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However, most", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 462, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 462, + 505, + 475 + ], + "score": 1.0, + "content": "of the GNN models, such as GCN (Kipf & Welling, 2017) and GAT (Velickovi ˇ c et al., 2018), learn ´", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 473, + 506, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 473, + 506, + 486 + ], + "score": 1.0, + "content": "the node representations by aggregating information over only the 2-hop neighborhood. Such shallow", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 484, + 506, + 498 + ], + "spans": [ + { + "bbox": [ + 105, + 484, + 506, + 498 + ], + "score": 1.0, + "content": "architectures limit their ability to extract information from higher-layer neighborhoods (Wang &", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 495, + 505, + 508 + ], + "spans": [ + { + "bbox": [ + 106, + 495, + 505, + 508 + ], + "score": 1.0, + "content": "Derr, 2021). But deep GNNs are prone to over-smoothing (Li et al., 2018), which suggests the node", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 506, + 505, + 519 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 505, + 519 + ], + "score": 1.0, + "content": "representations tend to converge to a certain vector and thus become indistinguishable. One solution", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 517, + 506, + 530 + ], + "spans": [ + { + "bbox": [ + 105, + 517, + 506, + 530 + ], + "score": 1.0, + "content": "to address this problem is to preserve the locality of node representations when increasing the number", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 528, + 505, + 541 + ], + "spans": [ + { + "bbox": [ + 106, + 528, + 505, + 541 + ], + "score": 1.0, + "content": "of layers. For example, JKNet (Xu et al., 2018) densely connects (Huang et al., 2017) each hidden", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 538, + 506, + 553 + ], + "spans": [ + { + "bbox": [ + 105, + 538, + 506, + 553 + ], + "score": 1.0, + "content": "layer to the final layer. GCNII (Chen et al., 2020) employs an initial residual to construct a skip", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 550, + 506, + 563 + ], + "spans": [ + { + "bbox": [ + 105, + 550, + 506, + 563 + ], + "score": 1.0, + "content": "connection from the input layer. Besides, Zeng et al. (2021) pointed out that the key for GNN is", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 561, + 506, + 574 + ], + "spans": [ + { + "bbox": [ + 106, + 561, + 506, + 574 + ], + "score": 1.0, + "content": "to smooth the local neighborhood into informative representation, no matter how deep it is. And", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 572, + 506, + 585 + ], + "spans": [ + { + "bbox": [ + 106, + 572, + 506, + 585 + ], + "score": 1.0, + "content": "they decouple the depth and scope of GNNs to help capture local graph structure. Prior works have", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 583, + 505, + 596 + ], + "spans": [ + { + "bbox": [ + 106, + 583, + 505, + 596 + ], + "score": 1.0, + "content": "emphasized the importance of local information, but one property of the graph is that the number of", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 594, + 505, + 606 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 505, + 606 + ], + "score": 1.0, + "content": "nodes in the local neighborhood is far fewer than higher-order neighbors. And this property limits the", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 605, + 506, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 506, + 618 + ], + "score": 1.0, + "content": "expressive power of GNNs due to the limited neighbors in the local structure. A very intuitive idea is", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 617, + 438, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 617, + 438, + 628 + ], + "score": 1.0, + "content": "to use data augmentation to increase the number of nodes in the local substructure.