": "Department of Biomedical Engineering, Mathematical Institute for Data Science, Johns Hopkins University, Baltimore, MD, USA",
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{
"givenName": "Ivan",
"surname": "Dokmanić",
"fullName": "Ivan Dokmanić",
"affiliation": "Department of Electrical and Computer Engineering, University of Illinois at Urbana Champaign, Champaign, IL, USA",
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"surname": "Vidal",
"fullName": "René Vidal",
"affiliation": "Department of Biomedical Engineering, Mathematical Institute for Data Science, Johns Hopkins University, Baltimore, MD, USA",
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"abstract": "Support vector machines (SVM) have drawn wide attention for the last two decades due to its extensive applications, so a vast body of work has developed optimization algorithms to solve SVM with various soft-margin losses. To distinguish all, in this paper, we aim at solving an ideal soft-margin loss SVM: <inline-formula><tex-math notation=\"LaTeX\">Z_$L_{0/1}$_Z</tex-math></inline-formula> soft-margin loss SVM (dubbed as <inline-formula><tex-math notation=\"LaTeX\">Z_$L_{0/1}$_Z</tex-math></inline-formula>-SVM). Many of the existing (non)convex soft-margin losses can be viewed as one of the surrogates of the <inline-formula><tex-math notation=\"LaTeX\">Z_$L_{0/1}$_Z</tex-math></inline-formula> soft-margin loss. Despite its discrete nature, we manage to establish the optimality theory for the <inline-formula><tex-math notation=\"LaTeX\">Z_$L_{0/1}$_Z</tex-math></inline-formula>-SVM including the existence of the optimal solutions, the relationship between them and P-stationary points. These not only enable us to deliver a rigorous definition of <inline-formula><tex-math notation=\"LaTeX\">Z_$L_{0/1}$_Z</tex-math></inline-formula> support vectors but also allow us to define a working set. Integrating such a working set, a fast alternating direction method of multipliers is then proposed with its limit point being a locally optimal solution to the <inline-formula><tex-math notation=\"LaTeX\">Z_$L_{0/1}$_Z</tex-math></inline-formula>-SVM. Finally, numerical experiments demonstrate that our proposed method outperforms some leading classification solvers from SVM communities, in terms of faster computational speed and a fewer number of support vectors. The bigger the data size is, the more evident its advantage appears.",
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"abstractType": "Regular",
"content": "Support vector machines (SVM) have drawn wide attention for the last two decades due to its extensive applications, so a vast body of work has developed optimization algorithms to solve SVM with various soft-margin losses. To distinguish all, in this paper, we aim at solving an ideal soft-margin loss SVM: <inline-formula><tex-math notation=\"LaTeX\">$L_{0/1}$</tex-math><alternatives><mml:math><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mn>0</mml:mn><mml:mo>/</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math><inline-graphic xlink:href=\"wang-ieq2-3092177.gif\"/></alternatives></inline-formula> soft-margin loss SVM (dubbed as <inline-formula><tex-math notation=\"LaTeX\">$L_{0/1}$</tex-math><alternatives><mml:math><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mn>0</mml:mn><mml:mo>/</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math><inline-graphic xlink:href=\"wang-ieq3-3092177.gif\"/></alternatives></inline-formula>-SVM). Many of the existing (non)convex soft-margin losses can be viewed as one of the surrogates of the <inline-formula><tex-math notation=\"LaTeX\">$L_{0/1}$</tex-math><alternatives><mml:math><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mn>0</mml:mn><mml:mo>/</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math><inline-graphic xlink:href=\"wang-ieq4-3092177.gif\"/></alternatives></inline-formula> soft-margin loss. Despite its discrete nature, we manage to establish the optimality theory for the <inline-formula><tex-math notation=\"LaTeX\">$L_{0/1}$</tex-math><alternatives><mml:math><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mn>0</mml:mn><mml:mo>/</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math><inline-graphic xlink:href=\"wang-ieq5-3092177.gif\"/></alternatives></inline-formula>-SVM including the existence of the optimal solutions, the relationship between them and P-stationary points. These not only enable us to deliver a rigorous definition of <inline-formula><tex-math notation=\"LaTeX\">$L_{0/1}$</tex-math><alternatives><mml:math><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mn>0</mml:mn><mml:mo>/</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math><inline-graphic xlink:href=\"wang-ieq6-3092177.gif\"/></alternatives></inline-formula> support vectors but also allow us to define a working set. Integrating such a working set, a fast alternating direction method of multipliers is then proposed with its limit point being a locally optimal solution to the <inline-formula><tex-math notation=\"LaTeX\">$L_{0/1}$</tex-math><alternatives><mml:math><mml:msub><mml:mi>L</mml:mi><mml:mrow><mml:mn>0</mml:mn><mml:mo>/</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math><inline-graphic xlink:href=\"wang-ieq7-3092177.gif\"/></alternatives></inline-formula>-SVM. Finally, numerical experiments demonstrate that our proposed method outperforms some leading classification solvers from SVM communities, in terms of faster computational speed and a fewer number of support vectors. The bigger the data size is, the more evident its advantage appears.",
"__typename": "ArticleAbstractType"
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],
"normalizedAbstract": "Support vector machines (SVM) have drawn wide attention for the last two decades due to its extensive applications, so a vast body of work has developed optimization algorithms to solve SVM with various soft-margin losses. To distinguish all, in this paper, we aim at solving an ideal soft-margin loss SVM: - soft-margin loss SVM (dubbed as --SVM). Many of the existing (non)convex soft-margin losses can be viewed as one of the surrogates of the - soft-margin loss. Despite its discrete nature, we manage to establish the optimality theory for the --SVM including the existence of the optimal solutions, the relationship between them and P-stationary points. These not only enable us to deliver a rigorous definition of - support vectors but also allow us to define a working set. Integrating such a working set, a fast alternating direction method of multipliers is then proposed with its limit point being a locally optimal solution to the --SVM. Finally, numerical experiments demonstrate that our proposed method outperforms some leading classification solvers from SVM communities, in terms of faster computational speed and a fewer number of support vectors. The bigger the data size is, the more evident its advantage appears.",
"title": "Support Vector Machine Classifier via <inline-formula><tex-math notation=\"LaTeX\">Z_$L_{0/1}$_Z</tex-math></inline-formula> Soft-Margin Loss",
"normalizedTitle": "Support Vector Machine Classifier via - Soft-Margin Loss",
"fno": "09464733",
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"Convex Programming",
"Optimisation",
"Pattern Classification",
"Support Vector Machines",
"Ideal Soft Margin Loss SVM",
"Existingconvex Soft Margin Losses",
"Support Vector Machines",
"Training",
"Optimization",
"Fasteners",
"Training Data",
"Standards",
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"Minimizer And P Stationary Point",
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{
"givenName": "Huajun",
"surname": "Wang",
"fullName": "Huajun Wang",
"affiliation": "Department of Applied Mathematics, Beijing Jiaotong University, Beijing, China",
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{
"givenName": "Yuanhai",
"surname": "Shao",
"fullName": "Yuanhai Shao",
"affiliation": "School of Management, Hainan University, Haikou, China",
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{
"givenName": "Shenglong",
"surname": "Zhou",
"fullName": "Shenglong Zhou",
"affiliation": "Department of Electrical and Electronic Engineering, Imperial College London, London, U.K.",
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{
"givenName": "Ce",
"surname": "Zhang",
"fullName": "Ce Zhang",
"affiliation": "Department of Applied Mathematics, Beijing Jiaotong University, Beijing, China",
"__typename": "ArticleAuthorType"
},
{
"givenName": "Naihua",
"surname": "Xiu",
"fullName": "Naihua Xiu",
"affiliation": "Department of Applied Mathematics, Beijing Jiaotong University, Beijing, China",
"__typename": "ArticleAuthorType"
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"doi": "10.1109/TC.2021.3086071",
