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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Statistical arbitrage using eigen portfolios [migrated]

I was trying to understand below paper https://www.math.nyu.edu/faculty/avellane/AvellanedaLeeStatArb071108.pdf Page 20 explains about "Entering a trade". I wan't to know clearly what it means to ...
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281 views

Is there any advantage of SVD over PCA?

I know how to calculate PCA and SVD mathematically and I know that both can be applied to Linear Least Squares regression. The main advantage of SVD mathematically seems to be that it can be applied ...
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36 views

Imputation of missing values for doing PCA in R [duplicate]

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 ...
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60 views

Small loadings in all variables, PCA analysis is ok?

I'm performing a PCA analysis on a set of 5 variables, whose correlation matrix is: ...
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37 views

Using principal components to perform further PCA

I am working with principal component analysis for the first time. I have managed to extract the principal components of one set of data (say data1) using prcomp(). ...
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39 views

strange loadings matrix after varimax rotation: PCA with prcomp in R

I'm running a PCA using the R function prcomp. This is the function: d2.pca <- prcomp(sel.d2,center = TRUE,scale. = TRUE) So variables are scaled an centered ...
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7 views

Bi-normal separation feature selection (BNS) in R

I'm doing binary classification on highly dimensional text data, with a biased class distribution. After reading this paper, i found out about BNS feature selection. Is there any package that ...
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22 views

How to program automated shrinkage for a subset of terms in R?

I've got data from a randomized experiment that includes a lot of covariates. I'm interested $\delta$ from a model of the form $y = g(\delta T + X'\beta+ \epsilon)$, where $T$ is randomly assigned and ...
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31 views

PCA on spatial precipitation data time series

I have precipitation time series data stored in a 3D matrix called 'pre' (dim1/2=position (index), dim3=time). I want to do a principal component analysis in order to detect the main variance and thus ...
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Do I need to transform object scores of principal components obtained from CATPCA before regressing?

As part of my internship I have obtained a dataset containing 11 categorical explanatory variables and a number of categorical response variables. Using CATPCA i have reduced my explanatory variables ...
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2answers
206 views

2D projection to maximise separability

I have a set of 500 points in 5D. Each point belongs to one of five classes, and the class labels are known. I’d like to visualise the dataset in 2D such that the classes would be separated as much ...
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2answers
55 views

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?
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1answer
72 views

Which PCA (or kernel PCA) basis better describes a single test sample?

I have two PCA bases obtained by decomposition of two groups of training data. I also have some samples of test data. How can I decide which PCA basis fits better each test sample? I tried to ...
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Does PCA need to be repeated for data sets with more than 2 dimensions?

Out of all PCA examples I have found, it has always been about finding the eigenvectors and eigenvalues of a data set in two dimensions, as in square matrices, which is 2 dimensional( correct me if ...
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1answer
144 views

What is the proper association measure of a variable with a PCA component?

I am using FactoMineR to reduce my data set of measurements to the latent variables. Now, the variable map is clear for me to interpret, but I am confused when ...
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26 views

PCA run on any 4 tenors of interest rate swaps results in identical or exact opposite zscores of the residuals

I'm stumped when I run PCA on 4 tenors on a yield curve, it can be any 4 tenors, any length of data, and it's always the same thing I observe. The z-scores of my residuals are identical to each ...
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2answers
59 views

How to interpret PCA for data reduction?

I have 19 currency pairs like USD.AUD, USD.CAD, etc. Also 82 cross currency pairs like ...
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39 views

How to perform a regression on principal components obtained from CATPCA in SPSS

As part of my internship I have obtained a dataset containing 11 categorical explanatory variables and a number of categorical response variables. Using CATPCA i have reduced my explanatory variables ...
3
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2answers
55 views

Classifying by performing PCA for positive and negative datasets separately

I have a dataset with binary labels, and I try to figure out whether the data can be classified and yield the ground-truth labels. I thought to try PCA for the data with each of the labels, and see ...
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27 views

Selection of variables using principal component analysis

I have constructed four dummy variables for the source of drinking water as homewell drinking, tube well drinking, agro well drinking & tap water. From the principal component analysis, I found ...
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38 views

How to interpret component matrix scores in Principal Components Analysis

Following on from this question I'm currently using Principal Components Analysis in SPSS to investigate dimension reduction across n (33) binary variables. This is for dimension reduction and to ...
2
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1answer
64 views

Identifying the coefficients of a principal component

Suppose that a two-dimensional random variable $X$ has a covariance matrix given by $$ \Sigma = \pmatrix {1 & -2\\ -2 & 4}$$ One of the three linear combinations below corresponds ...
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22 views

Is there any characterization of the score matrix obtained with PCA on a very correlated dataset?

I have a dataset $X$ of very correlated variables. With Principal Component Analysis I have computed the matrix of component scores $Z$. Is there any particular property of $Z$ in this case? I am ...
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2answers
54 views

Why is the eigenvector in PCA taken to be unit norm?

In deriving the eigenvectors for PCA, the vector is subject to the condition that it should be of unit length. Why is this so?
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24 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
103 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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45 views

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

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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36 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
73 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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56 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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34 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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21 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
126 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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1answer
30 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
45 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
109 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
22 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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18 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
57 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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61 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 ...
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1answer
56 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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36 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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56 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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49 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 ...
3
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1answer
51 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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21 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 $n \times k$ ...