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query stringlengths 1 13.4k | pos stringlengths 1 61k | neg stringlengths 1 63.9k | query_lang stringclasses 147
values | __index_level_0__ int64 0 3.11M |
|---|---|---|---|---|
Feature Selection by Joint Graph Sparse Coding | Online Learning for Matrix Factorization and Sparse Coding | A Randomized Clinical Trial of Eye Movement Desensitization and Reprocessing (EMDR), Fluoxetine, and Pill Placebo in the Treatment of Posttraumatic Stress Disorder: Treatment Effects and Long-Term Maintenance | eng_Latn | 1,000 |
Robust semi-supervised nonnegative matrix factorization | Locality Preserving Projections | Targeting adenosine for cancer immunotherapy | eng_Latn | 1,001 |
A Comparative Framework for Preconditioned Lasso Algorithms | The Adaptive Lasso and Its Oracle Properties | Tracking curved regularized optimization solution paths | eng_Latn | 1,002 |
Nonlinear Extensions of Reconstruction ICA | On optimization methods for deep learning | Pegasos: primal estimated sub-gradient solver for SVM | eng_Latn | 1,003 |
Manifold Regularized Discriminative Nonnegative Matrix Factorization With Fast Gradient Descent | Parameterisation of a stochastic model for human face identification | Functional foods against metabolic syndrome (obesity, diabetes, hypertension and dyslipidemia) and cardiovasular disease | eng_Latn | 1,004 |
When is a Convolutional Filter Easy To Learn? | How to Escape Saddle Points Efficiently | Global Optimality of Local Search for Low Rank Matrix Recovery | eng_Latn | 1,005 |
Phase Transitions for High Dimensional Clustering and Related Problems | A direct formulation for sparse PCA using semidefinite programming | Expokit: a software package for computing matrix exponentials | eng_Latn | 1,006 |
Understanding Alternating Minimization for Matrix Completion | A Simple Algorithm for Nuclear Norm Regularized Problems | Expertise modeling for matching papers with reviewers | eng_Latn | 1,007 |
Stable and Efficient Representation Learning with Nonnegativity Constraints | Non-negative matrix factorization with sparseness constraints | Unifying nearest neighbors collaborative filtering | eng_Latn | 1,008 |
An Asynchronous Parallel Stochastic Coordinate Descent Algorithm | Regression Shrinkage and Selection Via the Lasso | Adaptable Game Experience Based on Player's Performance and EEG | eng_Latn | 1,009 |
Large-Scale Online Feature Selection for Ultra-High Dimensional Sparse Data | On Similarity Preserving Feature Selection | Teaching Creativity and Inventive Problem Solving in Science | yue_Hant | 1,010 |
Iterative thresholding based image segmentation using 2D improved Otsu algorithm | Otsu Method and K-means | Matrix Tri-Factorization with Manifold Regularizations for Zero-Shot Learning | eng_Latn | 1,011 |
Interpreting Latent Variables in Factor Models via Convex Optimization | High-dimensional covariance estimation by minimizing $\ell_1$-penalized log-determinant divergence | Art Therapy and Mindfulness With Survivors of Political Violence: A Qualitative Study | eng_Latn | 1,012 |
Robust PCA via Nonconvex Rank Approximation | Bayesian Robust Principal Component Analysis | Data Driven Analysis on the Effect of Online Judge System | kor_Hang | 1,013 |
Algorithms and applications for approximate nonnegative matrix factorization | Algorithms, Initializations, and Convergence for the Nonnegative Matrix Factorization | Synaptic integrative mechanisms for spatial cognition | eng_Latn | 1,014 |
Sublinear Time Low-Rank Approximation of Positive Semidefinite Matrices | SPSD Matrix Approximation vis Column Selection: Theories, Algorithms, and Extensions | Scene Classification With Recurrent Attention of VHR Remote Sensing Images | eng_Latn | 1,015 |
Optimizing the performance of sparse matrix-vector multiplication | Concept Decompositions for Large Sparse Text Data Using Clustering | An Interactive Artificial Ant Approach to Non-photorealistic Rendering | eng_Latn | 1,016 |
F-SVM: Combination of Feature Transformation and SVM Learning via Convex Relaxation | Discriminative decorrelation for clustering and classification | Statistical learning theory | eng_Latn | 1,017 |
Optimal Statistical and Computational Rates for One Bit Matrix Completion. | Factorization meets the neighborhood: a multifaceted collaborative filtering model | Code3: A System for End-to-End Programming of Mobile Manipulator Robots for Novices and Experts | eng_Latn | 1,018 |
Sparse nonnegative matrix approximation : new formulations and algorithms | Regression Shrinkage and Selection Via the Lasso | Nonnegative Matrix Factorization for Spectral Data Analysis | eng_Latn | 1,019 |
Kernel Multivariate Analysis Framework for Supervised Subspace Learning: A Tutorial on Linear and Kernel Multivariate Methods | Nonlinear Component Analysis as a Kernel Eigenvalue Problem | Estimation of primary quantization matrix in double compressed jpeg images | eng_Latn | 1,020 |
Mutual information for symmetric rank-one matrix estimation: A proof of the replica formula | A direct formulation for sparse PCA using semidefinite programming | The role of positive and negative emotions in life-satisfaction judgment across nations | eng_Latn | 1,021 |
An Introduction to Dimensionality Reduction Using Matlab | A Global Geometric Framework for Nonlinear Dimensionality Reduction | Organizational Ambidexterity: Past, Present and Future | yue_Hant | 1,022 |
Depthwith nonlinearity creates no bad localminima in ResNets | Identifying and attacking the saddle point problem in high-dimensional non-convex optimization | Authorship analysis: Identifying the author of a program | eng_Latn | 1,023 |
A pilot study of the Video Observations Aarts and Aarts (VOAA): a new software program to measure motor behaviour in children with cerebral palsy | A new computer software program to score video observations, Video Observations Aarts and Aarts (VOAA) was developed to evaluate paediatric occupa- tional therapy interventions. The VOAA is an observation tool that assesses the fre- quency, duration and quality of arm/hand use in children, in particular those with cere... | ABSTRACTThis paper deals with the functional relation between multivariate methods of canonical correlation analysis (CCA), partial least squares (PLS) and also their kernelized versions. Both methods are determined by the solution of the respective optimization problem, and result in algorithms using spectral or singu... | eng_Latn | 1,024 |
How do I know the best model from lasso regression fitting/plot? | How can I choose the best model from LARS and LASSO regression? | Why is statistics calculated from raw data more accurate than statistic calculated from a frequency table? | eng_Latn | 1,025 |
I am working on a simple example of how to numerically solve the time-independent Schrodinger Equation for the infinite square well. I've used the Euler Method to find values of the wave function, $\psi (x)$, but now I've just realized something - I have no clue how to determine the energies from this! I know that anal... | This is my first question on here. I'm trying to numerically solve the Schrödinger equation for the and find the energy eigenvalues and eigenfunctions but I am confused about how exactly this should be done. I've solved some initial value problems in the past using iterative methods such as Runge–Kutta. I've read tha... | Please use UK pre-uni methods only (at least at first). Thank you. | eng_Latn | 1,026 |
Let M be mxn matrix then SVD of M will be UXW^* (sorry for X, assume summation). Then how does it generalizes eigen decomposition ? Since eigen decomposition is possible for nxn matrix and that are non-symmetric. | Principal component analysis (PCA) is usually explained via an eigen-decomposition of the covariance matrix. However, it can also be performed via singular value decomposition (SVD) of the data matrix $\mathbf X$. How does it work? What is the connection between these two approaches? What is the relationship between SV... | This question is about an efficient way to compute principal components. Many texts on linear PCA advocate using singular-value decomposition of the casewise data. That is, if we have data $\bf X$ and want to replace the variables (its columns) by principal components, we do SVD: $\bf X=USV'$, singular values (sq. ro... | eng_Latn | 1,027 |
I'm doing a data analysis on data with more than 100 dimensions. After that different ML-Algorithms like NN are applied to it. When I do a PCA in the first place to reduce dimensionality to somewhat like 3-10, I persistently get better results (as in less miss-predictions) than without it. My thought was that PCA sh... | Suppose I am running a regression $Y \sim X$. Why by selecting top $k$ principle components of $X$, does the model retain its predictive power on $Y$? I understand that from dimensionality-reduction/feature-selection point of view, if $v_1, v_2, ... v_k$ are the eigenvectors of covariance matrix of $X$ with top $k$ e... | I'm trying to install in VirtualBox but the installation get stuck at Do you want to install boot loader GRUB Some background: The VM was created from the Ubuntu 32-bit (x86) VirtualBox template The VM has 1 core + 3096 MB RAM Video memory: 32 MB PAE/NX enabled Hardware virtualization: both VTx and nested paginat... | eng_Latn | 1,028 |