"abstract": "Hardware realization of public-key cryptosystems often entails Montgomery modular multiplication (MMM), which is more efficient in residue number systems (RNS). A large pool of co-prime moduli allows for higher number of dynamically changeable moduli-set pairs for the required base extension, leading to ultra-wide key-lengths to accommodate the indispensable resistance to differential power-analysis (DPA) attacks. The moduli are often of the form <inline-formula><tex-math notation=\"LaTeX\">Z_${2^r} - {{\\delta }}$_Z</tex-math></inline-formula>, where <inline-formula><tex-math notation=\"LaTeX\">Z_$r$_Z</tex-math></inline-formula> denotes the width of residue channels. In a previous relevant RNS MMM design, with <inline-formula><tex-math notation=\"LaTeX\">Z_$r\\ = \\ 64$_Z</tex-math></inline-formula>, probability of a successful DPA attack is less than <inline-formula><tex-math notation=\"LaTeX\">Z_${2^{ - 66}}$_Z</tex-math></inline-formula>, where efficient arithmetic is obtained only for a limited set of moduli that are insufficient for key-lengths over 1024 bits. Here we propose a free-<inline-formula><tex-math notation=\"LaTeX\">Z_${{\\delta }}$_Z</tex-math></inline-formula> RNS MMM scheme, for up-to 8192-bit key-lengths and fast 16-bit residue channels, based on the proposed <inline-formula><tex-math notation=\"LaTeX\">Z_${{\\delta }}$_Z</tex-math></inline-formula>-independent modulo-(<inline-formula><tex-math notation=\"LaTeX\">Z_${2^r} - {{\\delta }}$_Z</tex-math></inline-formula>) adders and multipliers. Moreover, we propose an especial method for moduli selection that is required for base extension, leading to the same aforementioned DPA-resistance measure and much lower measures for key-lengths over 1024. The implementation results show <inline-formula><tex-math notation=\"LaTeX\">Z_$82,69,44\\ percent$_Z</tex-math></inline-formula> less RSA delay, for key-lengths <inline-formula><tex-math notation=\"LaTeX\">Z_$512,1024,2048$_Z</tex-math></inline-formula>, respectively of the home designs versus the 512-bit main reference design, and more than <inline-formula><tex-math notation=\"LaTeX\">Z_$5,100\\ percent$_Z</tex-math></inline-formula> for <inline-formula><tex-math notation=\"LaTeX\">Z_$4096,8192$_Z</tex-math></inline-formula> key-lengths, respectively, all per 512-bit encrypted messages.",
"abstracts": [
{
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"content": "Hardware realization of public-key cryptosystems often entails Montgomery modular multiplication (MMM), which is more efficient in residue number systems (RNS). A large pool of co-prime moduli allows for higher number of dynamically changeable moduli-set pairs for the required base extension, leading to ultra-wide key-lengths to accommodate the indispensable resistance to differential power-analysis (DPA) attacks. The moduli are often of the form <inline-formula><tex-math notation=\"LaTeX\">${2^r} - {{\\delta }}$</tex-math><alternatives><mml:math><mml:mrow><mml:msup><mml:mn>2</mml:mn><mml:mi>r</mml:mi></mml:msup><mml:mo>-</mml:mo><mml:mi>δ</mml:mi></mml:mrow></mml:math><inline-graphic xlink:href=\"jaberipur-ieq2-3086071.gif\"/></alternatives></inline-formula>, where <inline-formula><tex-math notation=\"LaTeX\">$r$</tex-math><alternatives><mml:math><mml:mi>r</mml:mi></mml:math><inline-graphic xlink:href=\"jaberipur-ieq3-3086071.gif\"/></alternatives></inline-formula> denotes the width of residue channels. In a previous relevant RNS MMM design, with <inline-formula><tex-math notation=\"LaTeX\">$r\\ = \\ 64$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>r</mml:mi><mml:mspace width=\"4pt\"/><mml:mo>=</mml:mo><mml:mspace width=\"4pt\"/><mml:mn>64</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\"jaberipur-ieq4-3086071.gif\"/></alternatives></inline-formula>, probability of a successful DPA attack is less than <inline-formula><tex-math notation=\"LaTeX\">${2^{ - 66}}$</tex-math><alternatives><mml:math><mml:msup><mml:mn>2</mml:mn><mml:mrow><mml:mo>-</mml:mo><mml:mn>66</mml:mn></mml:mrow></mml:msup></mml:math><inline-graphic xlink:href=\"jaberipur-ieq5-3086071.gif\"/></alternatives></inline-formula>, where efficient arithmetic is obtained only for a limited set of moduli that are insufficient for key-lengths over 1024 bits. Here we propose a free-<inline-formula><tex-math notation=\"LaTeX\">${{\\delta }}$</tex-math><alternatives><mml:math><mml:mi>δ</mml:mi></mml:math><inline-graphic xlink:href=\"jaberipur-ieq6-3086071.gif\"/></alternatives></inline-formula> RNS MMM scheme, for up-to 8192-bit key-lengths and fast 16-bit residue channels, based on the proposed <inline-formula><tex-math notation=\"LaTeX\">${{\\delta }}$</tex-math><alternatives><mml:math><mml:mi>δ</mml:mi></mml:math><inline-graphic xlink:href=\"jaberipur-ieq7-3086071.gif\"/></alternatives></inline-formula>-independent modulo-(<inline-formula><tex-math notation=\"LaTeX\">${2^r} - {{\\delta }}$</tex-math><alternatives><mml:math><mml:mrow><mml:msup><mml:mn>2</mml:mn><mml:mi>r</mml:mi></mml:msup><mml:mo>-</mml:mo><mml:mi>δ</mml:mi></mml:mrow></mml:math><inline-graphic xlink:href=\"jaberipur-ieq8-3086071.gif\"/></alternatives></inline-formula>) adders and multipliers. Moreover, we propose an especial method for moduli selection that is required for base extension, leading to the same aforementioned DPA-resistance measure and much lower measures for key-lengths over 1024. The implementation results show <inline-formula><tex-math notation=\"LaTeX\">$82,69,44\\ percent$</tex-math><alternatives><mml:math><mml:mrow><mml:mn>82</mml:mn><mml:mo>,</mml:mo><mml:mn>69</mml:mn><mml:mo>,</mml:mo><mml:mn>44</mml:mn><mml:mspace width=\"4pt\"/><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>c</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:math><inline-graphic xlink:href=\"jaberipur-ieq9-3086071.gif\"/></alternatives></inline-formula> less RSA delay, for key-lengths <inline-formula><tex-math notation=\"LaTeX\">$512,1024,2048$</tex-math><alternatives><mml:math><mml:mrow><mml:mn>512</mml:mn><mml:mo>,</mml:mo><mml:mn>1024</mml:mn><mml:mo>,</mml:mo><mml:mn>2048</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\"jaberipur-ieq10-3086071.gif\"/></alternatives></inline-formula>, respectively of the home designs versus the 512-bit main reference design, and more than <inline-formula><tex-math notation=\"LaTeX\">$5,100\\ percent$</tex-math><alternatives><mml:math><mml:mrow><mml:mn>5</mml:mn><mml:mo>,</mml:mo><mml:mn>100</mml:mn><mml:mspace width=\"4pt\"/><mml:mi>p</mml:mi><mml:mi>e</mml:mi><mml:mi>r</mml:mi><mml:mi>c</mml:mi><mml:mi>e</mml:mi><mml:mi>n</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:math><inline-graphic xlink:href=\"jaberipur-ieq11-3086071.gif\"/></alternatives></inline-formula> for <inline-formula><tex-math notation=\"LaTeX\">$4096,8192$</tex-math><alternatives><mml:math><mml:mrow><mml:mn>4096</mml:mn><mml:mo>,</mml:mo><mml:mn>8192</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\"jaberipur-ieq12-3086071.gif\"/></alternatives></inline-formula> key-lengths, respectively, all per 512-bit encrypted messages.",
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],
"normalizedAbstract": "Hardware realization of public-key cryptosystems often entails Montgomery modular multiplication (MMM), which is more efficient in residue number systems (RNS). A large pool of co-prime moduli allows for higher number of dynamically changeable moduli-set pairs for the required base extension, leading to ultra-wide key-lengths to accommodate the indispensable resistance to differential power-analysis (DPA) attacks. The moduli are often of the form -, where - denotes the width of residue channels. In a previous relevant RNS MMM design, with -, probability of a successful DPA attack is less than -, where efficient arithmetic is obtained only for a limited set of moduli that are insufficient for key-lengths over 1024 bits. Here we propose a free-- RNS MMM scheme, for up-to 8192-bit key-lengths and fast 16-bit residue channels, based on the proposed --independent modulo-(-) adders and multipliers. Moreover, we propose an especial method for moduli selection that is required for base extension, leading to the same aforementioned DPA-resistance measure and much lower measures for key-lengths over 1024. The implementation results show - less RSA delay, for key-lengths -, respectively of the home designs versus the 512-bit main reference design, and more than - for - key-lengths, respectively, all per 512-bit encrypted messages.",
"title": "Up to <inline-formula><tex-math notation=\"LaTeX\">Z_$8k$_Z</tex-math></inline-formula>-bit Modular Montgomery Multiplication in Residue Number Systems With Fast 16-bit Residue Channels",
"normalizedTitle": "Up to --bit Modular Montgomery Multiplication in Residue Number Systems With Fast 16-bit Residue Channels",
"fno": "09445629",
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"keywords": [
"Adders",
"Digital Arithmetic",
"Multiplying Circuits",
"Public Key Cryptography",
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"Residue Number Systems",
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"Public Key Cryptosystems",
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"Co Prime Moduli",
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"Required Base Extension",
"Ultra Wide Key Lengths",