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 30.5, + "bbox_fs": [ + 105, + 430, + 506, + 628 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 633, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 633, + 505, + 646 + ], + "spans": [ + { + "bbox": [ + 106, + 633, + 505, + 646 + ], + "score": 1.0, + "content": "However, existing graph data augmentation methods ignore the importance of local information", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 644, + 504, + 655 + ], + "spans": [ + { + "bbox": [ + 106, + 644, + 504, + 655 + ], + "score": 1.0, + "content": "and only perturb at the topology-level and feature-level from a global perspective, which can be", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 654, + 506, + 668 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 506, + 668 + ], + "score": 1.0, + "content": "divided into two categories: topology-level augmentation (Rong et al., 2020; Wang et al., 2020b; Zhao", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 666, + 506, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 506, + 678 + ], + "score": 1.0, + "content": "et al., 2021) and feature-level augmentation (Deng et al., 2019; Feng et al., 2019; Kong et al., 2020).", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 676, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 506, + 690 + ], + "score": 1.0, + "content": "Topology-level augmentation perturbs the adjacency matrix, yielding different graph structures. On", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "score": 1.0, + "content": "the other hand, existing feature-level augmentation mainly exploits perturbation of node attributes", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "score": 1.0, + "content": "guided by adversarial training (Deng et al., 2019; Feng et al., 2019; Kong et al., 2020). These", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 709, + 506, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 506, + 722 + ], + "score": 1.0, + "content": "augmentation techniques have two drawbacks. 1) Some of they employ full-batch training for", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 720, + 506, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 506, + 733 + ], + "score": 1.0, + "content": "augmentation, which is computationally expensive, and introduce some additional side effects such", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 83, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 83, + 505, + 95 + ], + "score": 1.0, + "content": "as over-smoothing. 2) The type of feature-level augmentation is coarse-grained, which focuses on", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 94, + 505, + 105 + ], + "spans": [ + { + "bbox": [ + 105, + 94, + 505, + 105 + ], + "score": 1.0, + "content": "global augmentation and overlooks the local information of the neighborhood. Moreover, to our best", + "type": "text", + "cross_page": true + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 105, + 505, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 505, + 118 + ], + "score": 1.0, + "content": "knowledge, none of the existing approaches combines both the feature representations and the graph", + "type": "text", + "cross_page": true + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 116, + 448, + 129 + ], + "spans": [ + { + "bbox": [ + 105, + 116, + 448, + 129 + ], + "score": 1.0, + "content": "topology, especially the local subgraph structures, for graph-level data augmentation.", + "type": "text", + "cross_page": true + } + ], + "index": 3 + } + ], + "index": 44, + "bbox_fs": [ + 105, + 633, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 127 + ], + "lines": [ + { + "bbox": [ + 105, + 83, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 83, + 505, + 95 + ], + "score": 1.0, + "content": "as over-smoothing. 2) The type of feature-level augmentation is coarse-grained, which focuses on", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 94, + 505, + 105 + ], + "spans": [ + { + "bbox": [ + 105, + 94, + 505, + 105 + ], + "score": 1.0, + "content": "global augmentation and overlooks the local information of the neighborhood. Moreover, to our best", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 105, + 505, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 505, + 118 + ], + "score": 1.0, + "content": "knowledge, none of the existing approaches combines both the feature representations and the graph", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 116, + 448, + 129 + ], + "spans": [ + { + "bbox": [ + 105, + 116, + 448, + 129 + ], + "score": 1.0, + "content": "topology, especially the local subgraph structures, for graph-level data augmentation.