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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Running K-mean after PCA SPSS [on hold]

Is there a script that computes factor scores using the component score coefficient matrix (SPSS PCA output), that can then be used as the basis for K-means clustering? As an alternative is there a ...
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7 views

Relative weights in regression analysis in SPSS: Matrix-approach vs. factor and regression

I am trying to perfome a relative weight analysis as described by Johnson (2000). I have 13 predictors to a more general indicator. Initially, I started by: running a principal component analysis ...
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2answers
50 views

What is the difference between ZCA whitening and PCA whitening?

I am confused about ZCA whitening and normal whitening (which is obtained by dividing principal components by the square roots of PCA eigenvalues). As far as I know, $$\mathbf x_\mathrm{ZCAwhite} = ...
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27 views

Why are Coefficient of each other principal component cannot be all of the same sign?

For the covariance matrix $\Sigma \in \mathcal{M}_{p,p}$, a positive-definitie (non-singular) matrix with its elements $\sigma_{ij} >0$ for all $i,j = 1,2,...,p$. How do I prove that the ...
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30 views

Can you do a PCA on 3-point Likert to weigh items 20k responses

I am developing an inventory tool that has 21 items. I need to determine the weight of each of the items, as the presence of some may give a higher overall rating to a scenario than the presence of ...
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1answer
64 views

How can there be a linear correlation between two PCA components?

I perform principal component analysis (PCA) on a dataset, and then plot the first and the second principal components. I get the following phenomenon: one principal component appears to be a linear ...
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48 views

Bartlett's Sphericity Test for PCA Failure

I am using XLStat for a PCA of time-series water chemistry data. I have 23 analytes and 29 samples. I am using a correlation matrix for PCA as I find it more interpretable in the context of ...
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0answers
32 views

How to de-correlate data points lying along two parallel hyperplanes (or two lines in a 2D space)?

I've encountered a question to de-correlate many data points sitting along two parallel lines in a 2D space, say $x=1$ and $x=-1$. And no labels are given to those data points, so supervised methods ...
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17 views

How to construct a regional severity index or riskiness score?

I have a set of regional variables for stroke that measures outcomes region wise. For example regional mortality for all ages for stroke, regional mortality for stroke for age group 65 to 75, regional ...
4
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1answer
78 views

How to apply a Gaussian radial basis function kernel PCA to nonlinear data?

I have an assignment to implement a Gaussian radial basis function-kernel principal component analysis (RBF-kernel PCA) and have some challenges here. It would be great if someone could point me to ...
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0answers
57 views

Principal component analysis with large number of predictors and small number of samples ($p\gg n$)

I have a data set with large number of predictors and small number of samples ($p \gg n$). I would like to apply PCA or factor analysis on it, to reduce dimensionality. I would like to know, is it ...
2
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1answer
24 views

Are eigenvectors obtained in Kernel PCA orthogonal?

As Kernel PCA is the same as PCA in higher dimension space, shouldn't the eigenvectors obtained be orthogonal? Suppose, I have $n$ data points and let $a$ and $b$ be two eigenvectors of covariance ...
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1answer
38 views

Is it valid to preprocess data with PCA before running Locally Linear Embedding (LLE)?

I have some very high dimensional data, and performing Locally Linear Embedding (LLE) is very time consuming. I also have to perform several LLEs, with varying parameters, to compute the optimal ...
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2answers
97 views

How to find which variables are most correlated with the first principal component?

I came across an article where the authors did a Principal Component Analysis on gene expression data, and found out the genes that are most correlated to the 1st principal component, and they used ...
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1answer
18 views

Generating even-sized clusters in scikit-learn [duplicate]

I'm attempting to generate approximately even-sized clusters of a PCA'd feature set in Scikit-learn, but I'm not having any luck. I'm only familiar with KMeans clustering, and with that algorithm the ...
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28 views

Standardizing data in Principal Component Analysis? [duplicate]

Since PCA is sensitive to scaling, I am thinking of standardizing each explanatory variable to have mean 0 and standard deviation 1. What are the drawbacks of such a standardization? Thank you.
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16 views

Problems with variable loading in prcomp()

I am using methylKit to perform an analysis on my MethylCAP-bisulfite data. The prcomp() function has been used in "PCASamples" (a command in methylKit) to do PCA ...
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22 views

Dimension reduction using Principal Component Analysis [duplicate]

I have basic question regarding PCA. I am given a task of reducing independent variables in a dataset of about 250,000 enteries and 400 independent variables because some of them are highly ...
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2answers
43 views

principal component analysis on train and test dataset

I have train and test data set to work on. I would like to apply PCA to reduce dimension. I am not sure, do I need to merge train and test data set together before applying PCA? Or I should apply ...
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55 views

Normality assumption in PCA

From Shapiro-Wilk's test I see that the responses to Likert (4point) items are not normally distributed, although Q-Q plots approximately indicate to normality. I have done PCA analysis on those items ...
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1answer
37 views

Why PCA performed on two similar data sets result in different number of components?

I have two data sets (2048 dimensions) collected under slightly different circumstances. I am using PCA to reduce the dimension of the data before passing it further for classification. Both data sets ...
3
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1answer
48 views

Excluding the scatter points from a feature

I have a set of data points that are supposed to sit on a locus and follow a pattern, but there are some scatter points from the main locus that cause uncertainty in my final analysis. I would like to ...
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0answers
34 views

Does PCA preserve observations (rows) of the data?