"Differential Power Analysis Attacks",
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"Main Reference Design",
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"abstract": "Answering reachability queries is one of the fundamental graph operations. One way to make acceleration is directly building index on the input graph. Considering that the size of the input graph has a great impact on the query performance, the other way is reducing the size of the input graph, such that the given queries can be answered over a smaller graph. Although the input graph can be reduced significantly in some cases by existing approaches, a smaller reduced graph does not always mean a positive effect on the query performance. In this paper, we study graph reduction to accelerate reachability queries answering. We propose a novel graph reduction approach, namely <inline-formula><tex-math notation=\"LaTeX\">Z_$\\mathsf{RCN}$_Z</tex-math></inline-formula> reduction, to reduce the input graph <inline-formula><tex-math notation=\"LaTeX\">Z_$G$_Z</tex-math></inline-formula> with <inline-formula><tex-math notation=\"LaTeX\">Z_$|V|$_Z</tex-math></inline-formula> nodes into a smaller one <inline-formula><tex-math notation=\"LaTeX\">Z_$G^{r}$_Z</tex-math></inline-formula> with <inline-formula><tex-math notation=\"LaTeX\">Z_$|V^r|$_Z</tex-math></inline-formula> nodes. Assume that the probability of a node of <inline-formula><tex-math notation=\"LaTeX\">Z_$G$_Z</tex-math></inline-formula> to be a query node is <inline-formula><tex-math notation=\"LaTeX\">Z_$1/|V|$_Z</tex-math></inline-formula>, we show that based on our approach, the lower bound probability that a query <inline-formula><tex-math notation=\"LaTeX\">Z_$q$_Z</tex-math></inline-formula> can be answered in constant time is <inline-formula><tex-math notation=\"LaTeX\">Z_$1-(\\frac{|V^r|}{|V|})^2$_Z</tex-math></inline-formula>, denoting that the probability that <inline-formula><tex-math notation=\"LaTeX\">Z_$q$_Z</tex-math></inline-formula> needs to be answered over the reduced graph is <inline-formula><tex-math notation=\"LaTeX\">Z_$(\\frac{|V^r|}{|V|})^2$_Z</tex-math></inline-formula>, which means the smaller the reduced graph, the larger the probability that <inline-formula><tex-math notation=\"LaTeX\">Z_$q$_Z</tex-math></inline-formula> can be answered in constant time. We show the difficulties of <inline-formula><tex-math notation=\"LaTeX\">Z_$\\mathsf{RCN}$_Z</tex-math></inline-formula> reduction and propose efficient algorithms to improve the reduction ratio. Based on the result of <inline-formula><tex-math notation=\"LaTeX\">Z_$\\mathsf{RCN}$_Z</tex-math></inline-formula> reduction, we further propose a novel labeling scheme to accelerate queries answering. We confirm the efficiency of our approach by extensive experimental results for graph reduction and reachability queries processing using 20 real datasets.",
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"content": "Answering reachability queries is one of the fundamental graph operations. One way to make acceleration is directly building index on the input graph. Considering that the size of the input graph has a great impact on the query performance, the other way is reducing the size of the input graph, such that the given queries can be answered over a smaller graph. Although the input graph can be reduced significantly in some cases by existing approaches, a smaller reduced graph does not always mean a positive effect on the query performance. In this paper, we study graph reduction to accelerate reachability queries answering. We propose a novel graph reduction approach, namely <inline-formula><tex-math notation=\"LaTeX\">$\\mathsf{RCN}$</tex-math><alternatives><mml:math><mml:mi mathvariant=\"sans-serif\">RCN</mml:mi></mml:math><inline-graphic xlink:href=\"zhou-ieq2-3108433.gif\"/></alternatives></inline-formula> reduction, to reduce the input graph <inline-formula><tex-math notation=\"LaTeX\">$G$</tex-math><alternatives><mml:math><mml:mi>G</mml:mi></mml:math><inline-graphic xlink:href=\"zhou-ieq3-3108433.gif\"/></alternatives></inline-formula> with <inline-formula><tex-math notation=\"LaTeX\">$|V|$</tex-math><alternatives><mml:math><mml:mrow><mml:mo>|</mml:mo><mml:mi>V</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"zhou-ieq4-3108433.gif\"/></alternatives></inline-formula> nodes into a smaller one <inline-formula><tex-math notation=\"LaTeX\">$G^{r}$</tex-math><alternatives><mml:math><mml:msup><mml:mi>G</mml:mi><mml:mi>r</mml:mi></mml:msup></mml:math><inline-graphic xlink:href=\"zhou-ieq5-3108433.gif\"/></alternatives></inline-formula> with <inline-formula><tex-math notation=\"LaTeX\">$|V^r|$</tex-math><alternatives><mml:math><mml:mrow><mml:mrow><mml:mo>|</mml:mo></mml:mrow><mml:msup><mml:mi>V</mml:mi><mml:mi>r</mml:mi></mml:msup><mml:mrow><mml:mo>|</mml:mo></mml:mrow></mml:mrow></mml:math><inline-graphic xlink:href=\"zhou-ieq6-3108433.gif\"/></alternatives></inline-formula> nodes. Assume that the probability of a node of <inline-formula><tex-math notation=\"LaTeX\">$G$</tex-math><alternatives><mml:math><mml:mi>G</mml:mi></mml:math><inline-graphic xlink:href=\"zhou-ieq7-3108433.gif\"/></alternatives></inline-formula> to be a query node is <inline-formula><tex-math notation=\"LaTeX\">$1/|V|$</tex-math><alternatives><mml:math><mml:mrow><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mo>|</mml:mo><mml:mi>V</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"zhou-ieq8-3108433.gif\"/></alternatives></inline-formula>, we show that based on our approach, the lower bound probability that a query <inline-formula><tex-math notation=\"LaTeX\">$q$</tex-math><alternatives><mml:math><mml:mi>q</mml:mi></mml:math><inline-graphic xlink:href=\"zhou-ieq9-3108433.gif\"/></alternatives></inline-formula> can be answered in constant time is <inline-formula><tex-math notation=\"LaTeX\">$1-(\\frac{|V^r|}{|V|})^2$</tex-math><alternatives><mml:math><mml:mrow><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mfrac><mml:mrow><mml:mrow><mml:mo>|</mml:mo></mml:mrow><mml:msup><mml:mi>V</mml:mi><mml:mi>r</mml:mi></mml:msup><mml:mrow><mml:mo>|</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mo>|</mml:mo><mml:mi>V</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:mfrac><mml:mo>)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:math><inline-graphic xlink:href=\"zhou-ieq10-3108433.gif\"/></alternatives></inline-formula>, denoting that the probability that <inline-formula><tex-math notation=\"LaTeX\">$q$</tex-math><alternatives><mml:math><mml:mi>q</mml:mi></mml:math><inline-graphic xlink:href=\"zhou-ieq11-3108433.gif\"/></alternatives></inline-formula> needs to be answered over the reduced graph is <inline-formula><tex-math notation=\"LaTeX\">$(\\frac{|V^r|}{|V|})^2$</tex-math><alternatives><mml:math><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mfrac><mml:mrow><mml:mrow><mml:mo>|</mml:mo></mml:mrow><mml:msup><mml:mi>V</mml:mi><mml:mi>r</mml:mi></mml:msup><mml:mrow><mml:mo>|</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mo>|</mml:mo><mml:mi>V</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:mfrac><mml:mo>)</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:math><inline-graphic xlink:href=\"zhou-ieq12-3108433.gif\"/></alternatives></inline-formula>, which means the smaller the reduced graph, the larger the probability that <inline-formula><tex-math notation=\"LaTeX\">$q$</tex-math><alternatives><mml:math><mml:mi>q</mml:mi></mml:math><inline-graphic xlink:href=\"zhou-ieq13-3108433.gif\"/></alternatives></inline-formula> can be answered in constant time. We show the difficulties of <inline-formula><tex-math notation=\"LaTeX\">$\\mathsf{RCN}$</tex-math><alternatives><mml:math><mml:mi mathvariant=\"sans-serif\">RCN</mml:mi></mml:math><inline-graphic xlink:href=\"zhou-ieq14-3108433.gif\"/></alternatives></inline-formula> reduction and propose efficient algorithms to improve the reduction ratio. Based on the result of <inline-formula><tex-math notation=\"LaTeX\">$\\mathsf{RCN}$</tex-math><alternatives><mml:math><mml:mi mathvariant=\"sans-serif\">RCN</mml:mi></mml:math><inline-graphic xlink:href=\"zhou-ieq15-3108433.gif\"/></alternatives></inline-formula> reduction, we further propose a novel labeling scheme to accelerate queries answering. We confirm the efficiency of our approach by extensive experimental results for graph reduction and reachability queries processing using 20 real datasets.",