I have a dataset with approximately 4000 rows and 150 columns. I want to predict the values of a single column (= target). The data is on cities (demography, social, economic, ... indicators). A lot of these are highly correlated, so I want to do a PCA - Principal Component Analysis. The problem is, that ~40% of the... | I used the prcomp() function to perform a PCA (principal component analysis) in R. However, there's a bug in that function such that the na.action parameter does not work. ; two users there offered two different ways of dealing with NA values. However, the problem with both solutions is that when there is an NA value, ... | Anyone on the Android Jelly Bean OS and not able to buy Apps/Books through wallet? I have just bought the Samsung GalaxyNote 800 and am facing this issue. The error is (RPC:S-7:AEC-0). What is the solution? | eng_Latn | 1,029 |
First of all, I would like to note that I have read similar topics in CrossValidated but I am not fully satisfied. I have a dataset which consists of an $N\times M$ binary matrix. 1 means that an action is performed and 0 that it is not. I apply PCA to the dataset and surprisingly get very good results, especially ... | In today's pattern recognition class my professor talked about PCA, eigenvectors and eigenvalues. I understood the mathematics of it. If I'm asked to find eigenvalues etc. I'll do it correctly like a machine. But I didn't understand it. I didn't get the purpose of it. I didn't get the feel of it. I strongly be... | I have a dataset that has both continuous and categorical data. I am analyzing by using PCA and am wondering if it is fine to include the categorical variables as a part of the analysis. My understanding is that PCA can only be applied to continuous variables. Is that correct? If it cannot be used for categorical data,... | eng_Latn | 1,030 |
I have a data matrix $X$ with shape $p\times n$. It might not matter but I interpret $X$ is $n$ vectors each containing $p$ features. Then I compute $Q = X X^{T} / n$. This implies that $Q$ is positive definite. I interpret $Q$ as covariance matrix of data which are columns of $X$. (Normally mean should be subtracte... | I have an expression for a covariance matrix $C$ in terms of the indices $i$ and $j$. In this way I can analytically calculate the elements of my covariance matrix, however when I try to invert $C$ matlab gives a warning about the matrix being close to singular. The inversion therefore doesn't work, by which I mean t... | The entire site is blank right now. The header and footer are shown, but no questions. | eng_Latn | 1,031 |
I'm learning about the Statistical learning and in the section comparing Lasso and Ridge Regression it shows that the main difference between these two problems is the way the constraint/penalty is formulated. In Lasso, the penalty is $\ell_1$ norm: $\lambda \sum |\beta_j|$, while in regression, the penalty is $\ell_... | I've been reading , and I would like to know why the Lasso provides variable selection and ridge regression doesn't. Both methods minimize the residual sum of squares and have a constraint on the possible values of the parameters $\beta$. For the Lasso, the constraint is $||\beta||_1 \le t$, whereas for ridge it is $|... | I recently ran across elliptic curve crypto-systems: (Brown University) (Wikipedia) (IEEE) (RSA.com) It seemed to me to be great alternative to RSA as the de-facto cryptosystems to be used in banking and financial systems and in the public key infrastructure for certificates, but is not used! If someone can exp... | eng_Latn | 1,032 |
I see that in PCA the first principal component maximizes the variances amongst all the points within the data set. What exactly does this mean, what does it show and what does every other principal component thereafter tell me? I read these really nice simple explanation on PCA that helped me understand PCA as a whol... | In today's pattern recognition class my professor talked about PCA, eigenvectors and eigenvalues. I understood the mathematics of it. If I'm asked to find eigenvalues etc. I'll do it correctly like a machine. But I didn't understand it. I didn't get the purpose of it. I didn't get the feel of it. I strongly be... | The new Top-Bar does not show reputation changes from Area 51. | eng_Latn | 1,033 |
I want to have two matrixes of $ A $ and $B$ of a certain size, multiply them together $C = AB$, do some operations on $C$ to make $C_2$ and then decompose the matrix into to matrices of the same size as $A$ and $B$ so that $A_2B_2 = C_2$. Which decomposition function can I use to achieve this? EDIT: This is not a du... | Wikipedia says "In the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions; each finds use among a particular class of problems." But in my opinion decomposition term should b... | Please use UK pre-uni methods only (at least at first). Thank you. | eng_Latn | 1,034 |
From a very general point of view, when you have a dataset $X$ and want to predict a label $y$, what is the purpose of beginning with a PCA (principal component analysis) first, and then doing the prediction itself (with logistic regression, or random forest or whatever) from both intuitive and theoretical reason? In w... | Suppose I am running a regression $Y \sim X$. Why by selecting top $k$ principle components of $X$, does the model retain its predictive power on $Y$? I understand that from dimensionality-reduction/feature-selection point of view, if $v_1, v_2, ... v_k$ are the eigenvectors of covariance matrix of $X$ with top $k$ e... | I have a dataset for which I have multiple sets of binary labels. For each set of labels, I train a classifier, evaluating it by cross-validation. I want to reduce dimensionality using principal component analysis (PCA). My question is: Is it possible to do the PCA once for the whole dataset and then use the new datas... | eng_Latn | 1,035 |
I'm working on a ranking problem where I want to measure the distance between a collection of query points (as a group) and each target point in my database. Each query point is part of the set of target points. I started with the Euclidean distance and cosine similarity by using the mean vector of the query points. Ho... | I have an issue which I could not solve, although I tried and I got some help on R forum. I am trying to calculate Mahalanobis distances on a data.frame, where I have several hundreds of groups and several hundreds of variables. Whatever I do, I get the system is computationally singular: reciprocal condition number e... | The new Top-Bar does not show reputation changes from Area 51. | eng_Latn | 1,036 |
To better understand SVD, I'm trying to recreate the values for U, S, and V using straight numpy, but I can't get the same results. According to numpy's for its implementation of SVD, it returns values for U, S, and V such that you can recreate your original dataset in the following way: (U*S) @ V = original_data ... | I am trying to do SVD by hand: m<-matrix(c(1,0,1,2,1,1,1,0,0),byrow=TRUE,nrow=3) U=eigen(m%*%t(m))$vector V=eigen(t(m)%*%m)$vector D=sqrt(diag(eigen(m%*%t(m))$values)) U1=svd(m)$u V1=svd(m)$v D1=diag(svd(m)$d) U1%*%D1%*%t(V1) U%*%D%*%t(V) But the last line does not return m back. Why? It seems to has something... | Please use UK pre-uni methods only (at least at first). Thank you. | eng_Latn | 1,037 |
Say I have 300 samples from a population containing two groups, A and B, and data for several variables. I have 150 from Group A and 150 from Group B. However, I know that Group A makes up roughly 20% of the population and group B makes up 80% and the two groups differ on the variables in question. Is there a way to w... | After some searching, I find very little on the incorporation of observation weights/measurement errors into principal components analysis. What I do find tends to rely on iterative approaches to include weightings (e.g., ). My question is why is this approach necessary? Why can't we use the eigenvectors of the weighte... | The new Top-Bar does not show reputation changes from Area 51. | eng_Latn | 1,038 |
