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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Using a PCA to reduce response variables or multivariate multiple regression?

Does it make sense to use a PCA on numerous response Y variables and then conduct a multiple regression or carry out a multivariate multiple regression all response variables as they are? I have 4 ...
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19 views

Predict/impute one cell of matrix using all other cells

The question: I want to predict/impute one missing cell of a matrix using the contents of all other cells. Anyone have ideas on how to do this? The context: The matrix is n people's responses to m ...
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31 views

Can Principal Component analyses be applied to a counting trait?

I am analyzing a segregating population of plants coming from an hybridization process. The experiment consists in several field plots (according to an augmented design). In each plot a segregating ...
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1answer
92 views

Pull out most important variables from PCA

I would like to get the most important variables from a PCA result. I see two clusters in the plot. I now that is possible that there is no only one variable causing this, so maybe I would have to get ...
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17 views

Rotation of Mean Centred Variables in Principle Components Analysis

I'm looking to manually (Excel) perform PCA without any statistical packages such as R, but having trouble understanding how to rotate the original variables to find the maximum variance for the new ...
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21 views

Can I use non-linear PCA (CATPCA?) on my multivariate dataset that contains nominal AND ordinal data?

In my multivariate dataset I have over 100 objects/cases that have been coded on 20 different variables. Several variables are ordinal and several variables are nominal. Is it possible to use ...
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41 views

Principal components using correlation matrix in R

My understanding is that prcomp and princomp work off the dataset itself (row of observations, across variables in the columns). ...
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13 views

Intuition behind which eigenvectors to use in PCA for orthogonal regression

I am learning PCA, and while this seems like an obvious question, I can't seem to understand some of the ideas behind which eigenvectors to use when performing orthogonal regression with PCA. My code ...
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29 views

Can seasonality be detected / explored with principal components analysis?

I have a rainfall data consisting of around 95 years for the rows and twelve months of the year for columns. So this is a 95x12 matrix, not a column vector. Can I derive any idea about the months to ...
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1answer
36 views

When is it appropriate to use PCA as a preprocessing step?

I understand that PCA is used for dimensionality reduction to be able to plot datasets in 2D or 3D. But I have also seen people applying PCA as a preprocessing step in classification scenarios where ...
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16 views

Is subtracting the mean from PCA necessary when using an SVD result that is feature scaled?

I've applied SVD to the original data matrix and eliminated insignificant columns and rows from U and V^T respectively using the Sigma values. I multiplied together my optimized U, Sigma, and V^T ...
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2answers
41 views

Is it important to convert “integer” variables (with 0 or 1 values) to factors?

I am working on a high-dimensional dataset (1776 variables). When I read the csv file, R loads variables (with 0 or 1 values) as class of "integer". Is it important to convert these variables to ...
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1answer
18 views

What is the range of values that can be expected in the result of Principal Component Analysis (PCA)?

I want to normalize all of my preprocessing techniques between 0 and 1 so I want to know what the PCA range of values is so that I can apply a proper normalization to it. I applied PCA by using the ...
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12 views

Reconstructing a vector after projection

Suppose one has a matrix of data $X$, which is $n$ observations by $p$ dimensions. Let $P_\perp$ be a projection onto some $k<p$ dimensional subspace. Suppose one computes the principal direction ...
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14 views

Feature selection from wavelet transformation in R

I am new to wavelets. Currently, I am developing a prediction model using time series data. I am using the wavelets package in R. I am taking part of the time ...
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1answer
47 views

good practice for dimensionality reduction using Principal Component Analysis (PCA) and/or Linear Discriminant Analysis (LDA)

Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) best practice Assuming I have a dataset for a supervised statistical classification task, e.g., via a Bayes' classifier. This ...
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21 views

Is there an ideal number of measures in PCA ?

Working on a problem of extracting a minimal sub-set of criteria in a siting problem, I resorted to PCA, I have only 26 individuals (measures), I naturally thought it would be wise to ask whether that ...
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22 views

Correlation tests – multivariate correlation matrix?

I just got comments from a reviewer to a submitted article and didn't understand what I should do very well. Here are the tests I performed: We first used principal components analysis (PCA) to ...
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4answers
228 views

Clustering binary categorical data

I have some data where I have certain classes (c1, c2, c3, c4 ...) and the data comprises of binary vectors where 1 and 0 denote that an entry belongs to a class or not. The number of classes will be ...
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4answers
68 views

Impractically long running time PCA command in R RStudio

I am using R in RStudio on OS X ver. 10.9.2 on 1.7 GHz Intel Core i7 with 8 GB RAM. I am trying to run a PCA command (prcomp) and plots on a dataset with ...
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1answer
68 views

Not normalizing data before PCA gives better explained variance ratio

I normalized my dataset then ran 3 component PCA to get small explained variance ratios ([0.50, 0.1, 0.05]). When I didn't normalize but whitened my dataset then ran 3 component PCA, I got high ...
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25 views

Representing a distance matrix in the plane [duplicate]

I've worked with observations as vectors with both continuous and categorical variables. In both cases one can use dimensionality reduction techniques such as PCA (in the latter case through ...
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29 views

PCA proof needed for proportion of variance explained by L PCs = mean R-square from regression on PC scores

I observed the following relation and would like to know where I can find a general proof for this: Assume a data matrix $A = [a_{ij}]_{t x k}$. 1) Perform principal component analysis (PCA) using ...
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52 views

Factor analysis - CATPCA combined with conventional PCA

I have some concerns regarding factor analysis and especially about combining the factor analysis for an ordinal scale (categorical data) - CATPCA with conventional PCA. Basically, I need to enter my ...
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26 views