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"normalizedAbstract": "Answering reachability queries is one of the fundamental graph operations. One way to make acceleration is directly building index on the input graph. Considering that the size of the input graph has a great impact on the query performance, the other way is reducing the size of the input graph, such that the given queries can be answered over a smaller graph. Although the input graph can be reduced significantly in some cases by existing approaches, a smaller reduced graph does not always mean a positive effect on the query performance. In this paper, we study graph reduction to accelerate reachability queries answering. We propose a novel graph reduction approach, namely - reduction, to reduce the input graph - with - nodes into a smaller one - with - nodes. Assume that the probability of a node of - to be a query node is -, we show that based on our approach, the lower bound probability that a query - can be answered in constant time is -, denoting that the probability that - needs to be answered over the reduced graph is -, which means the smaller the reduced graph, the larger the probability that - can be answered in constant time. We show the difficulties of - reduction and propose efficient algorithms to improve the reduction ratio. Based on the result of - reduction, we further propose a novel labeling scheme to accelerate queries answering. We confirm the efficiency of our approach by extensive experimental results for graph reduction and reachability queries processing using 20 real datasets.",
"title": "Fast Reachability Queries Answering Based on <inline-formula><tex-math notation=\"LaTeX\">Z_$\\mathsf{RCN}$_Z</tex-math></inline-formula> Reduction",
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"abstract": "While <inline-formula><tex-math notation=\"LaTeX\">Z_$360^{\\circ }$_Z</tex-math></inline-formula> cameras offer tremendous new possibilities in vision, graphics, and augmented reality, the spherical images they produce make visual recognition non-trivial. Ideally, <inline-formula><tex-math notation=\"LaTeX\">Z_$360^{\\circ }$_Z</tex-math></inline-formula> imagery could inherit the deep convolutional neural networks (CNNs) already trained with great success on perspective projection images. However, spherical images cannot be projected to a single plane without significant distortion, and existing methods to transfer CNNs from perspective to spherical images introduce significant computational costs and/or degradations in accuracy. We propose to <italic>learn</italic> a Spherical Convolution Network (SphConv) that translates a planar CNN to the equirectangular projection of <inline-formula><tex-math notation=\"LaTeX\">Z_$360^{\\circ }$_Z</tex-math></inline-formula> images. Given a source CNN for perspective images as input, SphConv learns to reproduce the flat filter outputs on <inline-formula><tex-math notation=\"LaTeX\">Z_$360^{\\circ }$_Z</tex-math></inline-formula> data, sensitive to the varying distortion effects across the viewing sphere. The key benefits are 1) efficient and accurate recognition for <inline-formula><tex-math notation=\"LaTeX\">Z_$360^{\\circ }$_Z</tex-math></inline-formula> images, and 2) the ability to leverage powerful pre-trained networks for perspective images. We further proposes two instantiation of SphConv—Spherical Kernel learns location dependent kernels on the sphere for SphConv, and Kernel Transformer Network learns a functional transformation that generates SphConv kernels from the source CNN. Among the two variants, Kernel Transformer Network has a much lower memory footprint at the cost of higher computational overhead. Validating our approach with multiple source CNNs and datasets, we show that SphConv using KTN successfully preserves the source CNN’s accuracy, while offering efficiency, transferability, and scalability to typical image resolutions. We further introduce a spherical Faster R-CNN model based on SphConv and show that we can learn a spherical object detector without any object annotation in <inline-formula><tex-math notation=\"LaTeX\">Z_$360^{\\circ }$_Z</tex-math></inline-formula> images.",
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"content": "While <inline-formula><tex-math notation=\"LaTeX\">$360^{\\circ }$</tex-math><alternatives><mml:math><mml:msup><mml:mn>360</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:math><inline-graphic xlink:href=\"su-ieq2-3113612.gif\"/></alternatives></inline-formula> cameras offer tremendous new possibilities in vision, graphics, and augmented reality, the spherical images they produce make visual recognition non-trivial. Ideally, <inline-formula><tex-math notation=\"LaTeX\">$360^{\\circ }$</tex-math><alternatives><mml:math><mml:msup><mml:mn>360</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:math><inline-graphic xlink:href=\"su-ieq3-3113612.gif\"/></alternatives></inline-formula> imagery could inherit the deep convolutional neural networks (CNNs) already trained with great success on perspective projection images. However, spherical images cannot be projected to a single plane without significant distortion, and existing methods to transfer CNNs from perspective to spherical images introduce significant computational costs and/or degradations in accuracy. We propose to <italic>learn</italic> a Spherical Convolution Network (SphConv) that translates a planar CNN to the equirectangular projection of <inline-formula><tex-math notation=\"LaTeX\">$360^{\\circ }$</tex-math><alternatives><mml:math><mml:msup><mml:mn>360</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:math><inline-graphic xlink:href=\"su-ieq4-3113612.gif\"/></alternatives></inline-formula> images. Given a source CNN for perspective images as input, SphConv learns to reproduce the flat filter outputs on <inline-formula><tex-math notation=\"LaTeX\">$360^{\\circ }$</tex-math><alternatives><mml:math><mml:msup><mml:mn>360</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:math><inline-graphic xlink:href=\"su-ieq5-3113612.gif\"/></alternatives></inline-formula> data, sensitive to the varying distortion effects across the viewing sphere. The key benefits are 1) efficient and accurate recognition for <inline-formula><tex-math notation=\"LaTeX\">$360^{\\circ }$</tex-math><alternatives><mml:math><mml:msup><mml:mn>360</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:math><inline-graphic xlink:href=\"su-ieq6-3113612.gif\"/></alternatives></inline-formula> images, and 2) the ability to leverage powerful pre-trained networks for perspective images. We further proposes two instantiation of SphConv—Spherical Kernel learns location dependent kernels on the sphere for SphConv, and Kernel Transformer Network learns a functional transformation that generates SphConv kernels from the source CNN. Among the two variants, Kernel Transformer Network has a much lower memory footprint at the cost of higher computational overhead. Validating our approach with multiple source CNNs and datasets, we show that SphConv using KTN successfully preserves the source CNN’s accuracy, while offering efficiency, transferability, and scalability to typical image resolutions. We further introduce a spherical Faster R-CNN model based on SphConv and show that we can learn a spherical object detector without any object annotation in <inline-formula><tex-math notation=\"LaTeX\">$360^{\\circ }$</tex-math><alternatives><mml:math><mml:msup><mml:mn>360</mml:mn><mml:mo>∘</mml:mo></mml:msup></mml:math><inline-graphic xlink:href=\"su-ieq7-3113612.gif\"/></alternatives></inline-formula> images.",
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"normalizedAbstract": "While - cameras offer tremendous new possibilities in vision, graphics, and augmented reality, the spherical images they produce make visual recognition non-trivial. Ideally, - imagery could inherit the deep convolutional neural networks (CNNs) already trained with great success on perspective projection images. However, spherical images cannot be projected to a single plane without significant distortion, and existing methods to transfer CNNs from perspective to spherical images introduce significant computational costs and/or degradations in accuracy. We propose to learn a Spherical Convolution Network (SphConv) that translates a planar CNN to the equirectangular projection of - images. Given a source CNN for perspective images as input, SphConv learns to reproduce the flat filter outputs on - data, sensitive to the varying distortion effects across the viewing sphere. The key benefits are 1) efficient and accurate recognition for - images, and 2) the ability to leverage powerful pre-trained networks for perspective images. We further proposes two instantiation of SphConv—Spherical Kernel learns location dependent kernels on the sphere for SphConv, and Kernel Transformer Network learns a functional transformation that generates SphConv kernels from the source CNN. Among the two variants, Kernel Transformer Network has a much lower memory footprint at the cost of higher computational overhead. Validating our approach with multiple source CNNs and datasets, we show that SphConv using KTN successfully preserves the source CNN’s accuracy, while offering efficiency, transferability, and scalability to typical image resolutions. We further introduce a spherical Faster R-CNN model based on SphConv and show that we can learn a spherical object detector without any object annotation in - images.",
"title": "Learning Spherical Convolution for <inline-formula><tex-math notation=\"LaTeX\">Z_$360^{\\circ }$_Z</tex-math></inline-formula> Recognition",