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 1.5 + }, + { + "type": "text", + "bbox": [ + 107, + 132, + 506, + 221 + ], + "lines": [ + { + "bbox": [ + 105, + 132, + 507, + 145 + ], + "spans": [ + { + "bbox": [ + 105, + 132, + 507, + 145 + ], + "score": 1.0, + "content": "In this work, we propose a framework: Local Augmentation for Graph Neural Networks (LA-GNNs),", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 144, + 507, + 156 + ], + "spans": [ + { + "bbox": [ + 105, + 144, + 507, + 156 + ], + "score": 1.0, + "content": "to further enhance the locality of node representations based on both the topology-level and feature-", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 154, + 506, + 166 + ], + "spans": [ + { + "bbox": [ + 106, + 154, + 506, + 166 + ], + "score": 1.0, + "content": "level information in the substructure. The term \"local augmentation\" refers to the generation of", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 165, + 506, + 178 + ], + "spans": [ + { + "bbox": [ + 106, + 165, + 506, + 178 + ], + "score": 1.0, + "content": "neighborhood features via a generative model conditioned on local structures and node features.", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 176, + 506, + 189 + ], + "spans": [ + { + "bbox": [ + 105, + 176, + 506, + 189 + ], + "score": 1.0, + "content": "Specifically, our proposed framework learns the conditional distribution of the connected neighbors’", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 187, + 506, + 200 + ], + "spans": [ + { + "bbox": [ + 105, + 187, + 506, + 200 + ], + "score": 1.0, + "content": "representations given the representation of the central node, bearing some similarities with the Skip-", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 198, + 506, + 210 + ], + "spans": [ + { + "bbox": [ + 105, + 198, + 506, + 210 + ], + "score": 1.0, + "content": "gram (Mikolov et al., 2013) and Deepwalk Perozzi et al. (2014), with the difference that our method", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 208, + 284, + 223 + ], + "spans": [ + { + "bbox": [ + 105, + 208, + 284, + 223 + ], + "score": 1.0, + "content": "does not base on word or graph embedding.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 7.5 + }, + { + "type": "text", + "bbox": [ + 107, + 226, + 505, + 380 + ], + "lines": [ + { + "bbox": [ + 105, + 225, + 505, + 239 + ], + "spans": [ + { + "bbox": [ + 105, + 225, + 505, + 239 + ], + "score": 1.0, + "content": "The motivation behind this work concludes three-fold. 1) Existing feature-level augmentation works", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 237, + 506, + 249 + ], + "spans": [ + { + "bbox": [ + 105, + 237, + 506, + 249 + ], + "score": 1.0, + "content": "primarily pay attention to global augmentation without considering the informative neighborhood. 2)", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 248, + 506, + 261 + ], + "spans": [ + { + "bbox": [ + 106, + 248, + 506, + 261 + ], + "score": 1.0, + "content": "The distributions of the representations of the neighbors are closely connected to the central node,", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 259, + 506, + 272 + ], + "spans": [ + { + "bbox": [ + 106, + 259, + 506, + 272 + ], + "score": 1.0, + "content": "making ample room for feature augmentation. 3) Preserving the locality of node representations is", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 270, + 506, + 282 + ], + "spans": [ + { + "bbox": [ + 105, + 270, + 237, + 282 + ], + "score": 1.0, + "content": "key to avoiding over-smoothing", + "type": "text" + }, + { + "bbox": [ + 238, + 270, + 251, + 280 + ], + "score": 0.27, + "content": "\\mathrm { { X u } }", + "type": "inline_equation" + }, + { + "bbox": [ + 252, + 270, + 506, + 282 + ], + "score": 1.0, + "content": "et al., 2018; Klicpera et al., 2019; Chen et al., 2020). And there", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 281, + 506, + 294 + ], + "spans": [ + { + "bbox": [ + 105, + 281, + 506, + 294 + ], + "score": 1.0, + "content": "are several benefits in applying local augmentation for the GNN training. First, local augmentation is", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 291, + 506, + 304 + ], + "spans": [ + { + "bbox": [ + 105, + 291, + 506, + 304 + ], + "score": 1.0, + "content": "essentially a data augmentation technique that can improve the generalization of the GNN models", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 302, + 505, + 315 + ], + "spans": [ + { + "bbox": [ + 106, + 302, + 505, + 315 + ], + "score": 1.0, + "content": "and prevent over-fitting. Second, we can recover some missing contextual information of the local", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 314, + 506, + 326 + ], + "spans": [ + { + "bbox": [ + 106, + 314, + 506, + 326 + ], + "score": 1.0, + "content": "neighborhood in an attributed graph via the generative model (Jia & Benson, 2020). Third, our", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 324, + 506, + 338 + ], + "spans": [ + { + "bbox": [ + 105, + 324, + 506, + 338 + ], + "score": 1.0, + "content": "proposed framework is flexible and can be applied to various popular backbone networks such", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 335, + 506, + 348 + ], + "spans": [ + { + "bbox": [ + 105, + 335, + 506, + 348 + ], + "score": 1.0, + "content": "as GCN (Kipf & Welling, 2017), GAT (Velickovi ˇ c et al., 2018), GCNII (Chen et al., 2020), and ´", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 346, + 505, + 360 + ], + "spans": [ + { + "bbox": [ + 105, + 346, + 505, + 360 + ], + "score": 1.0, + "content": "GRAND (Feng et al., 2020) to enhance their performance. Extensive experimental results demonstrate", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 357, + 506, + 371 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 506, + 371 + ], + "score": 1.0, + "content": "that our proposed framework could improve the performance of GNN variants on 7 benchmark", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 367, + 144, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 367, + 144, + 380 + ], + "score": 1.0, + "content": "datasets.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 18.5 + }, + { + "type": "title", + "bbox": [ + 108, + 395, + 200, + 408 + ], + "lines": [ + { + "bbox": [ + 104, + 394, + 201, + 411 + ], + "spans": [ + { + "bbox": [ + 104, + 394, + 201, + 411 + ], + "score": 1.0, + "content": "2 BACKGROUND", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 106, + 418, + 505, + 502 + ], + "lines": [ + { + "bbox": [ + 104, + 416, + 504, + 434 + ], + "spans": [ + { + "bbox": [ + 104, + 416, + 177, + 434 + ], + "score": 1.0, + "content": "Notations. 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\\psi , \\varphi ) = - K L ( q _ { \\varphi } ( \\mathbf { z } | \\mathbf { X } _ { j } , \\mathbf { X } _ { i } ) | | p _ { \\psi } ( \\mathbf { z } | \\mathbf { X } _ { i } ) ) + \\int q _ { \\varphi } ( \\mathbf { z } | \\mathbf { X } _ { j } , \\mathbf { X } _ { i } ) \\log p _ { \\psi } ( \\mathbf { X } _ { j } | \\mathbf { X } _ { i } , \\mathbf { z } ) \\mathrm { d } \\mathbf { z } ,", + "type": "interline_equation", + "image_path": "0a1fac39e36905a3a4546a8f12f4e8cd9c64dd90538a0a88ad47d0994d897420.jpg" + } + ] + } + ], + "index": 40, + "virtual_lines": [ + { + "bbox": [ + 111, + 655, + 487, + 681 + ], + "spans": [], + "index": 40 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 685, + 505, + 733 + ], + "lines": [ + { + "bbox": [ + 105, + 686, + 504, + 699 + ], + "spans": [ + { + "bbox": [ + 105, + 686, + 189, + 699 + ], + "score": 1.0, + "content": "where the encoder", + "type": "text" + }, + { + "bbox": [ + 189, + 686, + 373, + 699 + ], + "score": 0.92, + "content": "q _ { \\varphi } ( \\mathbf { z } | \\mathbf { X } _ { j } , \\mathbf { X } _ { i } ) \\ = \\ { \\mathcal { N } } ( f ( \\mathbf { X } _ { j } , \\mathbf { X } _ { i } ) , g ( \\mathbf { X } _ { j } , \\mathbf { X } _ { i } ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 373, + 686, + 432, + 699 + ], + "score": 1.0, + "content": "and decoder", + "type": "text" + }, + { + "bbox": [ + 433, + 686, + 504, + 699 + ], + "score": 0.89, + "content": "p _ { \\psi } ( { \\bf X } _ { j } | { \\bf X } _ { i } , { \\bf z } ) =", + "type": "inline_equation" + } + ], + "index": 41 + }, + { + "bbox": [ + 107, + 696, + 506, + 711 + ], + "spans": [ + { + "bbox": [ + 107, + 698, + 174, + 710 + ], + "score": 0.92, + "content": "\\mathcal { N } ( h ( \\mathbf { X } _ { i } , \\mathbf { z } ) , c I )", + "type": "inline_equation" + }, + { + "bbox": [ + 174, + 696, + 317, + 711 + ], + "score": 1.0, + "content": ". 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And we use GCN, GAT, GCNII, and GRAND as", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 261, + 506, + 273 + ], + "spans": [ + { + "bbox": [ + 105, + 261, + 506, + 273 + ], + "score": 1.0, + "content": "the backbones and test them on semi-supervised node classification tasks. 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This critical question makes the", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 565, + 505, + 576 + ], + "spans": [ + { + "bbox": [ + 106, + 565, + 505, + 576 + ], + "score": 1.0, + "content": "inferences inefficient. Inspired by Nielsen & Okoniewski (2019), we introduce active learning to", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 575, + 506, + 588 + ], + "spans": [ + { + "bbox": [ + 105, + 575, + 506, + 588 + ], + "score": 1.0, + "content": "capture the suitable generated feature matrix and the corresponding generator, which improves the", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 585, + 505, + 599 + ], + "spans": [ + { + "bbox": [ + 105, + 585, + 505, + 599 + ], + "score": 1.0, + "content": "inference efficiency and helps the optimization of the MLE. 