Principal component analysis is a technique to decompose an array of numerical data into a set of orthogonal vectors (uncorrelated linear combinations of the variables) called principal components. The first few principal components often suffice to grasp nearly all the multivariate variability of ...

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What are the advantages of kernel PCA over PCA?

I want to implement an algorithm in a paper which uses Kernel SVD to decompose a data matrix. So I have been reading materials about Kernel methods and kernel PCA etc. But it still is very obscure to ...
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Relationship between number of Principal components and Exploratory factors.

Would like to know is there any heuristic relationship between the number of components identified from PCA analysis and the number of hidden factors provided by EFA analysis on the same data set?
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37 views

PCA on non-centered data [duplicate]

How does the mean influence PCA? What happens if I use PCA on data with a mean $\ne0$?
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9 views

Motivation of Projection Pursuit

Given I understand why PCA aims to maximize variance, I wonder why finding non-gaussian projections is interesting for Projection Pursuit, i.e., what is the motivation of this reasoning?
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37 views

PCA and exploratory Factor analysis on the same data set

I would like to know if it makes any logical sense to perform principal component analysis (PCA) and exploratory factor analysis (EFA) on the same data set. I have heard professionals expressly ...
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17 views

Use PCA for pattern recognition

I have always used PCA as a preprocessing techniques. There are some people that use it for pattern recognition. Once I used pca to project my data in a 2 dimensional space and then I observed that ...
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Can mean values be seen as a form of PCA with a LOT of assumptions?

This question just occurred to me out of the blue. PCA is a way to reduce dimensions. Another way that is often (perhaps too often) used is to take mean values of two or more variables. This is done a ...
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19 views

MATLAB: leave-one-out-cross-validation for PCA

I'm trying to write my own function for PCA (of course there's a lot already written but I'm just interested in implementing stuff by myself). The main problem I encountered is the cross-validation ...
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20 views

Importance of multivariate normality assumption for BIC-like sparse model selection inference with PCA

I am reading a paper for robust, sparse PCA in which they propose a BIC-like criterion for selecting the appropriate value of the sparsity parameter $\lambda$. They define this as: ...
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1answer
19 views

use the same pca on test as training in weka

I have implement pca on training data and the result is ready. now I want to use the same pca on test . is there any way to perform the same pca on test as training in weka?
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14 views

whether PCA be conducted for a single dimension or simultaneously across multiple dimensions [closed]

whether PCA be conducted for a single dimension or simultaneously across multiple dimensions whether CFA be conducted for a single dimension or simultaneously across multiple dimensions I have gone ...
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25 views

Obtaining prediction equation from principal components analysis using 1st orthogonal component

Suppose you've collected data on factors $X_1, X_2, X_3, \ldots X_p$ and you're interested in creating a latent factor score $L = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + \ldots \beta_p X_p$ . For ...
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1answer
53 views

cluster plot: working and interpretation ?

Recently I have come across usage of cluster plot, which combines k-mean clustering along with PCA. The plot shows different clusters plotted using first two PCs. I have checked some of the threads ...
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30 views

Cluster analysis on related factors

I am analyzing a public data set of information security incident data and trying to find "clusters" of related factors. Specifically, each incident is analyzed using VERIS for the actor's variety ...
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186 views

Why does sphericity diagnosed by Bartlett's Test mean a PCA is inappropriate?

I understand that Bartlett's Test is concerned with determining if your samples are from populations with equal variances. If the samples are from populations with equal variances, then we fail to ...
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16 views

Is it correct to combine PCA and NMDS axes in a multiple regression?

I am considering to do a multiple regression in which some of the predictive variables are PCA (principal components) axes whereas others are NMDS (nonmetric muliple dimension scaling) axes. I would ...
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1answer
24 views

Result from Step by step PCA implementation differs from `matplotlib.mlab.PCA()`, would be nice if someone can help me finding the source

I was reading this nice article and tried to implement this step by step guide in Python, and then I compared the results using the Python function from the matplotlib library: ...
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1answer
34 views

Identify features corresponding to high singular/principal component values

In MATLAB, while SVD gives a diagonal matrix S of decreasing singular values, PCA gives a column vector LATENT of decreasing principal component values. How can S be used to obtain a subset of ...
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18 views

processing a sound file for analysis of different spoken languages

So i have sound files for 5 languages by 2 person, thus my input data has 10 sound files. Now i want to cluster them based on the languages (thus 5 clusters) and not based on the speaker/voice ( ...
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1answer
53 views

PCA loadings and valid principal components

I am a beginner and in the process of understanding PCA. I came across the following question Suppose we have a data set where each data point represents a single student's scores on a math test, ...
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12 views

Calculate the correlation between a principal component and a feature of the original data set in R?

I am interested in seeing the correlation between a particular principal component and a particular independent variable in my 'original' data set, that is, I'd like to calculate $\rho_{Y_{i},X_{k}} ...
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15 views

Method for analysing effect of model input

I work with a mechanistic model that uses climate data to simulate some specific output for different time steps and spatial locations. Now I want to investigate the effect of different climate data ...
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21 views

What does the predict() function on a PCA model return? [closed]

Specifically, when I add "newdata": ...
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1answer
24 views

Finding most significant data set within data

Basically, I'm conducting research based on two types of data: Noise levels and the temperature of a room. I've recoded data for 2 days.. I am using the spearman's correlation methods to determine ...
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20 views

Programming Multiple Variable PCA Ratios

I would like to generalize Paul Teetor's A Better Hedge Ratio, which uses prcomp() to determine a TLS ratio between two variables. I am hoping to extend this to multiple variables, but am having ...
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44 views

PCA and Linear Regression

I want to run PCA on a set of variables and then regress the scores on my dependent variable. I have the following questions: Should I scale and center my variables? If yes, should I also ...
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35 views

How deal with exponential distribution of data during principal component analysis

I am trying to do PCA on a series of variables (all are positive, real numbers) using correlation and varimax rotation. All the computation is done in R. Although I got high loadings for all ...
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16 views

How to calculate regularization parameter in generalized ridge regression given the degrees of freedom and input matrix?