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"givenName": "Yu-Chuan",
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"fullName": "Yu-Chuan Su",
"affiliation": "Department of Computer Science, University of Texas at Austin, Austin, TX, USA",
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"fullName": "Kristen Grauman",
"affiliation": "Department of Computer Science, University of Texas at Austin, Austin, TX, USA",
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"abstract": "Cyberspace is not a “vacuum space”, and it is normal that there are inevitable viruses and worms in cyberspace. Cyberspace security threats stem from the problem of endogenous security, which is caused by the incompleteness of theoretical system and technology of the information field itself. Thus it is impossible and unnecessary for us to build an “aseptic” cyberspace. On the contrast, we must focus on improving the “self-immunity” of network. Literally, endogenous security is an endogenous effect from its own structural factors rather than external ones. The <inline-formula><tex-math notation=\"LaTeX\">Z_$t/k$_Z</tex-math></inline-formula>-diagnosis strategy plays a very important role in measuring endogenous network security without prior knowledge, which can significantly enhance the self-diagnosing capability of network. As far as we know, few research involves <inline-formula><tex-math notation=\"LaTeX\">Z_$t/k$_Z</tex-math></inline-formula>-diagnosis algorithm and <inline-formula><tex-math notation=\"LaTeX\">Z_$t/k$_Z</tex-math></inline-formula>-diagnosability of interconnection networks under MM* model. In this article, we propose a fast <inline-formula><tex-math notation=\"LaTeX\">Z_$f(r,k+1)/k$_Z</tex-math></inline-formula>-diagnosis algorithm of complexity <inline-formula><tex-math notation=\"LaTeX\">Z_$O(Nr^2)$_Z</tex-math></inline-formula>, say <inline-formula><tex-math notation=\"LaTeX\">Z_$G$_Z</tex-math></inline-formula>MIS<inline-formula><tex-math notation=\"LaTeX\">Z_$k$_Z</tex-math></inline-formula>DIAGMM*, for a general <inline-formula><tex-math notation=\"LaTeX\">Z_$r$_Z</tex-math></inline-formula>-regular network <inline-formula><tex-math notation=\"LaTeX\">Z_$G$_Z</tex-math></inline-formula> under MM* model by designing a 0-comparison subgraph <inline-formula><tex-math notation=\"LaTeX\">Z_$M_0(G)$_Z</tex-math></inline-formula>, where <inline-formula><tex-math notation=\"LaTeX\">Z_$N$_Z</tex-math></inline-formula> is the size of <inline-formula><tex-math notation=\"LaTeX\">Z_$G$_Z</tex-math></inline-formula>. We determine that the <inline-formula><tex-math notation=\"LaTeX\">Z_$t/k$_Z</tex-math></inline-formula>-diagnosability <inline-formula><tex-math notation=\"LaTeX\">Z_$(t(G)/k)^M$_Z</tex-math></inline-formula> of <inline-formula><tex-math notation=\"LaTeX\">Z_$G$_Z</tex-math></inline-formula> under MM* model is <inline-formula><tex-math notation=\"LaTeX\">Z_$f(r,k+1)$_Z</tex-math></inline-formula> by <inline-formula><tex-math notation=\"LaTeX\">Z_$G$_Z</tex-math></inline-formula>MIS<inline-formula><tex-math notation=\"LaTeX\">Z_$k$_Z</tex-math></inline-formula>DIAGMM* algorithm. Moreover, we establish the <inline-formula><tex-math notation=\"LaTeX\">Z_$(t(G)/k)^M$_Z</tex-math></inline-formula> of some interconnection networks under MM* model, including BC networks, <inline-formula><tex-math notation=\"LaTeX\">Z_$(n,l)$_Z</tex-math></inline-formula>-star graph networks, and data center network DCells. Finally, we compare <inline-formula><tex-math notation=\"LaTeX\">Z_$(t(G)/k)^M$_Z</tex-math></inline-formula> with diagnosability, conditional diagnosability, pessimistic diagnosability, extra diagnosability, and good-neighbor diagnosability under MM* model. It can be seen that <inline-formula><tex-math notation=\"LaTeX\">Z_$(t(G)/k)^M$_Z</tex-math></inline-formula> is greater than other fault diagnosabilities in most cases.",
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"content": "Cyberspace is not a “vacuum space”, and it is normal that there are inevitable viruses and worms in cyberspace. Cyberspace security threats stem from the problem of endogenous security, which is caused by the incompleteness of theoretical system and technology of the information field itself. Thus it is impossible and unnecessary for us to build an “aseptic” cyberspace. On the contrast, we must focus on improving the “self-immunity” of network. Literally, endogenous security is an endogenous effect from its own structural factors rather than external ones. The <inline-formula><tex-math notation=\"LaTeX\">$t/k$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>t</mml:mi><mml:mo>/</mml:mo><mml:mi>k</mml:mi></mml:mrow></mml:math><inline-graphic xlink:href=\"lin-ieq2-3122440.gif\"/></alternatives></inline-formula>-diagnosis strategy plays a very important role in measuring endogenous network security without prior knowledge, which can significantly enhance the self-diagnosing capability of network. As far as we know, few research involves <inline-formula><tex-math notation=\"LaTeX\">$t/k$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>t</mml:mi><mml:mo>/</mml:mo><mml:mi>k</mml:mi></mml:mrow></mml:math><inline-graphic xlink:href=\"lin-ieq3-3122440.gif\"/></alternatives></inline-formula>-diagnosis algorithm and <inline-formula><tex-math notation=\"LaTeX\">$t/k$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>t</mml:mi><mml:mo>/</mml:mo><mml:mi>k</mml:mi></mml:mrow></mml:math><inline-graphic xlink:href=\"lin-ieq4-3122440.gif\"/></alternatives></inline-formula>-diagnosability of interconnection networks under MM* model. In this article, we propose a fast <inline-formula><tex-math notation=\"LaTeX\">$f(r,k+1)/k$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mi>k</mml:mi></mml:mrow></mml:math><inline-graphic xlink:href=\"lin-ieq5-3122440.gif\"/></alternatives></inline-formula>-diagnosis algorithm of complexity <inline-formula><tex-math notation=\"LaTeX\">$O(Nr^2)$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mi>N</mml:mi><mml:msup><mml:mi>r</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"lin-ieq6-3122440.gif\"/></alternatives></inline-formula>, say <inline-formula><tex-math notation=\"LaTeX\">$G$</tex-math><alternatives><mml:math><mml:mi>G</mml:mi></mml:math><inline-graphic xlink:href=\"lin-ieq7-3122440.gif\"/></alternatives></inline-formula>MIS<inline-formula><tex-math notation=\"LaTeX\">$k$</tex-math><alternatives><mml:math><mml:mi>k</mml:mi></mml:math><inline-graphic xlink:href=\"lin-ieq8-3122440.gif\"/></alternatives></inline-formula>DIAGMM*, for a general <inline-formula><tex-math notation=\"LaTeX\">$r$</tex-math><alternatives><mml:math><mml:mi>r</mml:mi></mml:math><inline-graphic xlink:href=\"lin-ieq9-3122440.gif\"/></alternatives></inline-formula>-regular network <inline-formula><tex-math notation=\"LaTeX\">$G$</tex-math><alternatives><mml:math><mml:mi>G</mml:mi></mml:math><inline-graphic xlink:href=\"lin-ieq10-3122440.gif\"/></alternatives></inline-formula> under MM* model by designing a 0-comparison subgraph <inline-formula><tex-math notation=\"LaTeX\">$M_0(G)$</tex-math><alternatives><mml:math><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>G</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math><inline-graphic xlink:href=\"lin-ieq11-3122440.gif\"/></alternatives></inline-formula>, where <inline-formula><tex-math notation=\"LaTeX\">$N$</tex-math><alternatives><mml:math><mml:mi>N</mml:mi></mml:math><inline-graphic xlink:href=\"lin-ieq12-3122440.gif\"/></alternatives></inline-formula> is the size of <inline-formula><tex-math notation=\"LaTeX\">$G$</tex-math><alternatives><mml:math><mml:mi>G</mml:mi></mml:math><inline-graphic xlink:href=\"lin-ieq13-3122440.gif\"/></alternatives></inline-formula>. We determine that the <inline-formula><tex-math notation=\"LaTeX\">$t/k$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>t</mml:mi><mml:mo>/</mml:mo><mml:mi>k</mml:mi></mml:mrow></mml:math><inline-graphic xlink:href=\"lin-ieq14-3122440.gif\"/></alternatives></inline-formula>-diagnosability <inline-formula><tex-math notation=\"LaTeX\">$(t(G)/k)^M$</tex-math><alternatives><mml:math><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>G</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>/</mml:mo><mml:mi>k</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>M</mml:mi></mml:msup></mml:math><inline-graphic xlink:href=\"lin-ieq15-3122440.gif\"/></alternatives></inline-formula> of <inline-formula><tex-math notation=\"LaTeX\">$G$</tex-math><alternatives><mml:math><mml:mi>G</mml:mi></mml:math><inline-graphic xlink:href=\"lin-ieq16-3122440.gif\"/></alternatives></inline-formula> under MM* model is <inline-formula><tex-math notation=\"LaTeX\">$f(r,k+1)$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>f</mml:mi><mml:mo>(</mml:mo><mml:mi>r</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"lin-ieq17-3122440.gif\"/></alternatives></inline-formula> by <inline-formula><tex-math notation=\"LaTeX\">$G$</tex-math><alternatives><mml:math><mml:mi>G</mml:mi></mml:math><inline-graphic