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we discuss the motivation of this work and provide some analysis.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 106, + 324, + 506, + 534 + ], + "lines": [ + { + "bbox": [ + 106, + 325, + 505, + 338 + ], + "spans": [ + { + "bbox": [ + 106, + 325, + 505, + 338 + ], + "score": 1.0, + "content": "Connection to EP-B and GraphSAGE We discuss how our proposed model distinguishes from", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 336, + 505, + 348 + ], + "spans": [ + { + "bbox": [ + 106, + 336, + 505, + 348 + ], + "score": 1.0, + "content": "the classical representation learning models on graphs. Previous methods such as EP-B (García-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 346, + 505, + 360 + ], + "spans": [ + { + "bbox": [ + 105, + 346, + 505, + 360 + ], + "score": 1.0, + "content": "Durán & Niepert, 2017) and GraphSAGE (Hamilton et al., 2017) rely on reconstruction loss function", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 357, + 505, + 371 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 505, + 371 + ], + "score": 1.0, + "content": "between the central node and its neighbors’ embeddings. 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Previous methods such as EP-B (García-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 346, + 505, + 360 + ], + "spans": [ + { + "bbox": [ + 105, + 346, + 505, + 360 + ], + "score": 1.0, + "content": "Durán & Niepert, 2017) and GraphSAGE (Hamilton et al., 2017) rely on reconstruction loss function", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 357, + 505, + 371 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 505, + 371 + ], + "score": 1.0, + "content": "between the central node and its neighbors’ embeddings. 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These approaches build upon the assumption that adjacent nodes share similar attributes.", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 468, + 505, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 468, + 505, + 480 + ], + "score": 1.0, + "content": "In contrast, our model does not rely on such assumption and instead generates the neighboring node", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 478, + 506, + 491 + ], + "spans": [ + { + "bbox": [ + 105, + 478, + 488, + 491 + ], + "score": 1.0, + "content": "features from the conditional distribution of central node representations. 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A comparison between the", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 500, + 505, + 513 + ], + "spans": [ + { + "bbox": [ + 105, + 500, + 505, + 513 + ], + "score": 1.0, + "content": "reconstruction-based representation learning on graphs and our proposed framework is illustrated", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 511, + 506, + 524 + ], + "spans": [ + { + "bbox": [ + 105, + 511, + 506, + 524 + ], + "score": 1.0, + "content": "in Figure 2. And our local augmentation method is the third paradigm to exploit neighbors in a", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 522, + 171, + 536 + ], + "spans": [ + { + "bbox": [ + 105, + 522, + 171, + 536 + ], + "score": 1.0, + "content": "generative way.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 24.5, + "bbox_fs": [ + 104, + 325, + 507, + 536 + ] + }, + { + "type": "image", + "bbox": [ + 122, + 550, + 486, + 624 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 122, + 550, + 486, + 624 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 122, + 550, + 486, + 624 + ], + "spans": [ + { + "bbox": [ + 122, + 550, + 486, + 624 + ], + "score": 0.963, + "type": "image", + "image_path": "02db34de261ebadeed56e54daa7a15cd3eaa86f7795ea776ca63ea498b28e4a9.jpg" + } + ] + } + ], + "index": 35, + "virtual_lines": [ + { + "bbox": [ + 122, + 550, + 486, + 574.6666666666666 + ], + "spans": [], + "index": 34 + }, + { + "bbox": [ + 122, + 574.6666666666666, + 486, + 599.3333333333333 + ], + "spans": [], + "index": 35 + }, + { + "bbox": [ + 122, + 599.3333333333333, + 486, + 623.9999999999999 + ], + "spans": [], + "index": 36 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 635, + 506, + 680 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 635, + 506, + 648 + ], + "spans": [ + { + "bbox": [ + 105, + 635, + 506, + 648 + ], + "score": 1.0, + "content": "Figure 2: (a) The original graph. (b) EP-B exploits the neighbors to reconstruct the central