Principal component analysis, psychometrics, and number of items required

I saw that questions regarding sample sizes and PCA are asked here quite frequently. However, I was not able to find exactly the information I need. I plan to do a psychometric study and conduct a ...
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27 views

Effect sizes from regression analysis and factor loadings

To do a meta analysis, I try to calculate effect sizes. In an article by Shah and Ward, the authors do a regression analysis after combining various factors by a CPA to four factors. The factor ...
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2answers
71 views

R and SPSS differences in pca loadings

I performed two principal components analyses: in R and in SPSS - using the same dataset and the same variables. I got the same results - at least to some point. The eigenvalues are the same (I used ...
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1answer
49 views

Principal component regression analysis using SPSS

I have done multiple regression analysis (MLR) of my data and find out $R^2$ and $r$, and then to remove multicollinearity problem I used PCA. This analysis generated PC equal to my variables, I ...
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1answer
24 views

Method to compare ratings from multiple different sources with missing data

I want a method to compare ratings from multiple sources and find a single measure that best reflects all the ratings. To give a specific example, let's call it "The fellowship review committee ...
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1answer
83 views

What is the difference between loadings and correlation loadings in pca and pls?

One common thing to do when doing Principal Component Analysis (pca) is to plot two loadings against each other to investigate the relationships between the variables. In the paper accompanying the ...
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1answer
55 views

factor analysis for given data with help of matlab

suppose that we have following data i have done covariance matrix and eigenvalue decomposition ...
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37 views

PCA eigenvalues meaning

When projecting the data set on the Eigen vectors of the co-variance matrix , the eigenvalues represent how much each example varies away from the mean of the data set in the projected direction , ...
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12 views

In R, how to predict with svm model in parallel using foreach/snow? [migrated]

I'm trying to improve the performance of my R program, which is using an SVM trained on PCAs, by using the foreach and doSNOW packages. I've already trained the models and am now passing my validation ...
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1answer
34 views

Question about PCA data recovery equation

In PCA , consider a 4 x 3 data matrix ( 4 examples each with 3 features ). After getting the 3 eigenvectors (a/b/c) and projecting data on the first 2 vectors, the equation looks like this : [ first ...
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18 views

Stock Returns Covariance Prediction - Number of Principal Components

I am working on the following problem. Given N days of stock returns, I compute the covariance matrix for stocks. I then use Probabilistic PCA to "shrink" the covariance matrix. I am trying different ...
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1answer
70 views

PCA on Binary Data

I having binary data set (yes/no), so can I apply PCA on that. Is it mathematically correct to do that. In my opinion Binary variable can only be subjected to logical operations, so how it can be ...
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28 views

Asymptotic principal component analysis

I understand how principal component analysis works. However, in a financial time series sense, I do not understand why the number of observations should be larger than the number of dimensions. I am ...
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1answer
40 views

Calculate principal components

Given the following data: ...
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1answer
46 views

Understanding PCA - How to calculate scores

I'm looking for advice to whether or not the following method is good and is standard for calculating PCA of the data. So the examples that I will give will be small. Given a matrix of $A = [4, 6, ...
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26 views

Principled approach for PCA on correlated variables?

Related to Should one remove highly correlated variables before doing PCA?, PCA is used a lot in population genetics to essentially cluster individuals into ethnic group based on their genetic markers ...
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1answer
19 views

Literature for Cross Validation on Sparse Data?

I've read a lot about Cross Validation to estimate prediction error, specifically for selecting the number of components in a PCA model (I'm not doing SVD/PCA, but it's very similar), but I can't find ...
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1answer
52 views

Are explanatory variables considered random in PCA?

One of properties of PCA states that the sum of the variances of the principal components is equal to the sum of the variances of the explanatory variables. I wonder how to interpret this as I've ...
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1answer
178 views

Steps done in factor analysis compared to steps done in PCA

I know basically how to express PCA (Principal component analysis) mathematicaly, but I would like to know steps that should be used for factor analysis. ...
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1answer
49 views

PCA-based dimensionality reduction when the number of data points is less than the number of variables

Assume we are given a $p \times n$ (variables $\times$ data points) data matrix $X$, with $p > n$ (i.e. more variables than data points). Performing PCA on such a matrix yields an $n \times n$ ...
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3answers
121 views

Problem with PCA in R (suspiciously high explained variance)

I have always been confused about how to properly interpret PCA results. My data looks like this and it's a big table with more than 5 million rows and 12 columns.(the first few lines are all 0...) ...
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2answers
138 views

Why does PCA maximize variance of the projection?

Christopher Bishop writes in his book (Pattern Recognition and Machine Learning) a proof, that each consecutive principal component maximizes the variance of the projection to one dimension, after the ...
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24 views

X,Y coordinates confidence ellipses and centroids

As I try to add my PCA ggbiplot a centroid I wonder is the center of the confidence ellipses (X,Y) are the same X,Y coordinates of the centroids?. If so how can I extract them? Thanks
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70 views

Calculate centroid in PCA

If I understand correctly in order to calculate a centroid in PCA I can calculate the mean of X points and Y points (e.g., PC1 and PC2). When I run a simple PCA (code below) I don’t get the centroid ...
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2answers
39 views

Example of PCA where low variation PC is “useful”

Normally in PC the first few PC's are used and the low variation PC's are dropped -as they do not explain much of the variation in the data. However, are there examples where the low variation PC's ...
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21 views

Multiple Correspondence Analysis percentages, and points near to one axis

I have done a multiple correspondence analysis based on 10 factors: every factor is a Yesor Noquestion. The first factor give ...