xlink:href=\"lin-ieq18-3122440.gif\"/></alternatives></inline-formula>MIS<inline-formula><tex-math notation=\"LaTeX\">$k$</tex-math><alternatives><mml:math><mml:mi>k</mml:mi></mml:math><inline-graphic xlink:href=\"lin-ieq19-3122440.gif\"/></alternatives></inline-formula>DIAGMM* algorithm. Moreover, we establish the <inline-formula><tex-math notation=\"LaTeX\">$(t(G)/k)^M$</tex-math><alternatives><mml:math><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>G</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>/</mml:mo><mml:mi>k</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>M</mml:mi></mml:msup></mml:math><inline-graphic xlink:href=\"lin-ieq20-3122440.gif\"/></alternatives></inline-formula> of some interconnection networks under MM* model, including BC networks, <inline-formula><tex-math notation=\"LaTeX\">$(n,l)$</tex-math><alternatives><mml:math><mml:mrow><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>l</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"lin-ieq21-3122440.gif\"/></alternatives></inline-formula>-star graph networks, and data center network DCells. Finally, we compare <inline-formula><tex-math notation=\"LaTeX\">$(t(G)/k)^M$</tex-math><alternatives><mml:math><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>G</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>/</mml:mo><mml:mi>k</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>M</mml:mi></mml:msup></mml:math><inline-graphic xlink:href=\"lin-ieq22-3122440.gif\"/></alternatives></inline-formula> with diagnosability, conditional diagnosability, pessimistic diagnosability, extra diagnosability, and good-neighbor diagnosability under MM* model. It can be seen that <inline-formula><tex-math notation=\"LaTeX\">$(t(G)/k)^M$</tex-math><alternatives><mml:math><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>G</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>/</mml:mo><mml:mi>k</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>M</mml:mi></mml:msup></mml:math><inline-graphic xlink:href=\"lin-ieq23-3122440.gif\"/></alternatives></inline-formula> is greater than other fault diagnosabilities in most cases.",
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"title": "A Fast <inline-formula><tex-math notation=\"LaTeX\">Z_$f(r,k+1)/k$_Z</tex-math></inline-formula>-Diagnosis for Interconnection Networks Under MM* Model",
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"givenName": "Yanze",
"surname": "Huang",
"fullName": "Yanze Huang",
"affiliation": "College of Computer and Cyber Security, Fujian Normal University, Fuzhou, Fujian, China",
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"givenName": "Limei",
"surname": "Lin",
"fullName": "Limei Lin",
"affiliation": "College of Computer and Cyber Security, Key Laboratory of Network Security and Cryptology, Fujian Normal University, Fuzhou, Fujian, China",
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{
"givenName": "Sun-Yuan",
"surname": "Hsieh",
"fullName": "Sun-Yuan Hsieh",
"affiliation": "Department of Computer Science and Information Engineering, National Cheng Kung University, Tainan, Taiwan",
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"abstract": "We propose a simulation-based dynamical motion prior for tracking human motion from video in presence of physical ground-person interactions. Most tracking approaches to date have focused on efficient inference algorithms and/or learning of prior kinematic motion models; however, few can explicitly account for the physical plausibility of recovered motion. Here, we aim to recover physically plausible motion of a single articulated human subject. Toward this end, we propose a full-body 3D physical simulation-based prior that explicitly incorporates a model of human dynamics into the Bayesian filtering framework. We consider the motion of the subject to be generated by a feedback “control loop” in which Newtonian physics approximates the rigid-body motion dynamics of the human and the environment through the application and integration of interaction forces, motor forces, and gravity. Interaction forces prevent physically impossible hypotheses, enable more appropriate reactions to the environment (e.g., ground contacts), and are produced from detected human-environment collisions. Motor forces actuate the body, ensure that proposed pose transitions are physically feasible, and are generated using a motion controller. For efficient inference in the resulting high-dimensional state space, we utilize an exemplar-based control strategy that reduces the effective search space of motor forces. As a result, we are able to recover physically plausible motion of human subjects from monocular and multiview video. We show, both quantitatively and qualitatively, that our approach performs favorably with respect to Bayesian filtering methods with standard motion priors.",
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"abstract": "Periodicity is a frequently happening phenomenon for social interactions in temporal networks. Mining periodic communities are essential to understanding periodic group behaviors in temporal networks. Unfortunately, most previous studies for community mining in temporal networks ignore the periodic patterns of communities. In this paper, we study the problem of seeking periodic communities in a temporal network, where each edge is associated with a set of timestamps. We propose novel models, including <inline-formula><tex-math notation=\"LaTeX\">Z_$\\sigma$_Z</tex-math></inline-formula>-periodic <inline-formula><tex-math notation=\"LaTeX\">Z_$k$_Z</tex-math></inline-formula>-core and <inline-formula><tex-math notation=\"LaTeX\">Z_$\\sigma$_Z</tex-math></inline-formula>-periodic <inline-formula><tex-math notation=\"LaTeX\">Z_$k$_Z</tex-math></inline-formula>-clique, that represent periodic communities in temporal networks. Specifically, a <inline-formula><tex-math notation=\"LaTeX\">Z_$\\sigma$_Z</tex-math></inline-formula>-periodic <inline-formula><tex-math notation=\"LaTeX\">Z_$k$_Z</tex-math></inline-formula>-core (or <inline-formula><tex-math notation=\"LaTeX\">Z_$\\sigma$_Z</tex-math></inline-formula>-periodic <inline-formula><tex-math notation=\"LaTeX\">Z_$k$_Z</tex-math></inline-formula>-clique) is a <inline-formula><tex-math notation=\"LaTeX\">Z_$k$_Z</tex-math></inline-formula>-core (or clique with size larger than <inline-formula><tex-math notation=\"LaTeX\">Z_$k$_Z</tex-math></inline-formula>) that appears at least <inline-formula><tex-math notation=\"LaTeX\">Z_$\\sigma$_Z</tex-math></inline-formula> times periodically in the temporal graph. The problem of searching periodic core is efficient but the resulting communities may be not enough cohesive; the problem of enumerating all periodic cliques is not efficient (NP-hard) but the resulting communities are very cohesive. To compute all of them efficiently, we first develop two effective graph reduction techniques to significantly prune the temporal graph. Then, we transform the temporal graph into a static graph and prove that mining the periodic communities in the temporal graph equals mining communities in the transformed graph. Subsequently, we propose a decomposition algorithm to search maximal <inline-formula><tex-math notation=\"LaTeX\">Z_$\\sigma$_Z</tex-math></inline-formula>-periodic <inline-formula><tex-math notation=\"LaTeX\">Z_$k$_Z</tex-math></inline-formula>-core, a Bron-Kerbosch style algorithm to enumerate all maximal <inline-formula><tex-math notation=\"LaTeX\">Z_$\\sigma$_Z</tex-math></inline-formula>-periodic <inline-formula><tex-math notation=\"LaTeX\">Z_$k$_Z</tex-math></inline-formula>-cliques, and a branch-and-bound style algorithm to find the maximum <inline-formula><tex-math notation=\"LaTeX\">Z_$\\sigma$_Z</tex-math></inline-formula>-periodic clique. The results of extensive experiments on five real-life datasets demonstrate the efficiency, scalability, and effectiveness of our algorithms.",