node’s", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 647, + 505, + 659 + ], + "spans": [ + { + "bbox": [ + 106, + 647, + 505, + 659 + ], + "score": 1.0, + "content": "embedding. (c) GraphSAGE encourages nearby nodes to have similar embeddings. (d) Given the", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 104, + 658, + 506, + 670 + ], + "spans": [ + { + "bbox": [ + 104, + 658, + 506, + 670 + ], + "score": 1.0, + "content": "representation of the central node, our aim is to infer the representations of the connected distribution", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 667, + 163, + 682 + ], + "spans": [ + { + "bbox": [ + 105, + 667, + 163, + 682 + ], + "score": 1.0, + "content": "of neighbors.", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 38.5 + } + ], + "index": 36.75 + }, + { + "type": "text", + "bbox": [ + 107, + 687, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 687, + 507, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 507, + 700 + ], + "score": 1.0, + "content": "Local Augmentation vs. General Augmentation General image augmentation algorithms in-", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 698, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 505, + 711 + ], + "score": 1.0, + "content": "clude geometric transformations, feature space augmentation, adversarial training, and generative", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 710, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 506, + 723 + ], + "score": 1.0, + "content": "adversarial networks (Shorten & Khoshgoftaar, 2019). It is impossible to apply geometric transfor-", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 721, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 505, + 733 + ], + "score": 1.0, + "content": "mations directly to graph data augmentation since graphs are sensitive to node permutation. General", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "adversarial training, feature space augmentation, and generative adversarial networks don’t take the", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "graph structure into account. Graphs consist of a set of identities with certain pairs of these identities", + "type": "text", + "cross_page": true + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 105, + 504, + 117 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 504, + 117 + ], + "score": 1.0, + "content": "connected by edges. We need to consider node features and the graph structure when designing the", + "type": "text", + "cross_page": true + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 505, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 505, + 128 + ], + "score": 1.0, + "content": "graph data augmentation framework. Our proposed method of local augmentation fully considers", + "type": "text", + "cross_page": true + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 125, + 505, + 140 + ], + "spans": [ + { + "bbox": [ + 105, + 125, + 505, + 140 + ], + "score": 1.0, + "content": "these two points. By extracting the neighbors’ feature vectors, we have enough data points to learn the", + "type": "text", + "cross_page": true + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 136, + 505, + 150 + ], + "spans": [ + { + "bbox": [ + 105, + 136, + 505, + 150 + ], + "score": 1.0, + "content": "distribution. There are two benefits to designing local augmentation. First, by taking the sub-graph", + "type": "text", + "cross_page": true + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 148, + 505, + 161 + ], + "spans": [ + { + "bbox": [ + 105, + 148, + 505, + 161 + ], + "score": 1.0, + "content": "structure and feature representation associated with this sub-graph structure as input for the generative", + "type": "text", + "cross_page": true + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 158, + 505, + 172 + ], + "spans": [ + { + "bbox": [ + 105, + 158, + 505, + 172 + ], + "score": 1.0, + "content": "model, we can learn the information of the sub-graph structure. Second, the number of data points", + "type": "text", + "cross_page": true + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 170, + 505, + 183 + ], + "spans": [ + { + "bbox": [ + 105, + 170, + 505, + 183 + ], + "score": 1.0, + "content": "to learn the distribution depends on the node degree. This assures that we have enough data points", + "type": "text", + "cross_page": true + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 181, + 454, + 194 + ], + "spans": [ + { + "bbox": [ + 105, + 181, + 454, + 194 + ], + "score": 1.0, + "content": "compared with the general feature augmentation and we can learn a