I have already posted my problem in stackoverflow, I am not sure if this might be problematic, and I am not sure, if the post is shown in both communities. If so I will delete. I am trying to apply principal component analysis, to reduce the dimensions of my data. 200x146 , 200 observations(samples) with 146 features(... | In today's pattern recognition class my professor talked about PCA, eigenvectors and eigenvalues. I understood the mathematics of it. If I'm asked to find eigenvalues etc. I'll do it correctly like a machine. But I didn't understand it. I didn't get the purpose of it. I didn't get the feel of it. I strongly be... | I've read a lot about PCA, including various tutorials and questions (such as , , , and ). The geometric problem that PCA is trying to optimize is clear to me: PCA tries to find the first principal component by minimizing the reconstruction (projection) error, which simultaneously maximizes the variance of the projec... | eng_Latn | 1,039 |
Am I right that "spectral decomposition" for symmetric matrix and "singular value decomposition" for non square matrix? Any clarification would be appreciated. | I have understood how ridge regression shrinks coefficients towards zero geometrically. Moreover I know how to prove that in the special "Orthonormal Case," but I am confused how that works in the general case via "Spectral decomposition." | This question is about an efficient way to compute principal components. Many texts on linear PCA advocate using singular-value decomposition of the casewise data. That is, if we have data $\bf X$ and want to replace the variables (its columns) by principal components, we do SVD: $\bf X=USV'$, singular values (sq. ro... | eng_Latn | 1,040 |
I know that Principal Component Analysis (PCA) is the eigenvector of the covariance matrix. It is used as a tool for dimensional reduction. What I am confused about is whether the PCA give weights to original features in order to find out which features explain the data the most or does it come up with new set of abstr... | In today's pattern recognition class my professor talked about PCA, eigenvectors and eigenvalues. I understood the mathematics of it. If I'm asked to find eigenvalues etc. I'll do it correctly like a machine. But I didn't understand it. I didn't get the purpose of it. I didn't get the feel of it. I strongly be... | What are the main differences between performing principal component analysis (PCA) on the correlation matrix and on the covariance matrix? Do they give the same results? | eng_Latn | 1,041 |
I believe I have a problem understanding PCA: I would like to use this technique to reduce the number of features of my problem. I originally have 10,000 features and 500 samples. However, the use of PCA will limit my number of principal components to the smallest between the number of samples (columns of my data matr... | In PCA, when the number of dimensions $d$ is greater than (or even equal to) the number of samples $N$, why is it that you will have at most $N-1$ non-zero eigenvectors? In other words, the rank of the covariance matrix amongst the $d\ge N$ dimensions is $N-1$. Example: Your samples are vectorized images, which are of... | I want to make it so I always have 50 entities in an area. So when 1 dies/despawns/leaves the area I want it to detect that and summon in a new entity, and yes I do want them to die/despawn/leave the area so preventing those things is not an option. | eng_Latn | 1,042 |
I would like to execute multidimensional scaling () based on a matrix of Pearson correlation coefficients. The function takes a dissimilarity matrix as an input and I therefore need to convert my similarity matrix into a dissimilarity/distance matrix. What is the correct way of doing so? According to answer, a simil... | In Random forest algorithm, Breiman (author) constructs similarity matrix as follows: Send all learning examples down each tree in the forest If two examples land in the same leaf increment corresponding element in similarity matrix by 1 Normalize the matrix with number of trees He says: The proximities between... | $M$ = mass of the Sun $m$ = mass of the Earth $r$ = distance between the Earth and the Sun The sun is converting mass into energy by nuclear fusion. $$F = \frac{GMm}{r^2} = \frac{mv^2}{r} \rightarrow r = \frac{GM}{v^2}$$ $$\Delta E = \Delta M c^2 = (M_{t} - M_{t+\Delta t}) c^2 \rightarrow \Delta M = \Delta E / c^... | eng_Latn | 1,043 |
Prove the orthogonal complement of the row space of $A $is ${0}$ implies $Ax = 0$ has only the trivial solution | I am trying to understand how to find the orthogonal complement of a subspace $M$ of a vector space $V$. From my understanding, $M^\perp$ is also a subspace of $V$ where all its vectors are perpendicular (orthogonal) to the columns of $M$, which would mean that the dot product of those vectors with each column of $M$... | Let random vector $x = (x_1,...,x_n)$ follow multivariate normal distribution with mean $m$ and covariance matrix $S$. If $S$ is symmetric and positive definite (which is the usual case) then one can generate random samples from $x$ by first sampling indepently $r_1,...,r_n$ from standard normal and then using formula ... | eng_Latn | 1,044 |
I want to know that in PCA analysis or FAMD the lengths of arrows in correlation circle plot(which can be plotted by bellow code) is equal to which parameter(coefficient estimates,cos2,contribution,...) while their coordinates represent their loadings? fviz_pca_var(res.pca) res.pca is the result of fitting PCA anal... | I am looking to implement a biplot for principal component analysis (PCA) in JavaScript. My question is, how do I determine the coordinates of the arrows from the $U,V,D$ output of the singular vector decomposition (SVD) of the data matrix? Here is an example biplot produced by R: biplot(prcomp(iris[,1:4])) I tri... | Anyone on the Android Jelly Bean OS and not able to buy Apps/Books through wallet? I have just bought the Samsung GalaxyNote 800 and am facing this issue. The error is (RPC:S-7:AEC-0). What is the solution? | eng_Latn | 1,045 |
I will confine my question to the simple case of constructing a linear fit of one independent variable $X$ and one dependent variable $Y$, with no intercept term. The sample predictions are $\hat y_i = \beta x_i$. Define the $p$-norm as $$L^p = \left(\sum_{i=1}^n \vert y_i - \hat y_i \vert^p \right)^\frac{1}{p}$$ An... | Is there any software package to solve the linear regression with the objective of minimizing the L-infinity norm. | I was doing the problem $$ A+B=AB\implies AB=BA. $$ $AB=BA$ means they're invertible, but I can't figure out how to show that $A+B=AB$ implies invertibility. | eng_Latn | 1,046 |
Mathematics behind Activation functions In Machine learning we use activation functions to give non-linearity to the output of neuron. But what is the exact non-linearity in this context? How it differs in different activation functions(e.g. sigmoid, relu ...)? | Comprehensive list of activation functions in neural networks with pros/cons Are there any reference document(s) that give a comprehensive list of activation functions in neural networks along with their pros/cons (and ideally some pointers to publications where they were successful or not so successful)? | What's the relationship between initial eigenvalues and sums of squared loadings in factor analysis? On the one hand I read in a comment that: You can't speak of "eigenvalues" after rotation, even orthogonal rotation. Perhaps you mean sum of squared loadings for a principal component, after rotation. When rota... | eng_Latn | 1,047 |
PCA loading with weights on samples I want to run PCA on a set of data, but I'd like to weigh each row of the input matrix(i.e. each data point) based on how recent it is. In other words, in my calculations of the PCs, I'd like more recent data points to be more important. How can I achieve this? | Weighted principal components analysis After some searching, I find very little on the incorporation of observation weights/measurement errors into principal components analysis. What I do find tends to rely on iterative approaches to include weightings (e.g., ). My question is why is this approach necessary? Why can't... | One-hot vs dummy encoding in Scikit-learn There are two different ways to encoding categorical variables. Say, one categorical variable has n values. converts it into n variables, while converts it into n-1 variables. If we have k categorical variables, each of which has n values. One hot encoding ends up with kn var... | eng_Latn | 1,048 |
What is the meaning of higher order derivatives like d²y/dx² I know velocity and acceleration are higher order derivatives of the position vector. Any other examples? What is the physical significance of higher order derivatives.? | Names of higher-order derivatives Specific derivatives have specific names. First order is often called tangency/velocity, second order is curvature/acceleration. I've also come across words like Jerk, Yank, Jounce, Jolt, Surge and Lurch for 3rd and 4th order derivatives. Is there a widely agreed list of names for thes... | How can top principal components retain the predictive power on a dependent variable (or even lead to better predictions)? Suppose I am running a regression $Y \sim X$. Why by selecting top $k$ principle components of $X$, does the model retain its predictive power on $Y$? I understand that from dimensionality-reduct... | eng_Latn | 1,049 |