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"content": "Deep convolutional neural networks (DCNNs) are currently the method of choice both for generative, as well as for discriminative learning in computer vision and machine learning. The success of DCNNs can be attributed to the careful selection of their building blocks (e.g., residual blocks, rectifiers, sophisticated normalization schemes, to mention but a few). In this paper, we propose <inline-formula><tex-math notation=\"LaTeX\">$\\Pi$</tex-math><alternatives><mml:math><mml:mi>Π</mml:mi></mml:math><inline-graphic xlink:href=\"chrysos-ieq1-3058891.gif\"/></alternatives></inline-formula>-Nets, a new class of function approximators based on polynomial expansions. <inline-formula><tex-math notation=\"LaTeX\">$\\Pi$</tex-math><alternatives><mml:math><mml:mi>Π</mml:mi></mml:math><inline-graphic xlink:href=\"chrysos-ieq2-3058891.gif\"/></alternatives></inline-formula>-Nets are polynomial neural networks, i.e., the output is a high-order polynomial of the input. The unknown parameters, which are naturally represented by high-order tensors, are estimated through a collective tensor factorization with factors sharing. We introduce three tensor decompositions that significantly reduce the number of parameters and show how they can be efficiently implemented by hierarchical neural networks. We empirically demonstrate that <inline-formula><tex-math notation=\"LaTeX\">$\\Pi$</tex-math><alternatives><mml:math><mml:mi>Π</mml:mi></mml:math><inline-graphic xlink:href=\"chrysos-ieq3-3058891.gif\"/></alternatives></inline-formula>-Nets are very expressive and they even produce good results without the use of non-linear activation functions in a large battery of tasks and signals, i.e., images, graphs, and audio. When used in conjunction with activation functions, <inline-formula><tex-math notation=\"LaTeX\">$\\Pi$</tex-math><alternatives><mml:math><mml:mi>Π</mml:mi></mml:math><inline-graphic xlink:href=\"chrysos-ieq4-3058891.gif\"/></alternatives></inline-formula>-Nets produce state-of-the-art results in three challenging tasks, i.e., image generation, face verification and 3D mesh representation learning. The source code is available at <uri>https://github.com/grigorisg9gr/polynomial_nets</uri>.",
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"normalizedAbstract": "Deep convolutional neural networks (DCNNs) are currently the method of choice both for generative, as well as for discriminative learning in computer vision and machine learning. The success of DCNNs can be attributed to the careful selection of their building blocks (e.g., residual blocks, rectifiers, sophisticated normalization schemes, to mention but a few). In this paper, we propose --Nets, a new class of function approximators based on polynomial expansions. --Nets are polynomial neural networks, i.e., the output is a high-order polynomial of the input. The unknown parameters, which are naturally represented by high-order tensors, are estimated through a collective tensor factorization with factors sharing. We introduce three tensor decompositions that significantly reduce the number of parameters and show how they can be efficiently implemented by hierarchical neural networks. We empirically demonstrate that --Nets are very expressive and they even produce good results without the use of non-linear activation functions in a large battery of tasks and signals, i.e., images, graphs, and audio. When used in conjunction with activation functions, --Nets produce state-of-the-art results in three challenging tasks, i.e., image generation, face verification and 3D mesh representation learning. The source code is available at https://github.com/grigorisg9gr/polynomial_nets.",
"title": "Deep Polynomial Neural Networks",
"normalizedTitle": "Deep Polynomial Neural Networks",
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"Computer Vision",
"Convolution",
"Function Approximation",
"Image Representation",
"Learning Artificial Intelligence",
"Neural Nets",
"Polynomials",
"Tensors",
"Collective Tensor Factorization",
"Tensor Decompositions",
"Hierarchical Neural Networks",
"X 03 A 0 Nets",
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"Image Generation",
"3 D Mesh Representation Learning",
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"Convolutional Neural Networks",
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"Computer Vision",
"Machine Learning",
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"Polynomial Expansions",
"High Order Polynomial",
"Unknown Parameters",
"High Order Tensors",
"Tensors",
"Neural Networks",
"Task Analysis",
"Faces",
"Training",
"Matrix Decomposition",
"Convolutional Neural Networks",
"Polynomial Neural Networks",
"Tensor Decompositions",
"High Order Polynomials",
"Generative Models",
"Discriminative Models",
"Face Verification"
],
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{
"givenName": "Grigorios G.",
"surname": "Chrysos",
"fullName": "Grigorios G. Chrysos",
"affiliation": "Department of Electrical Engineering, Ecole Polytechnique Federale de Lausanne (EPFL), Lausanne, Switzerland",
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"givenName": "Stylianos",
"surname": "Moschoglou",
"fullName": "Stylianos Moschoglou",
"affiliation": "Department of Computing, Imperial College London, London, U.K",
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{
"givenName": "Giorgos",
"surname": "Bouritsas",
"fullName": "Giorgos Bouritsas",
"affiliation": "Department of Computing, Imperial College London, London, U.K",
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{
"givenName": "Jiankang",
"surname": "Deng",
"fullName": "Jiankang Deng",
"affiliation": "Department of Computing, Imperial College London, London, U.K",
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{
"givenName": "Yannis",
"surname": "Panagakis",
"fullName": "Yannis Panagakis",
"affiliation": "Department of Informatics and Telecommunications, University of Athens, Athens, Greece",
"__typename": "ArticleAuthorType"
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{
"givenName": "Stefanos",
"surname": "Zafeiriou",
"fullName": "Stefanos Zafeiriou",
"affiliation": "Department of Computing, Imperial College London, London, U.K",
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"abstract": "Data summarization that presents a small subset of a dataset to users has been widely applied in numerous applications and systems. Many datasets are coded with hierarchical terminologies, e.g., gene ontology, disease ontology, to name a few. In this paper, we study the weighted tree summarization. We motivate and formulate our <inline-formula><tex-math notation=\"LaTeX\">Z_${\\mathsf {kWTS}}$_Z</tex-math></inline-formula>-<inline-formula><tex-math notation=\"LaTeX\">Z_${\\mathsf {problem}}$_Z</tex-math></inline-formula> as selecting a diverse set of <inline-formula><tex-math notation=\"LaTeX\">Z_$k$_Z</tex-math></inline-formula> nodes to <underline>s</underline>ummarize a hierarchical <underline>t</underline>ree <inline-formula><tex-math notation=\"LaTeX\">Z_$T$_Z</tex-math></inline-formula> with <underline>w</underline>eighted terminologies. We first propose an efficient greedy tree summarization algorithm <inline-formula><tex-math notation=\"LaTeX\">Z_${\\mathsf {GTS}}$_Z</tex-math></inline-formula>. It solves the problem with <inline-formula><tex-math notation=\"LaTeX\">Z_$(1-1/e)$_Z</tex-math></inline-formula>-approximation guarantee. Although <inline-formula><tex-math notation=\"LaTeX\">Z_${\\mathsf {GTS}}$_Z</tex-math></inline-formula> achieves quality-guaranteed answers approximately, but it is still not optimal. To tackle the problem optimally, we further develop a dynamic programming algorithm <inline-formula><tex-math notation=\"LaTeX\">Z_${\\mathsf {OTS}}$_Z</tex-math></inline-formula> to obtain optimal answers for <inline-formula><tex-math notation=\"LaTeX\">Z_${\\mathsf {kWTS}}$_Z</tex-math></inline-formula>-<inline-formula><tex-math notation=\"LaTeX\">Z_${\\mathsf {problem}}$_Z</tex-math></inline-formula> in <inline-formula><tex-math notation=\"LaTeX\">Z_$O(nhk^3)$_Z</tex-math></inline-formula> time, where <inline-formula><tex-math notation=\"LaTeX\">Z_$n, h$_Z</tex-math></inline-formula> are the node size and height in tree <inline-formula><tex-math notation=\"LaTeX\">Z_$T$_Z</tex-math></inline-formula>. The algorithm complexity and correctness of <inline-formula><tex-math notation=\"LaTeX\">Z_${\\mathsf {OTS}}$_Z</tex-math></inline-formula> are theoretically analyzed. In addition, we propose a useful optimization technique of tree reduction to remove useless nodes with zero weights and shrink the tree into a smaller one, which ensures the efficiency acceleration of both <inline-formula><tex-math notation=\"LaTeX\">Z_${\\mathsf {GTS}}$_Z</tex-math></inline-formula> and <inline-formula><tex-math notation=\"LaTeX\">Z_${\\mathsf {OTS}}$_Z</tex-math></inline-formula> in real-world datasets. Moreover, we illustrate one useful application of graph visualization based on the answer of <inline-formula><tex-math notation=\"LaTeX\">Z_$k$_Z</tex-math></inline-formula>-sized tree summarization and show it in a novel case study. Extensive experimental results on real-world datasets show the effectiveness and efficiency of our proposed approximate and optimal algorithms for tree summarization. Furthermore, we conduct a usability evaluation of attractive topic recommendation on ACM Computing Classification System dataset to validate the usefulness of our model and algorithms.",