Say I have a data matrix of size $N \times P$ where $N$ is the number of samples and $P$ is the number of features. Now, if I do principal component analysis, I get another data matrix of size $N ...
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49 views

Principal component Regression Using R

Can anyone explain principal component regression with the help of an example and the code in R? How to interpret the result of a principal component regression? How to find the individual effect of ...
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55 views

PCA scores and cluster analysis

I have obtained PCA scores (Anderson-Rubin) and thought to use them in cluster analysis, but have got confused how to make interpretations based on them or as what type of variable they should be ...
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42 views

Validity of PCA obtained results

If I have built a certain construct measuring scale aggregating items from different previously validated scales, I am unsure what strategy would be best to validate my resulting scale. I intend to ...
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44 views

How to increase the proportion of explained variance in PCA?

When I was performing a PCA on a large data set, I only get the PC1 explaining about 25% of variance and PC2 about 20%, PC3 about 15%, PC4 about 10%... So I wonder if there is a way to increase the ...
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1answer
50 views

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 ...
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14 views

Individual item reliability in factor analysis

Im currently testing the reliability and validity of the SERVQUAL model (measuring just the items for each dimension. Hence these items should load on just factor). My supervisor wants me to include ...
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18 views

Calculate the variance explained in matrix Y by matrix X

I have two matrices corresponding to the same set of $n$ samples, with $j$ and $k$ variables, respectively ($j > 10000$, $k > 10000$). $X$ is an $n \times j$ matrix and $Y$ is an $n \times k$ ...
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25 views

Appropriate PCA/ EFA rotation method

Question about appropriate PCA/ EFA rotation method. While I see that oblique rotation methods (e.g. promax) are suggested for correlated data (and I have correlated data) I see that the majority of ...
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1answer
30 views

Binomial data and PCA and cluster analysis

I have obtained responses on around 48 items measuring employer attractiveness. The goal of my analysis is to cluster respondents according to these employer attractiveness dimensions. I plan to ...
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1answer
37 views

Principal component (PC) as a substitute for colinear covariates?

I am working on a spatial linear regression and I can tell there is collinearity between covariates. Can I use PCA (Principal Component Analysis) images instead of original covariates to estimate the ...
3
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28 views

Is there a test/technique/method for comparing principal components decompositions between samples?

Is there any methodical way to compare the directions, magnitudes, etc of PCA results for different samples? I'm leaving the nature of the test deliberately vague because I'd like to hear all the ...
2
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0answers
50 views

Using principal component analysis to reduce dimensions of data in R [closed]

I have a dataset which includes 4 separate measures of intelligence. To simplify my analysis, I wanted to express them as "g" a variable based on the shared variation of the 4 measures. A paper I read ...
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1answer
35 views

Why do we use only the first component scores to construct different indices?

I have seen that in constructing indices by PCA the scores of only the first component is used. Although the first principle component explains the most variation contained in the data, often the VAF ...
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21 views

Multiple Factor analysis and squared cosines

I am a bit confused on how to proceed using the MFA analysis from FactoMineR in my data set. I am currently working with activity results of 15 bacteria (b1, b2, b3, b4, b5,.., b15), divided into 3 ...
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2answers
77 views

PCA: which original variables are used to construct a new variable?

Consider a new variable that is linear combination of original variables (e.g. one of the principal components). How can we find out which original variables "product" the new variable?
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1answer
52 views

PCA vs SVD - understanding difference and preference of SVD over PCA [duplicate]

I understand that PCA and SVD are similar - PCA removes the mean and SVD doesn't? I think I have an understanding of PCA - you would use it to reduce dimensions of data and separate it out into ...
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1answer
40 views

R caret - how to combine principal components and non-principal-component predictors?

Consider the following example. Suppose I want to model x in DF2 using everything else. While it makes sense to do ...
2
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1answer
63 views

Is it a good idea to use log scale on scree plots for PCA/ICA/FA?

I always found the concept of determining the "ideal" number of components/factors for an ICA/PCA/FA via a scree plot useful and quick, but also a bit shaky. In an effort to try to make the scree ...
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20 views

Determine concrete important factors in pca

after using the R function pcromp () I get how many factors might be important. How to determine what are these factors? Which statistical tool could I use? I appreciate your reply!
2
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1answer
113 views

Some questions on Principal Component Analysis (PCA)

I am trying to understand some descriptions about PCA (the first 2 are from Wikipedia): 1) Principal components are guaranteed to be independent only if the data set is jointly normally distributed. ...
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0answers
31 views

PCA + L1 equivalent to elastic net?

I am performing a logistic regression on a rather big dataset (700k+ samples and 1k+ features). I suspect that a lot of these features will be highly correlated and multicollinearity can be an issue. ...
3
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1answer
62 views

Reference for dimension reduction techniques

This is a follow-up question to Is PCA appropriate for comparing subsets of panel data?. It turns out that, yes, PCA is appropriate. But there are also many other ways to reduce n-dimensional data to ...
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25 views

Minimizing the Training data

I have a grey-box model of the form Y= a + b X1 + c X2. Where a, b and c are the coefficients based on regression. The regression variables X1 and X2 are determined based on ...
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51 views

How to create a composite of several variables without throwing information away

I want to create an index as a composite of several variables. It was recommend to me to use PCA. However, PCA discards too much information - essentially throwing away several of the variables in ...
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22 views

how to handle occlusion for face recognition?

If there some occlusion on face (such as sunglasses, mask, scarf), the recognition rate will decrease steeply? How to handle this case? I have do a survey, the PCA reconstruction method have been ...
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10 views

calculation of composite scores from factor analysis

We're designing a survey where we ask students to indicate their level of agreement (likert scale 1 - Strongly agree....5 - Strongly disagree. We ran factor analysis on the data and obtained 4 ...
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2answers
72 views

Is PCA appropriate for comparing subsets of panel data?

I have a large panel (5000+ subjects, 4 variables over 182 periods), and I've identified particular Granger-causal relationship in a large subset of those subjects (30% or so). I would like to somehow ...