Usage Scenarios for Auto Encoders as alternatives to PCA Is there ever a practical situation where one would use a linear autoencoder over PCA? | What're the differences between PCA and autoencoder? Both PCA and autoencoder can do demension reduction, so what are the difference between them? In what situation I should use one over another? | Does a correlation matrix of two variables always have the same eigenvectors? I perform Principal Component Analysis using two variables that are standardized. This is done by applying a SVD on the correlation matrix of the concerned variates. However, the SVD gives me the same eigenvector (weights) irrespective of wha... | eng_Latn | 1,050 |
Reversing SVD back to the original variables I have a data matrix $M$ that has $n$ samples (rows) described by $m$ variables (columns) $X_1,X_2,\ldots X_m$. I do a SVD to reduce the $m$ dimensions to just 3 dimensions. I understand that the $x,y,z$ coordinates (i.e., the SVD values) are calculated from the eigenvectors... | How to reverse PCA and reconstruct original variables from several principal components? Principal component analysis (PCA) can be used for dimensionality reduction. After such dimensionality reduction is performed, how can one approximately reconstruct the original variables/features from a small number of principal c... | How to find a 4D vector perpendicular to 3 other 4D vectors? In 3 dimensions it is possible to find a vector c (one of infinitely many) perpendicular to two vectors a and b using the cross product. Is there any way of extending this to 4 dimensions, i.e. given three vectors a, b, and c finding a vector d perpendicular ... | eng_Latn | 1,051 |
Why is the magnitude of the gradient equal to the maximum rate of change at that point? I understand the concept of the gradient being a vector of the partials of f with respect to each variable, so essentially the gradient gives you a direction in the input field to travel in order to get the maximum increase in the f... | Gradient and Swiftest Ascent I want to understand intuitively why it is that the gradient gives the direction of steepest ascent. (I will consider the case of $f:\mathbb{R}^2\to\mathbb{R}$) The standard proof is to note that the directional derivative is $$D_vf=v\cdot \nabla f=|\nabla f|\,\cos\theta$$ which is maximiz... | How can top principal components retain the predictive power on a dependent variable (or even lead to better predictions)? Suppose I am running a regression $Y \sim X$. Why by selecting top $k$ principle components of $X$, does the model retain its predictive power on $Y$? I understand that from dimensionality-reduct... | eng_Latn | 1,052 |
Which independent variables are most important in predicting the response variable? I'm a biologist, and I have a large dataset that I'm trying to analyze. Here are the variables I'm working with: levels of 211 different metabolites in 16 different blood samples (predictor variables) how well each of the 16 blood sam... | Detecting significant predictors out of many independent variables In a dataset of two non-overlapping populations (patients & healthy, total $n=60$) I would like to find (out of $300$ independent variables) significant predictors for a continuous dependent variable. Correlation between predictors is present. I am ... | How to reverse PCA and reconstruct original variables from several principal components? Principal component analysis (PCA) can be used for dimensionality reduction. After such dimensionality reduction is performed, how can one approximately reconstruct the original variables/features from a small number of principal c... | eng_Latn | 1,053 |
When using regularization wouldnt it make all parameters very small? In regularization, we add square of thetas multiplied by lambda(excluding theta_0). The value of lambda is high because values of theta should be close to zero to neglect the value of its associated feature. Now my question is when we apply gradient d... | Why does shrinkage work? In order to solve problems of model selection, a number of methods (LASSO, ridge regression, etc.) will shrink the coefficients of predictor variables towards zero. I am looking for an intuitive explanation of why this improves predictive ability. If the true effect of the variable was actually... | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a linear algebra problem (with eigenvectors)? I've read a lot about PCA, including various tutorials and questions (such as , , , and ). The geometric problem that PCA is trying to optimize is clear to me: PCA tries to fin... | eng_Latn | 1,054 |
Unstable projection in LDA space in $n<p$ situation I'm trying to classify (LDA) few samples (n=12) in a high dimensional feature space (p=24) into 3 classes. First I reduced the dimension of my initial dataset with a PCA, keeping only the first two Eigen vectors. Update: turns out, I was actually using all 11 PCs for... | Does it make sense to combine PCA and LDA? Assume I have a dataset for a supervised statistical classification task, e.g., via a Bayes' classifier. This dataset consists of 20 features and I want to boil it down to 2 features via dimensionality reduction techniques such as Principal Component Analysis (PCA) and/or Line... | Fit mixture of distributions to your time-series data in R I have time-series data containing 1440 observations and the plot of the data is I want to fit the Gaussian Mixture Models (GMM) to the above plot, and for the same I am using Mclust function of package. Finally, I want a fit somewhat like this: On using M... | eng_Latn | 1,055 |
Can you sell part of a pack to buy another pack in AL? Adventurer's League player guide: Selling Equipment. You can sell any mundane equipment that your character possesses using the normal rules in the PHB. Purchasing Equipment. You can purchase any equipment found in the PHB with your starting gold. Starting charac... | Can I sell starting gear in Adventurers League play? I'm starting a new AL game (as a player) and I have a question that's not addressed in the AL material. According to Adventurers League Player's Guide (page 4) When you create your D&D Adventurers League character for the current season, take starting equipm... | What's the relationship between initial eigenvalues and sums of squared loadings in factor analysis? On the one hand I read in a comment that: You can't speak of "eigenvalues" after rotation, even orthogonal rotation. Perhaps you mean sum of squared loadings for a principal component, after rotation. When rota... | eng_Latn | 1,056 |
How is linear momentum conserved after collision while part of linear kinetic energy contributes to angular kinetic energy Referring to the famous example of a horizontally moving sticky ball that collides (and sticks) at the tip of a vertically floating rod, then the combination moves along the ball's incident course ... | How can momentum but not energy be conserved in an inelastic collision? In inelastic collisions, kinetic energy changes, so the velocities of the objects also change. So how is momentum conserved in inelastic collisions? | Principal component analysis "backwards": how much variance of the data is explained by a given linear combination of the variables? I have carried out a principal components analysis of six variables $A$, $B$, $C$, $D$, $E$ and $F$. If I understand correctly, unrotated PC1 tells me what linear combination of these var... | eng_Latn | 1,057 |
Why is "condensed nearest neighbour" Parametric? Definition of "condensed nearest neighbour", at training time it chooses the c "best" training examples (where c is a hyper-parameter), and at test time uses the usual KNN prediction but based only on these c training examples. So far, I looked-up many references and w... | Parametric vs non-parametric machine learning methods I looked-up many references and websites and researched on how to determine if a method is between parametric or non-parametric. I came up with below definitions, A parametric algorithm has a fixed number of parameters. In contrast, a non-parametric algorithm us... | How exactly to compute the ridge regression penalty parameter given the constraint? The accepted answer in does a great job of showing that there is a one-to-one correspondence between $c$ and $\lambda$ in the two formulations of the ridge regression: $$ \underset{\beta}{min}(y-X\beta)^T(y-X\beta) + \lambda\beta^T\bet... | eng_Latn | 1,058 |
