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Questions tagged [pca]

Principal component analysis (PCA) is a linear dimensionality reduction technique. It reduces a multivariate dataset to a smaller set of constructed variables preserving as much information (as much variance) as possible. These variables, called principal components, are linear combinations of the input variables.

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Using PCA in domain adaptation

In literature, I see people using (Kernelized) Principle Component Analysis, not for feature extraction, but for domain adaptation. In other words, I have data from a source domain and I would like to ...
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Using Principal Components from one data set to visualize data in another [on hold]

I have two correlation matrices, matrix1 and matrix. I want to be able to do something like this where I plot matrix2 according to the first and second principal components of matrix1. I know that <...
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How do I use principal components as predictors in linear regression?

I followed the instructions from this open Stanford lecture on PCR. I have a couple of questions, but first I'll post the code with my comments. ...
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Is it normal for principle components to have the same SD?

I'm trying to determine outliers of a PCA by calculating the sd of the eigenvectors - however it returns the sd as equal for each PC. 1) Is this normal and 2) Is this the right approach for ...
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How to quantify the agreement between the same parameter from two different data sets

I am looking at Arctic ice thickness from two different Earth-orbiting satellites A and B. I'm interested in quantifying how well these two datasets agree, but I'm struggling over what parameters to ...
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Dealing with correlated variables and choosing between models

One of the things I've always been confused about is the framework around model selection in the cases where $n$ predictor variables $x_i$'s are correlated. My thoughts on the different approaches: ...
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How to construct PCA projections uncorrelated with another variable?

Let's say I have 11 variables. I want to run a PCA on first 10 variables such that the projections are uncorrelated with variable 11. By construction and orthogonality of the eigenvectors, the ...
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Determining the Direction of Eigenvectors in PCA [duplicate]

I'm using R to get the principal components for several datasets. An example result, using prcomp yields: ...
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How to handle missing data in PPCA

I am implementing a paper "Probabilistic Principal Component Analysis" (PPCA) which deals with a dataset where each vector suffers from at least one missing value missing values. Generally, PPCA ...
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Idea behind change of basis and how it relates to projecting your points onto principal components

I would like to clarify if my understanding is correct. In the traditional X-Y coordinate system, our choice of basis vectors are $\vec{i} = (1, 0)$ and $\vec{j} = (0, 1)$ and when you I have a point $...
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Can I use PCA after lasso variable selection?

I have a data regarding life satisfaction, of more than 2000 observations and 265 variables (most are categorical variables). I want to build a model, estimating the effects of society problems on the ...
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How to use log probabilities in PCA mixture EM algorithm

I'm trying to implement PCA mixtures (Tipping & Bishop 2006 Appendix C) on the Tobomovirus. I'll summarize the mathematical background and algorithm here: For a single PCA model, we assume a ...
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Promax PCA interpretation in order to validate singular items - Structure or Pattern Matrix?

I am doing a promax PCA analysis. I have a big dataset (over 1000 subjects) and about 50 items. I am trying to validate the singular items. My final aim is to exclude non-relevant items (those which ...
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LDA - solving singularity problem of within classes matrix

I would like to solve the problem in LDA where the within classes matrix is singular if the number of samples is lower than the number of dimensions (which is true in my case, used on images of faces)....
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Principal Component Analysis Singluar value

While studying PCA, I saw this question but not able to solve. Given a data matrix X that is taller than it is wide, prove that every right singular vector of X with singular value s is an eigenvector ...
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PCA: violation of the normal distribution assumption

I try to understand why normal distribution is an assumption for PCA and what might happens when it is violated. I found one answer on this plattform and a lot of different answers in literature. It ...
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Normalizing vs Scaling before PCA

I know there's a lot of content about PCA pre-processing, but I am still somewhat confused. I have a dataset that contains some clear patterns: 1 variable is whether a person has financial resources (...
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How do I calculate my RCs for SSA for prediction (like I would for principle components)?

So the essential structure of what I am hoping to do is to create a neural network that uses the Reconstructed Components (RCs) from Singular Spectrum Analysis (SSA) to predict my outcome variable in ...
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Smoothing of experimental data for PCA

I am applying PCA to a set of spectrophotometric measurements with the aim of differentiating two groups of substances. The many small wiggles on the right-hand side of the curves (the region above ~...
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Principal component analysis for variable reduction

In the textbook “Principal Component Analysis” Jolliffe (§9.2) suggests the following method for variable reduction: “When the variables fall into well-defined clusters, there will be one high-...
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How to find complete log likelihood for mixture of PPCA

In Appendix C of a paper by Michael E. Tipping and Christopher M. Bishop about mixture models for probabilistic PCA, the probability of a single data vector $\mathbf{t}$ is expressed as a mixture of ...
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How to interpret a given 2D co-variance matrix?

I am trying to solve a problem regarding revision for my Big Data module. I have two main questions. 1) Given a predefined co-variance matrix: A cluster of points is distributed in a two-...
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PCA to recover factors used during data generation. Why doesn't it work?

I often found that the results of a PCA or any kind of factor analysis are interpreted in a "causal" fashion. I.e. if a principal component with high variance explanation is found, this is interpreted,...
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How does the three-component PCA model in Bishop and Tipping 1999 work?

In section 4.2 of Bishop and Tipping's "Probabilistic Principal Component Analysis" (Microsoft Research), we are shown three different plots that are said to have something to do with a three-...
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If I center my kernel does it no longer remain positive semidefinite?? If so why is it being used in algorithms like kernel pca?