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"content": "Data summarization that presents a small subset of a dataset to users has been widely applied in numerous applications and systems. Many datasets are coded with hierarchical terminologies, e.g., gene ontology, disease ontology, to name a few. In this paper, we study the weighted tree summarization. We motivate and formulate our <inline-formula><tex-math notation=\"LaTeX\">${\\mathsf {kWTS}}$</tex-math><alternatives><mml:math><mml:mi mathvariant=\"sans-serif\">kWTS</mml:mi></mml:math><inline-graphic xlink:href=\"zhu-ieq1-3120722.gif\"/></alternatives></inline-formula>-<inline-formula><tex-math notation=\"LaTeX\">${\\mathsf {problem}}$</tex-math><alternatives><mml:math><mml:mi mathvariant=\"sans-serif\">problem</mml:mi></mml:math><inline-graphic xlink:href=\"zhu-ieq2-3120722.gif\"/></alternatives></inline-formula> as selecting a diverse set of <inline-formula><tex-math notation=\"LaTeX\">$k$</tex-math><alternatives><mml:math><mml:mi>k</mml:mi></mml:math><inline-graphic xlink:href=\"zhu-ieq3-3120722.gif\"/></alternatives></inline-formula> nodes to <underline>s</underline>ummarize a hierarchical <underline>t</underline>ree <inline-formula><tex-math notation=\"LaTeX\">$T$</tex-math><alternatives><mml:math><mml:mi>T</mml:mi></mml:math><inline-graphic xlink:href=\"zhu-ieq4-3120722.gif\"/></alternatives></inline-formula> with <underline>w</underline>eighted terminologies. We first propose an efficient greedy tree summarization algorithm <inline-formula><tex-math notation=\"LaTeX\">${\\mathsf {GTS}}$</tex-math><alternatives><mml:math><mml:mi mathvariant=\"sans-serif\">GTS</mml:mi></mml:math><inline-graphic xlink:href=\"zhu-ieq5-3120722.gif\"/></alternatives></inline-formula>. It solves the problem with <inline-formula><tex-math notation=\"LaTeX\">$(1-1/e)$</tex-math><alternatives><mml:math><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mi>e</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"zhu-ieq6-3120722.gif\"/></alternatives></inline-formula>-approximation guarantee. Although <inline-formula><tex-math notation=\"LaTeX\">${\\mathsf {GTS}}$</tex-math><alternatives><mml:math><mml:mi mathvariant=\"sans-serif\">GTS</mml:mi></mml:math><inline-graphic xlink:href=\"zhu-ieq7-3120722.gif\"/></alternatives></inline-formula> achieves quality-guaranteed answers approximately, but it is still not optimal. To tackle the problem optimally, we further develop a dynamic programming algorithm <inline-formula><tex-math notation=\"LaTeX\">${\\mathsf {OTS}}$</tex-math><alternatives><mml:math><mml:mi mathvariant=\"sans-serif\">OTS</mml:mi></mml:math><inline-graphic xlink:href=\"zhu-ieq8-3120722.gif\"/></alternatives></inline-formula> to obtain optimal answers for <inline-formula><tex-math notation=\"LaTeX\">${\\mathsf {kWTS}}$</tex-math><alternatives><mml:math><mml:mi mathvariant=\"sans-serif\">kWTS</mml:mi></mml:math><inline-graphic xlink:href=\"zhu-ieq9-3120722.gif\"/></alternatives></inline-formula>-<inline-formula><tex-math notation=\"LaTeX\">${\\mathsf {problem}}$</tex-math><alternatives><mml:math><mml:mi mathvariant=\"sans-serif\">problem</mml:mi></mml:math><inline-graphic xlink:href=\"zhu-ieq10-3120722.gif\"/></alternatives></inline-formula> in <inline-formula><tex-math notation=\"LaTeX\">$O(nhk^3)$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mi>h</mml:mi><mml:msup><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msup><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"zhu-ieq11-3120722.gif\"/></alternatives></inline-formula> time, where <inline-formula><tex-math notation=\"LaTeX\">$n, h$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>h</mml:mi></mml:mrow></mml:math><inline-graphic xlink:href=\"zhu-ieq12-3120722.gif\"/></alternatives></inline-formula> are the node size and height in tree <inline-formula><tex-math notation=\"LaTeX\">$T$</tex-math><alternatives><mml:math><mml:mi>T</mml:mi></mml:math><inline-graphic xlink:href=\"zhu-ieq13-3120722.gif\"/></alternatives></inline-formula>. The algorithm complexity and correctness of <inline-formula><tex-math notation=\"LaTeX\">${\\mathsf {OTS}}$</tex-math><alternatives><mml:math><mml:mi mathvariant=\"sans-serif\">OTS</mml:mi></mml:math><inline-graphic xlink:href=\"zhu-ieq14-3120722.gif\"/></alternatives></inline-formula> are theoretically analyzed. In addition, we propose a useful optimization technique of tree reduction to remove useless nodes with zero weights and shrink the tree into a smaller one, which ensures the efficiency acceleration of both <inline-formula><tex-math notation=\"LaTeX\">${\\mathsf {GTS}}$</tex-math><alternatives><mml:math><mml:mi mathvariant=\"sans-serif\">GTS</mml:mi></mml:math><inline-graphic xlink:href=\"zhu-ieq15-3120722.gif\"/></alternatives></inline-formula> and <inline-formula><tex-math notation=\"LaTeX\">${\\mathsf {OTS}}$</tex-math><alternatives><mml:math><mml:mi mathvariant=\"sans-serif\">OTS</mml:mi></mml:math><inline-graphic xlink:href=\"zhu-ieq16-3120722.gif\"/></alternatives></inline-formula> in real-world datasets. Moreover, we illustrate one useful application of graph visualization based on the answer of <inline-formula><tex-math notation=\"LaTeX\">$k$</tex-math><alternatives><mml:math><mml:mi>k</mml:mi></mml:math><inline-graphic xlink:href=\"zhu-ieq17-3120722.gif\"/></alternatives></inline-formula>-sized tree summarization and show it in a novel case study. Extensive experimental results on real-world datasets show the effectiveness and efficiency of our proposed approximate and optimal algorithms for tree summarization. Furthermore, we conduct a usability evaluation of attractive topic recommendation on ACM Computing Classification System dataset to validate the usefulness of our model and algorithms.",
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"normalizedAbstract": "Data summarization that presents a small subset of a dataset to users has been widely applied in numerous applications and systems. Many datasets are coded with hierarchical terminologies, e.g., gene ontology, disease ontology, to name a few. In this paper, we study the weighted tree summarization. We motivate and formulate our --- as selecting a diverse set of - nodes to summarize a hierarchical tree - with weighted terminologies. We first propose an efficient greedy tree summarization algorithm -. It solves the problem with --approximation guarantee. Although - achieves quality-guaranteed answers approximately, but it is still not optimal. To tackle the problem optimally, we further develop a dynamic programming algorithm - to obtain optimal answers for --- in - time, where - are the node size and height in tree -. The algorithm complexity and correctness of - are theoretically analyzed. In addition, we propose a useful optimization technique of tree reduction to remove useless nodes with zero weights and shrink the tree into a smaller one, which ensures the efficiency acceleration of both - and - in real-world datasets. Moreover, we illustrate one useful application of graph visualization based on the answer of --sized tree summarization and show it in a novel case study. Extensive experimental results on real-world datasets show the effectiveness and efficiency of our proposed approximate and optimal algorithms for tree summarization. Furthermore, we conduct a usability evaluation of attractive topic recommendation on ACM Computing Classification System dataset to validate the usefulness of our model and algorithms.",
"title": "Efficient and Optimal Algorithms for Tree Summarization With Weighted Terminologies",
"normalizedTitle": "Efficient and Optimal Algorithms for Tree Summarization With Weighted Terminologies",
"fno": "09580703",
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"keywords": [
"Approximation Theory",
"Computational Complexity",
"Data Mining",
"Data Visualisation",
"Diseases",
"Dynamic Programming",
"Graph Theory",
"Greedy Algorithms",
"Ontologies Artificial Intelligence",
"Optimisation",
"Pattern Classification",
"Query Processing",
"Tree Data Structures",
"Trees Mathematics",
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"authors": [
{
"givenName": "Xuliang",
"surname": "Zhu",
"fullName": "Xuliang Zhu",
"affiliation": "Department of Computer Science, Hong Kong Baptist University, Hong Kong, China",
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{
"givenName": "Xin",
"surname": "Huang",
"fullName": "Xin Huang",
"affiliation": "Department of Computer Science, Hong Kong Baptist University, Hong Kong, China",
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{
"givenName": "Byron",
"surname": "Choi",
"fullName": "Byron Choi",
"affiliation": "Department of Computer Science, Hong Kong Baptist University, Hong Kong, China",
"__typename": "ArticleAuthorType"
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{
"givenName": "Jianliang",
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"fullName": "Jianliang Xu",
"affiliation": "Department of Computer Science, Hong Kong Baptist University, Hong Kong, China",
"__typename": "ArticleAuthorType"
},
{
"givenName": "William K.",
"surname": "Cheung",
"fullName": "William K. Cheung",
"affiliation": "Department of Computer Science, Hong Kong Baptist University, Hong Kong, China",
"__typename": "ArticleAuthorType"
},
{
"givenName": "Yanchun",
"surname": "Zhang",
"fullName": "Yanchun Zhang",
"affiliation": "Guangzhou University, Guangzhou, China",
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{
"givenName": "Jiming",
"surname": "Liu",
"fullName": "Jiming Liu",
"affiliation": "Department of Computer Science, Hong Kong Baptist University, Hong Kong, China",
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