Is PostBQP experimentally relevant? Far from my expertise, but sheer curiosity. I've read that ("a complexity class consisting of all of the computational problems solvable in polynomial time on a quantum Turing machine with postselection and bounded error") is very powerful. Still, I don't understand the practical s... | What is postselection in quantum computing? A quantum computer can efficiently solve problems lying in the complexity class . I have seen a claim the one can (potentially, because we don't know whether BQP is a proper subset or equal to PP) increase the efficiency of a quantum computer by applying postselection and tha... | How can top principal components retain the predictive power on a dependent variable (or even lead to better predictions)? Suppose I am running a regression $Y \sim X$. Why by selecting top $k$ principle components of $X$, does the model retain its predictive power on $Y$? I understand that from dimensionality-reduct... | eng_Latn | 1,059 |
Prove spectral radius of a primitive matrix is 1 Let $P \in M (n \times n, \mathbb{R})$ be a primitive matrix. $1$ is a eigenvalue of $P$ and $(1,\dots,1)$ is the associated right eigenvector. How can show that the spectral radius $\rho(P):=$max$\{|\lambda| : \lambda$ is a eigenvalue of $P\}$ of $P$ is 1? Hint: Use ... | Proof that the largest eigenvalue of a stochastic matrix is $1$ The largest eigenvalue of a (i.e. a matrix whose entries are positive and whose rows add up to $1$) is $1$. Wikipedia marks this as a special case of the , but I wonder if there is a simpler (more direct) way to demonstrate this result. | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a linear algebra problem (with eigenvectors)? I've read a lot about PCA, including various tutorials and questions (such as , , , and ). The geometric problem that PCA is trying to optimize is clear to me: PCA tries to fin... | eng_Latn | 1,060 |
Geometric Proof for the shortest path cube sides problem A spider in one edge of a cube (length of all side = $l$) wants to get to an insect on the other edge of the cube. obviously the spider cannot fly and must walk on the sides of the cube to get to the insects. Find the shortest path possible. (See the image below)... | How to find the shortest path between opposite vertices of a cube, traveling on its surface? I am stuck with the following problem that says: Let $A,B$ be the ends of the longest diagonal of the unit cube . The length of the shortest path from $A$ to $B$ along the surface is : $\sqrt{3}\,\,$ 2.$\,\,1+\sqrt... | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a linear algebra problem (with eigenvectors)? I've read a lot about PCA, including various tutorials and questions (such as , , , and ). The geometric problem that PCA is trying to optimize is clear to me: PCA tries to fin... | eng_Latn | 1,061 |
How to use v.kernel? I am studying the use of GRASS GIS within QGIS and I need a little help with the understanding of the v.kernel module. I didn't find any human help within the manual (very cryptic) I have a point data vector and I need to study the density of the points distribution in my mapset using a bandwidth ... | How do you use GRASS's v.kernel? I am flummoxed on how to use GRASS's v.kernel. I have a vector layer of around 2.5 million points. I want to make a heat map using v.kernel to show concentrations, since I have variable instances with overlapping points, sometimes huge overlaps. I've already gotten this vector layer i... | How exactly to compute the ridge regression penalty parameter given the constraint? The accepted answer in does a great job of showing that there is a one-to-one correspondence between $c$ and $\lambda$ in the two formulations of the ridge regression: $$ \underset{\beta}{min}(y-X\beta)^T(y-X\beta) + \lambda\beta^T\bet... | eng_Latn | 1,062 |
Principal Component Analysis PCA Terms and relationships: eigenvalues, eigenvectors, loadings, score matrix, and SVD I've read many websites, blogs, pdfs on this top but struggle to put the picture together in simple math terms, that explains how some of the terms relate to each other / are computed. Let's assume that... | Relationship between SVD and PCA. How to use SVD to perform PCA? Principal component analysis (PCA) is usually explained via an eigen-decomposition of the covariance matrix. However, it can also be performed via singular value decomposition (SVD) of the data matrix $\mathbf X$. How does it work? What is the connection ... | Question on the correlation between two dependent variables I'm working on this question and it's stumping me. Let $S_n = X_1 + \ldots + X_n$ (with $n>=1$) be a random walk with $X_1, \ldots, X_n$ be iid RV's. $$ E(X_k)=\mu,\,{\rm Var}(X_k)=\sigma^2. $$ Find the covariance of $S_n$ and $S_m$ Can anyone he... | eng_Latn | 1,063 |
Using the 'U' Matrix of SVD as Feature Reduction This is a follow-up to the question asked regarding SVD and dimensionality reduction (). In that question I asked how to use SVD for dimensionality reduction. Although not stated, the ultimate goal here is to use the reduced feature set and input them into a classificat... | Relationship between SVD and PCA. How to use SVD to perform PCA? Principal component analysis (PCA) is usually explained via an eigen-decomposition of the covariance matrix. However, it can also be performed via singular value decomposition (SVD) of the data matrix $\mathbf X$. How does it work? What is the connection ... | The proof of shrinking coefficients using ridge regression through "spectral decomposition" I have understood how ridge regression shrinks coefficients towards zero geometrically. Moreover I know how to prove that in the special "Orthonormal Case," but I am confused how that works in the general case via "Spectral deco... | eng_Latn | 1,064 |
PCA Why covariance matrix? At PCA why we find the Eigenvalues of the covariance matrix and not the eigenvalues of the matrix $A\times A^T$, where $A$ is the data matrix and $A^T$ its transpose? I saw a professor at YouTube who explained PCA but he said that the solution is the eigenvalues of $A\times A^T$. | Relationship between SVD and PCA. How to use SVD to perform PCA? Principal component analysis (PCA) is usually explained via an eigen-decomposition of the covariance matrix. However, it can also be performed via singular value decomposition (SVD) of the data matrix $\mathbf X$. How does it work? What is the connection ... | How does leave-one-out cross-validation work? How to select the final model out of $n$ different models? I have some data and I want to build a model (say a linear regression model) out of this data. In a next step, I want to apply Leave-One-Out Cross-Validation (LOOCV) on the model so see how good it performs. If I u... | eng_Latn | 1,065 |
How does the hyperparameter lambda affect L2 norm Let's say I have L2 regularization in ridge regression: How would I go about giving a formal mathematical proof that I know that the larger the lambda the smaller the L2 norm. But, I don't know how to give a mathematical proof | The proof of shrinking coefficients using ridge regression through "spectral decomposition" I have understood how ridge regression shrinks coefficients towards zero geometrically. Moreover I know how to prove that in the special "Orthonormal Case," but I am confused how that works in the general case via "Spectral deco... | Is there a command for large middle delimiters consistent with \bigl and \bigr? After browsing through related threads, I am now of the understanding (please correct me if I am wrong) that the rule of thumb is to use the \bigl,\bigr pair with brackets, parentheses, etc. for operators like sums, products, and integrals,... | eng_Latn | 1,066 |
Implementation of PCA using SVD without creating covariance matrix So I'm currently taking a Machine Learning course and have correctly submitted my implementation of PCA. I used SVD. Here it is Octave. function [U, S] = pca(X) %PCA Run principal component analysis on the dataset X % [U, S, X] = pca(X) computes eige... | Relationship between SVD and PCA. How to use SVD to perform PCA? Principal component analysis (PCA) is usually explained via an eigen-decomposition of the covariance matrix. However, it can also be performed via singular value decomposition (SVD) of the data matrix $\mathbf X$. How does it work? What is the connection ... | Given the key, the plain text and the cipher text can I calculate the IV used in CBC mode? If I have the plain text, the ciphertext and the key for an AES-128 CBC operation, can I determine the IV, even if I don't know the padding (assuming the padding follows one of the more common formats)? I believe it should be po... | eng_Latn | 1,067 |