If I center my kernel then can it still be used in operations where a positive semi-definite kernel is required such as SVM and ridge regression? I am centering my kernel as follows: $$K_c(\mathbf{t}...
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Equity Risk Model using an autoencoder

I am trying to create a statistical equity risk model using an autoencoder in a similar fashion to how one would use PCA to derive the systematic and specific risk components of a stock's returns. I ...
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Feature reduction of Biological time series signals

I have a data set of biological signals (PSG signals); the dimension of the signals is high (850 features for each sample). I am looking for the best way to reduce the dimensionality of the signals. ...
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PCA: should standardization be applied on features or samples?

I am struggling a little bit with PCA. I understand that standardization is an important part of the algorithm but I do not understand which elements should be standardized. Let's say I have a 10x100 ...
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Detecting insufficient communalities in R

Given is this sorted factor analysis: ...
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Use PCA to discover the most impactful variables on the original data set?

I am trying to find a way to statistically show that some variables in my data set are more important than others to determine its classification. I have an example data set with three variables from ...
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Interpreting PCA with varimax rotation

I have problems understanding the Factor Component Analysis of the paper: "Measuring thirty facets of the Five Factor Model with a 120-item public domain inventory: Development of the IPIP-NEO-120". ...
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PCA used for regression

Can anybody point me to a thorough example where PCA was used for predictive purposes and it compared favorably to regular linear regression (i.e., perhaps a lower RMSE using the PCA components ...
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is it necessary to have same scale of IDV in PCA [duplicate]

Can PCA be done if my data have both likert data and discrete (ordinal and nominal)as independent variables?
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What is connection between Pearson correlation coefficient and proportion of variance explained in PCA?

PCA procedure includes SVD of Covariance matrix. Based on eigenvalues we can find a proportion of variance explained by related Principal Components (eigenvectors). ...
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Why do PCA loadings given by sqrt(eigenvalue)*eigenvector yield correlations between PCs and original variables?

I did a lot of reading in this blog and elsewhere about PCA, SVD, loadings etc. But I still don't understand why loadings, which represent correlations between principal components and the original ...
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PCA on scaled data: does this mean loadings =eigenvalue=correlation

I am doing a Principle Component Analysis and I am getting a bit lost in the mathematics. If I get it right loadings = eigenvector * sqrt(eigenvalue) And loadings are the correlation between the ...
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Screening data prior to PCA v. PLS

I have a very large time series matrix $X$, where the number of observations (rows) $n$ is much smaller than the number of input variables (columns) $p$. My aim is to use the information in $X$ to ...
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Units in Principal Component Analysis

If I have a data set with 6 variables (A, B, C, D) all measured in different units (eg. m, kg, s, K) and I perform principal component analysis to transform this into two Principal Axes, how do I ...
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How many dimensions can I use with model based clustering (mclust)?

I keep reading mclust doesn't work well with high dimensions. i HAVE 18 dimensions, is that too high? If it is too high, should I pre-process my data with PCA and then throw the result to the basic ...
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Nipals and prcomp differences and data size relationship [closed]

I'm pretty new in R and data analysis and I found a strange behaviour which I wanted to discuss with you. I had a 486 observation of 5000+ variables and I want to cluster them with Mclust. Each value ...
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Is this a good approach to check for batch effect?

I am not the best in maths, and slowly diving into statistical analysis. I know there is a lot of possibility to check batch effects, I just want a very simple way on my case. I have a dataframe of ...
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PCA interpreting coefficients

down vote favorite had a question on something I thought was pretty basic, but just not getting this. I have three variables, and three principal components rateprev1 rateprev2 rateprev3 0.03831 0....
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PCA influence of duplicates

I am using sklearn IPCA decomposition and surprised that if I delete duplicates from my dataset, the result differs from the "unclean" one. What is the reason? As I think, the variance is the same. ...
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Cross Correlation between two RVs and PCA

What is the difference between the maximum value of cross-correlation value of RVs X, Y and maximum eigenvalue of Covariance matrix of these same RVs X and Y? Are both same and just represents the ...
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Principal Component Analysis with weights

In a Principal Component setting, I want to solve the minimization problem $$\min_{\{f_t\}^T_{t=1}, \Gamma} SSR$$ where $$ SSR = \sum^T_{t=1}(y_t - \Gamma f_t)' R'_t R_t (y_t - \Gamma f_t)$$ $...
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A question about pca and gene function analysis

I'm new to bioinformatics, and I have a pretty basic question. Let's say I have a bunch of genes {Xi} and I want to know which one has the most significant on some measurable phenotypic trait Y. Now I ...
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Change in eigenvalues due to perturbation to a correlation matrix

Let $A$ be a $m \times n$ matrix defined as $ A = \Big[\frac{a_1}{\|a_1\|} \cdots \frac{a_n}{\|a_n\|}\Big]$ and $a_k \in \mathbb{R}^{m\times 1}$ where $k \in [1,\dots,n]$. Now, we define a ...
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Can PCA factors be correlated?

Are principal factors in principal component analysis always uncorrelated, or can they end up being correlated? If so, how and why?
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How would PCA help preserve privacy?

For example, if we have a recommender system based on some data like MovieLens, where we have a matrix of user / movie pairings, how would reducing the dimensionality of the dataset help with privacy?
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How do we know we're maximizing the Lagrangian objective function in PCA?

In Principal Component Analysis, we start with $m$ observations $x_1,\dots,x_m$, each of which is an $n$-dimensional vector. Assume we have centered the data; that is, we have subtracted the variable ...