better distribution.", + "type": "text", + "cross_page": true + } + ], + "index": 9 + } + ], + "index": 42.5, + "bbox_fs": [ + 105, + 687, + 507, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 192 + ], + "lines": [ + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "adversarial training, feature space augmentation, and generative adversarial networks don’t take the", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "graph structure into account. Graphs consist of a set of identities with certain pairs of these identities", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 105, + 504, + 117 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 504, + 117 + ], + "score": 1.0, + "content": "connected by edges. We need to consider node features and the graph structure when designing the", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 505, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 505, + 128 + ], + "score": 1.0, + "content": "graph data augmentation framework. Our proposed method of local augmentation fully considers", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 125, + 505, + 140 + ], + "spans": [ + { + "bbox": [ + 105, + 125, + 505, + 140 + ], + "score": 1.0, + "content": "these two points. By extracting the neighbors’ feature vectors, we have enough data points to learn the", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 136, + 505, + 150 + ], + "spans": [ + { + "bbox": [ + 105, + 136, + 505, + 150 + ], + "score": 1.0, + "content": "distribution. There are two benefits to designing local augmentation. First, by taking the sub-graph", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 148, + 505, + 161 + ], + "spans": [ + { + "bbox": [ + 105, + 148, + 505, + 161 + ], + "score": 1.0, + "content": "structure and feature representation associated with this sub-graph structure as input for the generative", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 158, + 505, + 172 + ], + "spans": [ + { + "bbox": [ + 105, + 158, + 505, + 172 + ], + "score": 1.0, + "content": "model, we can learn the information of the sub-graph structure. Second, the number of data points", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 170, + 505, + 183 + ], + "spans": [ + { + "bbox": [ + 105, + 170, + 505, + 183 + ], + "score": 1.0, + "content": "to learn the distribution depends on the node degree. This assures that we have enough data points", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 181, + 454, + 194 + ], + "spans": [ + { + "bbox": [ + 105, + 181, + 454, + 194 + ], + "score": 1.0, + "content": "compared with the general feature augmentation and we can learn a better distribution.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 4.5 + }, + { + "type": "text", + "bbox": [ + 107, + 205, + 505, + 282 + ], + "lines": [ + { + "bbox": [ + 106, + 204, + 506, + 218 + ], + "spans": [ + { + "bbox": [ + 106, + 204, + 506, + 218 + ], + "score": 1.0, + "content": "Complementing missing information Jia & Benson (2020) points out that some attribute informa-", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 217, + 505, + 228 + ], + "spans": [ + { + "bbox": [ + 106, + 217, + 505, + 228 + ], + "score": 1.0, + "content": "tion might be missing on a subset of vertices. By learning the distribution of node representations from", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 226, + 506, + 239 + ], + "spans": [ + { + "bbox": [ + 105, + 226, + 506, + 239 + ], + "score": 1.0, + "content": "the observed data, we can utilize the produced node representations from the generative model to com-", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 239, + 505, + 249 + ], + "spans": [ + { + "bbox": [ + 106, + 239, + 505, + 249 + ], + "score": 1.0, + "content": "plement the information missing in the nodes’ attributes, which boosts the robustness of downstream", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 248, + 506, + 261 + ], + "spans": [ + { + "bbox": [ + 105, + 248, + 506, + 261 + ], + "score": 1.0, + "content": "tasks. 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Chebyshev (Defferrard et al.,2016)81.269.874.4
APPNP (Klicpera et al.,2019)83.871.679.7
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GAT (Velickovic et al., 2018)83.070.40OM
LA-GAT83.972.3OOM
GCNII (Chen et al.,2020) LA-GCNII85.273.180.0
85.273.781.6
GRAND (Feng et al.,2020)85.475.482.7
LA-GRAND85.875.883.3
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MethodSquirrelActorChameleonCornell
APPNP21.632.133.058.7
S²GC21.327.830.257.2
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LA-GCNII28.632.732.556.6