I perform Principal Component Analysis using two variables that are standardized. This is done by applying a SVD on the correlation matrix of the concerned variates. However, the SVD gives me the same eigenvector (weights) irrespective of what the two variables are. It's always [.70710678, .70710678]. I find this stran... | I've been testing PCA via SVD to decompose a simple time series data matrix, $X$. I have two signals $x_1(t)$ and $x_2(t)$ in a data matrix where $M$ rows represents each timepoint sample and each column represents $x_1$ and $x_2$. The mean signal, $\hat{x}$, is defined as the mean along the row axis (average of $x_1... | The new Top-Bar does not show reputation changes from Area 51. | eng_Latn | 1,068 |
I'm working on an implementation of PCA that works on very large data sets. Based on my understanding of the algorithm, the first step is to do an of the input m x n matrix, X. This SVD looks like X = WΣVT. The "interesting" output Y of this process -- , "The PCA transformation that preserves dimensionality (that is,... | Principal component analysis (PCA) is usually explained via an eigen-decomposition of the covariance matrix. However, it can also be performed via singular value decomposition (SVD) of the data matrix $\mathbf X$. How does it work? What is the connection between these two approaches? What is the relationship between SV... | Is it (always) true that $$\mathrm{Var}\left(\sum\limits_{i=1}^m{X_i}\right) = \sum\limits_{i=1}^m{\mathrm{Var}(X_i)} \>?$$ | eng_Latn | 1,069 |
Is there any customs problem while checking at the airport? | I am planning to travel to India (COK airport, Kerala) from United States. I want to take my laptop as well as my tablet (iPad). Am I allowed to take both in my backpack with my documents related my work. I think I am allowed to take only one computer as per the rule. Will the customs consider my iPad as a computer? W... | I have 10 years of daily returns data for 28 different currencies. I wish to extract the first principal component, but rather than operate PCA on the whole 10 years, I want to rollapply a 2 year window, because the currencies' behaviours evolve and so I wish to reflect this. However I have a major problem, that is tha... | eng_Latn | 1,070 |
I am currently trying to use classification analysis for some EEG data. As such data is of very high dimensionality, I am looking at using PCA for dimensionality reduction to prevent overfitting of the classification models. My data structure is approximately 50 (rows, observations) times 38000 (columns, variables). I... | In PCA, when the number of dimensions $d$ is greater than (or even equal to) the number of samples $N$, why is it that you will have at most $N-1$ non-zero eigenvectors? In other words, the rank of the covariance matrix amongst the $d\ge N$ dimensions is $N-1$. Example: Your samples are vectorized images, which are of... | The entire site is blank right now. The header and footer are shown, but no questions. | eng_Latn | 1,071 |
I have read many articles about PLS, but I could not understand the mathematical description yet. I know that it is quite similar to principal component regression (PCR), except that it takes into account the direction of the response variable. Could you please provide for me a simple mathematical explanation e.g the ... | Can anyone recommend a good exposition of the theory behind partial least squares regression (available online) for someone who understands SVD and PCA? I have looked at many sources online and have not found anything that had the right combination of rigor and accessibility. I have looked into The Elements of Stat... | The entire site is blank right now. The header and footer are shown, but no questions. | eng_Latn | 1,072 |
Lets say $a_1, a_n$ are normed vectors. Why is the set $C = \{\Sigma_{i=1}^n \lambda_ia_i: \lambda_i \ge0\}$ closed? The $\lambda$'s can be any non-negative numbers. So C is the set of all non-negative linear combinations of the n vectors. I tried both the method with open balls, and the method with a converging sequ... | Looking for the proof of the lemma asserting that the conical surface (envelope) is a closed space. Thank you. | I am trying to fit a SVM to my data. My dataset contains 3 classes and I am performing 10 fold cross validation (in LibSVM): ./svm-train -g 0.5 -c 10 -e 0.1 -v 10 training_data The help thereby states: -c cost : set the parameter C of C-SVC, epsilon-SVR, and nu-SVR (default 1) For me, providing higher cost (C) v... | eng_Latn | 1,073 |
When should we use PCA over factor analysis? Aren't they essentially the same thing except that factor analysis is modeling observed variables as linear combinations of unobserved factors? Whereas PCA is modeling components as linear combinations of observed variables? | It seems that a number of the statistical packages that I use wrap these two concepts together. However, I'm wondering if there are different assumptions or data 'formalities' that must be true to use one over the other. A real example would be incredibly useful. | For a given data matrix $A$ (with variables in columns and data points in rows), it seems like $A^TA$ plays an important role in statistics. For example, it is an important part of the analytical solution of ordinary least squares. Or, for PCA, its eigenvectors are the principal components of the data. I understand ho... | eng_Latn | 1,074 |
Let random vector $x = (x_1,...,x_n)$ follow multivariate normal distribution with mean $m$ and covariance matrix $S$. If $S$ is symmetric and positive definite (which is the usual case) then one can generate random samples from $x$ by first sampling indepently $r_1,...,r_n$ from standard normal and then using formula ... | I estimated the sample covariance matrix $C$ of a sample and get a symmetric matrix. With $C$, I would like to create $n$-variate normal distributed r.n. but therefore I need the Cholesky decomposition of $C$. What should I do if $C$ is not positive definite? | Let random vector $x = (x_1,...,x_n)$ follow multivariate normal distribution with mean $m$ and covariance matrix $S$. If $S$ is symmetric and positive definite (which is the usual case) then one can generate random samples from $x$ by first sampling indepently $r_1,...,r_n$ from standard normal and then using formula ... | eng_Latn | 1,075 |
Why in spontaneous symmetry breaking do we only look at the scalar fields? In all the examples of SSB in our course/the books (even in our SUSY course) we have just looked at minima of the scalar potential. Why do we restrict ourselves to the scalars, why not also minimise the fermions and vector bosons? | Why cannot fermions have non-zero vacuum expectation value? In quantum field theory, scalar can take non-zero vacuum expectation value (vev). And this way they break symmetry of the Lagrangian. Now my question is what will happen if the fermions in the theory take non-zero vacuum expectation value? What forbids fermion... | How can top principal components retain the predictive power on a dependent variable (or even lead to better predictions)? Suppose I am running a regression $Y \sim X$. Why by selecting top $k$ principle components of $X$, does the model retain its predictive power on $Y$? I understand that from dimensionality-reduct... | eng_Latn | 1,076 |
All function only checks last element of vector in R Sorry about my last lengthy post. Here is a more condensed problem that I am running into with the all function. As an example, below you can see my console output in which the all function seems to only check whether the last element of x satisfies the all conditio... | Is floating point math broken? Consider the following code: 0.1 + 0.2 == 0.3 -> false 0.1 + 0.2 -> 0.30000000000000004 Why do these inaccuracies happen? | Local polynomial regression: Why does the variance increase monotonically in the degree? How can I show that the variance of local polynomial regression is increasing with the degree of the polynomial (Exercise 6.3 in Elements of Statistical Learning, second edition)? This question has been asked but the answer just ... | yue_Hant | 1,077 |
Adding more samples to ordinary regression is equall to ridge regression I am a beginner in machine learning. I have a question why adding more samples to a data set is equal to adding regularization term to the loss function? (In other words why can I add more samples to my data set and solve OLS instead of solving r... | How to derive the ridge regression solution? I am having some issues with the derivation of the solution for ridge regression. I know the regression solution without the regularization term: $$\beta = (X^TX)^{-1}X^Ty.$$ But after adding the L2 term $\lambda\|\beta\|_2^2$ to the cost function, how come the solution b... | What's the relationship between initial eigenvalues and sums of squared loadings in factor analysis? On the one hand I read in a comment that: You can't speak of "eigenvalues" after rotation, even orthogonal rotation. Perhaps you mean sum of squared loadings for a principal component, after rotation. When rota... | eng_Latn | 1,078 |