I read a Q/A from here which is extremely nice. In the above Q/Answer the tuning parameter $λ$ was a scalar. But in my problem it is a vector $\lambda$ for a generalized ridge regression case. The ...
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1answer
14 views

Use pc scores to check mulitvariate normality

How can you check multivariate normality, using the scores from the PCA? Or what can we expect about the scores if the data is multivariate normal distributed?
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1answer
30 views

Correlation of many 1d vectors

Let's say I have many 1 dimensional vectors of the same dimensions which I want to compare to each other. What I'm really looking for is to check whether they are all very similar, or not, and to ...
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62 views

What is a “contrast” in a Principal Component Analysis (PCA)?

I have been studying how to interpret principal components. I recently came across an example of a particular eigenvector: $$e_j^T = \left[ \frac{\sqrt{2} }{2}, \frac{-\sqrt{2} }{2}, 0, \dots,0 ...
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23 views

Interpreting a PCA Biplot of a time series?

I had a question in regards to PCA with times series data, and specifically how to possibly interpret it. Normally, PCA is used by other software that I use in relation to de-noising a data set by ...
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30 views

Can component scores be used for further analyses, e.g. cluster analysis?

I have done a principal component analysis using SPSS and now have 3 components. 2 components have 4 items in the subscale, and 1 component has 3 items. Component scores using regression for each ...
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29 views

Post-PCA analysis phase

Using PCA analysis, I was able to reduce the initial 23 variables into 10 principal components. But I do not understand what to do with this insight. I mean, how do I validate this information on, ...
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1answer
65 views

How do principal components change upon the addition of new data?

How do the components from PCA change on addition of new data (i.e., $\frac{d(PC_1(x))}{d({\rm var}(x))}$? I am looking for any mathematical formulas and proofs (since it would be easy to ...
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41 views

Matlab - draw biplot on nonclassical MDS interpration?

How can I draw similar biplot like you can on PCA, so I could compare these two vizualization techniques / methods? I got dissimilarities and distances of my data in simple plot, but I would like it ...
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Loadings shoot up in last few components in Partial Least Squares

I'm trying out the partial least squares method of applying regression to a set of highly collinear predictor variables. When using the pls r package, I noticed ...
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24 views

Comparing isomap residual variance to pca variance

I am using R princomp function (from stats package) to run a PCA on a data set and I want to compare its output to that of the nonlinear dimensionality reduction method ISOMAP, which I am using under ...
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KPCA in R proportion of variability explained

I'm using kpca function from kernlab and try to get the proportion of variance explained by each component as in standard pca. I ...
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9 views

Kernel PCA number of components

When using Kernel PCA for dimensionality reduction is there any simple criterion which can be used to determine the number of components to use? I am using Kernel PCA with linear kernel, which would ...
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43 views

PCA figure formatting options in R

I've completed PCA analysis, in R with VEGAN package, of some ecological data on tree health. There are 80 trees total (so, 80 'sites') divided into four treatment categories. I've got the data ...
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1answer
126 views

Interpreting Principal Component Analysis output

If I have 50 variables in my PCA, I get a matrix of eigenvectors and eigenvalues out (I am using the MATLAB function eig). I have normalised the eigenvalues to sum ...
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35 views

Significant difference between two correlation matrices

We have two huge correlation matrices at different experimental conditions. If we want to identify the significant differences between these matrices , what would be the ideal method. I have ...
2
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1answer
75 views

Fourier bases for a stationary signal & relation to PCA for natural images

Why does PCA of a translation-invariant signal give a Fourier basis? I've found proofs for this, but I'd love some intuitions. Any help is greatly appreciated! EDIT: Sorry that this question ...
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1answer
33 views

SVD & ICA — or why doesn't the other rotation matrix in SVD solve for independent components?

When data are a linear mixture of non-gaussian sources, it can be shown that with a rotation, an independent rescaling of each of the rotated axes, and a second rotation you can recover the original, ...
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253 views

A toy model of Principal Components Analysis in R

I'm working in R through an excellent PCA tutorial by Lindsay I Smith and am getting stuck in the last stage. The R script below takes us up to the stage (on p.19) where the original data is being ...
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32 views

Variable magnitudes and principal component analysis

I am completing some PCA on various sets of data, some with 30 time-series variables, some with about 100 (meaning matrices with between 30 and 100 columns). I know that the covariance matrix is ...
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33 views

Principal Components Analysis

I'm recently reading a tutorial on Principal component analysis( A tutorial on principal components analysis/Lindsay I Smith). At the end it discusses about "getting the old data back". I'm wondering ...
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11 views

Error trying to reduce my data dimentions [duplicate]

I'm trying to produce a linear regression model, but I only have 25 observations and 34 predictors. I'm trying feature selection, ...
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1answer
84 views

What does “PCA (Principal Component Analysis) spheres the data” mean?

I was reading some notes and it says that PCA can "sphere the data". What they define to me as "sphering the data" is dividing each dimension by the square root of the corresponding eigenvalue. I am ...