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MethodCoraCiteseerPubmed
Chebyshev (Defferrard et al.,2016)81.269.874.4
APPNP (Klicpera et al.,2019)83.871.679.7
MixHop (Abu-El-Haija et al.,2019)81.971.480.8
Graph U-net (Gao& Ji,2019)84.473.279.6
GSNN-M (Wang et al.,2020a)83.972.279.1
S²GC (Zhu & Koniusz,2021)83.573.680.2
GCN (Kipf & Welling,2017)81.670.378.9
G-GCN (Zhu et al.,2020)83.771.380.9
DropEdge-GCN (Rong et al.,2020)82.872.379.6
GAUG-O-GCN (Zhao et al.,2021)83.673.379.3
LA-GCN84.172.581.3
GAT (Velickovic et al., 2018)83.070.40OM
LA-GAT83.972.3OOM
GCNII (Chen et al.,2020) LA-GCNII85.273.180.0
85.273.781.6
GRAND (Feng et al.,2020)85.475.482.7
LA-GRAND85.875.883.3
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MethodSquirrelActorChameleonCornell
APPNP21.632.133.058.7
S²GC21.327.830.257.2
GCN22.526.225.155.7
DropEdge-GCN21.926.525.053.6
LA-GCN23.227.028.956.1
GAT24.227.234.855.8
LA-GAT28.227.438.656.5
GCNII25.331.930.257.3
LA-GCNII28.632.732.556.6
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By eliminating the possibility that these confounding", + "type": "text" + } + ], + "index": 76 + }, + { + "bbox": [ + 105, + 628, + 505, + 641 + ], + "spans": [ + { + "bbox": [ + 105, + 628, + 505, + 641 + ], + "score": 1.0, + "content": "factors irrelevant to our core approach may contribute to the final performance, it’s evident that the", + "type": "text" + } + ], + "index": 77 + }, + { + "bbox": [ + 105, + 639, + 506, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 639, + 506, + 651 + ], + "score": 1.0, + "content": "performance gain in Table 2 and 3 are due to our proposed generative local augmentation framework.", + "type": "text" + } + ], + "index": 78 + } + ], + "index": 76.5 + }, + { + "type": "title", + "bbox": [ + 108, + 666, + 306, + 677 + ], + "lines": [ + { + "bbox": [ + 105, + 666, + 307, + 679 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 307, + 679 + ], + "score": 1.0, + "content": "5.4 ROBUSTNESS TO MISSING INFORMATION", + "type": "text" + } + ], + "index": 79 + } + ], + "index": 79 + }, + { + "type": "text", + "bbox": [ + 108, + 687, + 505, + 731 + ], + "lines": [ + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "score": 1.0, + "content": "In this section, we conduct experiments to verify that our proposed framework can robustify down-", + "type": "text" + } + ], + "index": 80 + }, + { + "bbox": [ + 106, + 699, + 505, + 710 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 505, + 710 + ], + "score": 1.0, + "content": "stream tasks against missing information in the feature attributes. 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MethodCoraCiteseerPubmed
GCN81.670.378.9
GCNII85.273.180.0
GCN + width82.071.479.5
GCN + concatenation81.871.678.8
GCN + plain neighborhood80.968.875.0
GCNII + width85.173.180.2
GCNII + concatenation85.273.380.2
GCNII + plain neighborhood83.371.978.1
LA-GCN84.172.581.3
LA-GCNII85.273.781.6
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Since there exists large redundancy", + "type": "text", + "cross_page": true + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 104, + 505, + 117 + ], + "spans": [ + { + "bbox": [ + 105, + 104, + 505, + 117 + ], + "score": 1.0, + "content": "in the features of the Pubmed dataset, the performance of GCN and LA-GCN decreases little as the", + "type": "text", + "cross_page": true + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 505, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 505, + 128 + ], + "score": 1.0, + "content": "mask ratio increases and the gap of the performance does not enlarge. 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DatasetCoraCiteseerPubmed
Mask Ratio0.10.20.40.80.10.20.40.80.10.20.40.8
GCN81.0(↓0.6)80.6(↓1.0)80.1(↓1.5)76.0 (↓5.6)70.1(↓0.2)69.3 (↓1.0)67.2 (↓3.1)61.0(↓9.3)78.5(↓0.4)78.5(↓0.4)77.5 (↓1.4)76.9 (↓2.0)
LA-GCN83.5 (↓0.6)83.1(↓1.0)81.6(↓2.5)81.1 (↓3.0)72.2(↓0.3)71.7 (↓0.8)69.3 (↓3.2)65.9 (↓6.6)81.4(↓0.1)80.9 (↓0.6)80.5 (↓1.0)79.4 (↓2.1)
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Mask Ratio0.10.20.40.80.10.20.40.80.10.20.40.8
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LA-GCN83.5 (↓0.6)83.1(↓1.0)81.6(↓2.5)81.1 (↓3.0)72.2(↓0.3)71.7 (↓0.8)69.3 (↓3.2)65.9 (↓6.6)81.4(↓0.1)80.9 (↓0.6)80.5 (↓1.0)79.4 (↓2.1)
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WebKB1 is a webpage dataset collected", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 220, + 505, + 233 + ], + "spans": [ + { + "bbox": [ + 105, + 220, + 505, + 233 + ], + "score": 1.0, + "content": "from various universities. We use the one subdataset of it, Cornell. 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