Is there a geometric intuition for integration by parts? Is there a geometric intuition for integration by parts? $$\int f(x)g'(x)\,dx = f(x)g(x) - \int g(x)f'(x)\,dx$$ This can, of course, be shown algebraically by product rule, but still where is geometric intuition? I have seen geometry of IBP using parametric equat... | What is integration by parts, really? Integration by parts comes up a lot - for instance, it appears in the definition of a weak derivative / distributional derivative, or as a tool that one can use to turn information about higher derivatives of a function into information about an integral of that function. Concrete ... | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a linear algebra problem (with eigenvectors)? I've read a lot about PCA, including various tutorials and questions (such as , , , and ). The geometric problem that PCA is trying to optimize is clear to me: PCA tries to fin... | eng_Latn | 1,079 |
Does matrix multiplication preserve positive semi-definiteness [PSD]? If $A,B$ are two PSD matrices, will $AB$ also be PSD? | Is the product of symmetric positive semidefinite matrices positive definite? I see on Wikipedia that the product of two commuting symmetric positive definite matrices is also positive definite. Does the same result hold for the product of two positive semidefinite matrices? My proof of the positive definite case fall... | What's the relationship between initial eigenvalues and sums of squared loadings in factor analysis? On the one hand I read in a comment that: You can't speak of "eigenvalues" after rotation, even orthogonal rotation. Perhaps you mean sum of squared loadings for a principal component, after rotation. When rota... | eng_Latn | 1,080 |
Diagonalization: Eigenvalues Vs Elementary Row Operations Using elementary row operations, a matrix A $\in \mathrm{R}^{n \times n} $ can be reduced to a Row-Reduced Echelon (RRE) form. Using the RRE form of A, the bases of Nullspace and Range can be obtained. The RRE form of A is a triangular (almost diagonal) form of ... | What is the importance of eigenvalues/eigenvectors? What is the importance of eigenvalues/eigenvectors? | Recursive feature elimination and one-hot & dummy encoding? When using RFE in linear regression and logistic regression, do we one-hot encode the features (K levels and K dummy features) or dummy-encode the features (K levels and K-1 dummy features leaving one out). As per a comment by @Matthew Drury in an answer (UR... | eng_Latn | 1,081 |
Artificial Neural Network with continuous and binary variables I have a dataset with numerical (continuous) and categorical variables. I want to fit an artificial neural network. To do so, I have transformed my categorical variables by using the 1-of-k method, so I now have a bunch of binary variables. I am using the N... | Neural Network: MLP for regression with 3 continuous features, 1 categorical I am starting to study Neural Network. I want to build a MLP where I will feed it: 3 features which are continuous one feature which is categorical (48 classes) How can I do this? Before adding the categorical feature, I was using 'relu' ... | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a linear algebra problem (with eigenvectors)? I've read a lot about PCA, including various tutorials and questions (such as , , , and ). The geometric problem that PCA is trying to optimize is clear to me: PCA tries to fin... | eng_Latn | 1,082 |
Use of this positive semi-definite matrix in optimization? We know that any matrix of the form $A^TA$ is positive semi-definite where $A^T$ is the transpose of $A$. Now how can we use this result in optimization? Edit: The importance of positive semi-definite matrices is almost clear, but my question is specific to $A... | Why are symmetric positive definite (SPD) matrices so important? I know the definition of symmetric positive definite (SPD) matrix, but want to understand more. Why are they so important, intuitively? Here is what I know. What else? For a given data, Co-variance matrix is SPD. Co-variance matrix is a important met... | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a linear algebra problem (with eigenvectors)? I've read a lot about PCA, including various tutorials and questions (such as , , , and ). The geometric problem that PCA is trying to optimize is clear to me: PCA tries to fin... | eng_Latn | 1,083 |
PCA returns the same pair of principal axes for completely different 2D datasets I noticed a (seemingly) weird behavior while using sklearn's on 2D datasets: I kept getting the same principal axes: $\pm\left(\begin{gathered}\sqrt{0.5}\\ \sqrt{0.5} \end{gathered} \right)$ and $\pm\left(\begin{gathered}\sqrt{0.5}\\ -\s... | Does a correlation matrix of two variables always have the same eigenvectors? I perform Principal Component Analysis using two variables that are standardized. This is done by applying a SVD on the correlation matrix of the concerned variates. However, the SVD gives me the same eigenvector (weights) irrespective of wha... | Local polynomial regression: Why does the variance increase monotonically in the degree? How can I show that the variance of local polynomial regression is increasing with the degree of the polynomial (Exercise 6.3 in Elements of Statistical Learning, second edition)? This question has been asked but the answer just ... | eng_Latn | 1,084 |
Why does the p-value of a composite null hypothesis have a supremum attached it? I noticed that there is a definition of the p-value in my textbook. It is defined as the p-value of a composite null hypothesis and it says the following: I have no idea why it is written with a supremum. I've spent hours pondering this... | Why is the p-value written with a supremum? I noticed that there is a definition of the pvalue in my textbook is defined says the following: I have no idea why it is written with a supremum. I've spent hours pondering this, does anyone have enough of a background to help me with this? Thank you! | How can top principal components retain the predictive power on a dependent variable (or even lead to better predictions)? Suppose I am running a regression $Y \sim X$. Why by selecting top $k$ principle components of $X$, does the model retain its predictive power on $Y$? I understand that from dimensionality-reduct... | eng_Latn | 1,085 |
Inversion in $GF(2^8)$ AES I was wondering how you would calculate the S-box in AES. I found that you have to calculate the inverse of the polynomials in $GF(2^8)$. I found out that to calculate the inverse, you have to use the Extended Euclidean Algorithm. What I can't figure out is how do you apply this to a polynomi... | Multiplicative inverse in $\operatorname{GF}(2^8)$? I know how to do multiplication over ${\rm GF}(2^8)$: uint8_t gmul(uint8_t a, uint8_t b) { uint8_t p=0; uint8_t carry; int i; for(i=0;i<8;i++) { if(b & 1) p ^=a; carry = a & 0x80; a = a<<1; ... | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a linear algebra problem (with eigenvectors)? I've read a lot about PCA, including various tutorials and questions (such as , , , and ). The geometric problem that PCA is trying to optimize is clear to me: PCA tries to fin... | eng_Latn | 1,086 |
How to extend Raster layer without pixel value data losing I got 2 different raster layers one of them black and white representing the river road. This river raster has pixel values stand for height. I want to extend the size of river in order to show, if the water increases which areas would be under the water But i ... | Increasing Flood Plain I am doing a project where we are attempting to determine how many more buildings would flood if the FEMA flood plain increased by 1',2' and 5'. I have the elev of the flood plain rasters from lidar data, but I am having trouble figuring out how much more area will be inundated by the rises I des... | Before running a ridge regression model, do I need to preform variable selection? I am currently constructing a model that uses last year's departmental information to predict employee churn for the current year. I have 55 features and 318 departments in my data set. A good portion of my independent variables are cor... | eng_Latn | 1,087 |
AES/CBC fixed Initial vector use-case I am using AES/CBC to encrypt my http cookie. I never encrypt the same cookie value twice so my understanding is I don't need to use a random initial vector - using a fixed initial vector is fine for this case. A random initial vector is needed if we may encrypt the same message mo... | Is AES in CBC mode secure if a known and/or fixed IV is used? I have a need to encrypt credentials for a third-party app used by a secured internal app. Over on ITSec.SE, I was helpfully shown a scheme to encrypt the third-party credentials based on a hash of the credentials for the internal app. I picked AES as the ... | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a linear algebra problem (with eigenvectors)? I've read a lot about PCA, including various tutorials and questions (such as , , , and ). The geometric problem that PCA is trying to optimize is clear to me: PCA tries to fin... | eng_Latn | 1,088 |
Selection of an ARIMA model looking at the ACF and PACF I am using the table below as model selection tool (at least as starting point) Let's say that I choose a proper model according to the table and I get nice ACF and PACF out of it, but either my AR term or my MA term is pretty high, is there a way to simplify i... | How does ACF & PACF identify the order of MA and AR terms? It's been more than 2 years that I am working on different time series. I have read on many articles that ACF is used to identify order of MA term, and PACF for AR. There is a thumb rule that for MA, the lag where ACF shuts off suddenly is the order of MA and s... | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a linear algebra problem (with eigenvectors)? I've read a lot about PCA, including various tutorials and questions (such as , , , and ). The geometric problem that PCA is trying to optimize is clear to me: PCA tries to fin... | eng_Latn | 1,089 |
how to choose the best logit model I have two logit regression models with different AIC. I'm using R. my first model has significant variables and AIC 192.7436. And my second model has 1 non-significant variables but with smaller AIC 192.4468. Which model is the best? | Should I remove non-significant variables from my regression model I have run a multiple linear regression using stepwise regression to select the best model, however the best model returned has a non-significant variable. When I remove this the AIC value goes up indicating the model without the significant variable is... | What's the relationship between initial eigenvalues and sums of squared loadings in factor analysis? On the one hand I read in a comment that: You can't speak of "eigenvalues" after rotation, even orthogonal rotation. Perhaps you mean sum of squared loadings for a principal component, after rotation. When rota... | eng_Latn | 1,090 |
How to apply border radius after drawing a rectangle? Photoshop doesn't support to apply border radius after drawing of rectangle. I found and tried myself but seems to be not working. Is there any step is missed or is there any other idea to apply border radius after drawing a rectangle? | Photoshop CS6 Resize Rectangle with Rounded Corners This question is about Photoshop CS6. Hopefully the feature was added in this version. Before posting I looked up Google and and but didn't find an answer for CS6. So the question is: Is there a feature within CS6 or a script that allows to resize a vector element ... | Understanding Lasso Regression's sparsity geometrically Whenever someone writes about Lasso and Ridge Regression thy draw this diagram with the circle or with the diamond. In the case of the diamond (Lasso regression) it is then always stated that Lasso forces one of the coefficients to 0. Therefor it introduces spa... | eng_Latn | 1,091 |
Statistics in properties different from statistics in attribute table (Arc) I have generic signed integer raster downloaded from the ORNL DAAC. It is a single band raster. I looked at the statistics in the properties of the raster i.e min, max, mean and std dev. I then calculated the statistics of the value column ... | Explaining different Standard Deviation results from same data in ArcGIS Desktop and MS Excel? I have done some interpolation in Geostatistical Analyst in ArcGIS and I got the Standard Deviation (SD) a bit different from the SD that I calculated in Excel Spreadsheet. What algorithm does each package use? Why are the ... | How can top principal components retain the predictive power on a dependent variable (or even lead to better predictions)? Suppose I am running a regression $Y \sim X$. Why by selecting top $k$ principle components of $X$, does the model retain its predictive power on $Y$? I understand that from dimensionality-reduct... | eng_Latn | 1,092 |
SVD for PCA: Why would one standardize the data matrix? As explained in amoeba's beautiful answer one can use a singular value decomposition of the data matrix, $\mathbf{X} = \mathbf{USV}^\top$, to do a principal component analysis, if it is assumed that the data matrix $\mathbf{X}$ is centered. The principal directio... | PCA on correlation or covariance? What are the main differences between performing principal component analysis (PCA) on the correlation matrix and on the covariance matrix? Do they give the same results? | What does $b_i\mid b_{i+1}$ mean in this context? In the computational topology literature, the reduction algorithm for computing the Smith normal form of a boundary matrix uses the notation $b_j > 1 \: \text{ and }\: b_j\mid b_{j+1}$ in the context of the diagonal elements of the Smith matrix. Can anyone give me an... | eng_Latn | 1,093 |
Vandermonde Determinant with one column replaced How to calculate the A(n) Vandermonde matrix determinant if the column with powers n-1 is replaced with powers n? | Value of Vandermonde type determinant Let $x_1,...,x_n $ are distinct real numbers. Is it a formula for the Vandermonde type determinant $V(x_1, \cdots,x_n)$ whose last column is $x_1^k,\ \cdots,\ x_n^k$, where $k \geq n$, instead of $x_1^{n-1},\ \cdots,\ x_n^{n-1}$? Thanks | What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a linear algebra problem (with eigenvectors)? I've read a lot about PCA, including various tutorials and questions (such as , , , and ). The geometric problem that PCA is trying to optimize is clear to me: PCA tries to fin... | eng_Latn | 1,094 |
Sparse (Weighted) Adjacency Matrix & SparseArray: encoding multiple weights at a given edge | Why won't SparseArray let me store values with the head List? | The rank of Jacobian matrix at a point of affine variety is independent of choice of generators | eng_Latn | 1,095 |
Reversed indices How do I type 1A in LaTeX as in the snippet below? | Left and right subscript / superscript I am trying to put two subscripts at the left and right of a character. For example, something like: _{t} p_{x} where p is in the middle. How do you do this? | Inverse of a diagonal matrix plus a constant I am looking for an efficient solution for inverting a matrix of the following form: $$D+aP$$ where $D$ is a (full-rank) diagonal matrix, $a$ is a constant, and $P$ is an all-ones matrix. gives a solution to the special case where all diagonal entries of $D$ are the sam... | eng_Latn | 1,096 |
Dimension reduction for discrete qualitative and aggregated variables I know about PCA for multiple dimensions of continuous features but here is a problem I have some trouble to find a method for. I don't have a list of individual countries but rather a discrete classification of countries, and for each line (which I... | Categorical Principal Component Analysis - using Count, Continuous, Ordinal variables together I have some variables and I want to reduce their number for further analysis. I initially thought of combining them using factor analysis. But since the variables are of all kinds (rating, count, ordinal, continuous dollar am... | Nielsen & Chuang Exercise 2.2 - “Matrix representations: example” Reproduced from Exercise 2.2 of Nielsen & Chuang's Quantum Computation and Quantum Information (10th Anniversary Edition): Suppose $V$ is a vector space with basis vectors $|0\rangle$ and $|1\rangle$, and $A$ is a linear operator from $V$ to $V$ ... | eng_Latn | 1,097 |
Can someone explain the simple intution between Principal component 1, 2, ... etc in PCA? | Making sense of principal component analysis, eigenvectors & eigenvalues | Using principal component analysis (PCA) for feature selection | eng_Latn | 1,098 |
Principal component analysis (PCA) vs. method of principal components for factor analysis (FA) I have just read as follows: One of the biggest reasons for the confusion between the two [principal component analysis (PCA) and factor analysis (FA)] has to do with the fact that one of the factor extraction methods in... | Best factor extraction methods in factor analysis SPSS offers several methods of factor extraction: Principal components (which isn't factor analysis at all) Unweighted least squares Generalized least squares Maximum Likelihood Principal Axis Alpha factoring Image factoring Ignoring the first method, which isn't fa... | Determining best fitting curve fitting function out of linear, exponential, and logarithmic functions Context: From a question on Mathematics Stack Exchange , someone has a set of $x-y$ points, and wants to fit a curve to it, linear, exponential or logarithmic. The usual method is to start by choosing one of these (w... | eng_Latn | 1,099 |
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