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 ...

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Principal Component Analysis and generalized variance

I'm trying to prove that the first $k$ directions found by PCA maximize the generalized variance, i.e. the determinant of the covariance matrix. Basically, I'm trying to prove that $$ \...
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15 views

Projection on weighted kernel PCA basis

I'm performing a sort of weighted kernel PCA, where the weights of samples can be negative. The weights of all samples are given by the diagonal weight matrix $D$. The data matrix is the $n \times d$ ...
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70 views

Toy example dataset for testing PCA implementation

I want to check my implementation of dimensionality reduction with PCA, so I'm looking for a test case. I have found other implementations on the web as well, so I will be comparing with those too. ...
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22 views

How do I predict original components from PCA analysis?

I have the following dataframe ...
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18 views

Why do loadings of princomp in R report identical proportion of variance for all principal components? [duplicate]

I'm trying to run a few tests using princomp in R. In princomp there is a value called <...
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28 views

Implementation of PCA using SVD without creating covariance matrix

So I'm currently taking a Machine Learning course and have correctly submitted my implementation of PCA. I used SVD. Here it is Octave. ...
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9 views

Problem with syntetic data generating for Probabilistic PCA and Factor Analysis (FA) comparison - methodology

I am trying to understand a short example related to dimension reduction from python scikit-learn.org official documentation for long time and unfortunately I am not successful. I don't have problems ...
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How to separate two classes when the features values predicting them are so similar ?

What should be my approach. I got 13 principal components from 21 numerical features. The 13 features have a gaussian distribution. The plot below is between the top two components. Should I clean the ...
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16 views

Is it possible to yield high-dimensional data from its low-dimensional point in KPCA?

With PCA, it is possible to reconstruct high-dimensional data from its low-dimensional point by $$ x_i' = Pb + \bar X $$ Where $\bar X$ is the mean of training set $X$, $P$ is the eigenvectors and $b$ ...
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114 views

Can PCA allow to identify redundant variables that can be removed before doing cluster analysis?

I hope this is suitable for this forum: I am new to PCA and what I ultimately want to do is perform cluster analysis on my dataset. I have 20 physical descriptor variables for organisms, each with ...
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14 views

What to do when EFA requires more factors but the number of variables is low?

There's a lot of information on the forum about the differences between principal components analysis (PCA) and exploratory factor analysis (EFA) (for example here and here). I am new to both methods, ...
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32 views

How the Correlation Matrix is built for PCA in Weka?

Just to give a context, I want to use PCA (Principal Component Analysis) to identify which attributes are similar to others, so I can use just one (or a subset) of them. The correlation matrix of n ...
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14 views

Reference request about feature maps in ML

Can someone kindly link to some recent papers on understanding feature maps in ML? It would help to get an idea of what are the recent issues there that people have been working on with regards to ...
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The combination of PCA and MCA results

I'm researching about making a wealth score Based on a number of quantitative and qualitative socio-economic variables. for this approach I decided get Score of quantitative variables (6 VARIABLES) by ...
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How do i use PCA? [duplicate]

I am not sure i understood the concept of PCA that well. I know it is used to reduce the dimensionality by the help of the eigenvector and eigenvalues of the covariance matrix, and thereby compute ...
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1answer
77 views

How is the principal component applied on to the data?

I am bit unsure (Or might be overthinking this) or is the chosen PC somehow applied on to the data, to reduce the dimentionality of the data, or how does one use PC to do any form of mathematical ...
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1answer
63 views

How can I experiment with lagrange multiplier in PCA optimization

Suppose we want to solve following optimization problem (it is a PCA problem in this post) $$ \underset{\mathbf w}{\text{maximize}}~~ \mathbf w^\top \mathbf{Cw} \\ \text{s.t.}~~~~~~ \|\mathbf w\|_2=1 ...
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2answers
50 views

In PCA, does significance/importance of a PC correlate with explained variance?

For PCA eigenvalues S = [1.74 1.45 0.93 0.77 0.50 0.30 0.25 0.13 0.00 ...] where the 2 first PCs explain more than 50% of the variance, is PC1 the most important/...
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10 views

Calculating index from principal components

I am facing a problem where I need to calculate composite index from set of variables. As the variables are fairly correlated I have applied PCA to remove overlapping information and I got principal ...
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3answers
25 views

Principal component analysis result

I'm trying to understand the result of PCA, thought you can help me to understand better. ...
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38 views

The effect of non-positive-definite covariance matrix (in $p>n$ case) on PCA

Gene data has large number of dimensions as compared to samples. This leads to a non-positive-definite covariance matrix. In R when I try to use princomp which does ...
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54 views

Interpreting overlapping arrows on a PCA biplot: does it mean that the variables are redundant?

I'm new in principal component analysis (PCA) and I don't really understand the biplot representation of its results, so I would really appreciate some guidance. Having the example of the illustration ...
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18 views

Creating one performance measure

I want to create one operational performance score for each day so that we know if the performance was good or bad in our call centers, to be able to compare days, and to be proactive in maximizing ...
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39 views

Is there a relationship between partial correlation and spectral decomposition?

I am wondering if there is a known relationship between the matrix of partial correlation (for example, I would like to regress out the influence of the first PC on the data) and the correlation ...
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35 views

Generating samples from high-dimensional multivariate Gaussian with few training samples

Say I have a $n\times d$ dataset $D$ where $n\ll d$ ($n$ number of observations, $d$ number of dimensions). Currently, if I want $m$ samples from $D$ assuming it is multivariate Gaussian, I can do ...
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26 views

Does it make sense to do PCA before kernel regression?

I have a set of features extracted from the same samples and I'm learning a kernel ridge regression. Now, especially for feature fusion, reducing the number of features before combining them seems ...
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1answer
36 views

Equal representation of variables in Principal Component Analysis

I have 8 variables that I want to combine into one performance score. I am doing PCA and taking the first three components (~62% of variance), then adding the three scores for each record from these ...
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37 views

Information on PCA and it's applications

Edit: I'm currently doing some research into Principal Component Analysis (PCA) and I'm looking to implement some different forms of PCA algorithms in Matlab. I'm looking to use it for fault ...
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How can one measure the R-squared of a PLS regression model's Test set in MATLAB?

I was following this tutorial for PLS regression in MATLAB. They show how to choose the number of components for the model, but the yfit that they calculate, refers to the training set of the model if ...
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Imputation introduces negative values when using imputePCA() from the missMDA package in R?

I am testing out various imputation methods on my data and would like to use imputePCA. It imputes the missing values with no error messages, but when I check the completeObs matrix some of the ...
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379 views

What is an intuitive explanation for how PCA turns from a geometric problem (with distances) to a linear algebra problem (with eigenvectors)?

I've read a lot about PCA, including various tutorials and questions (such as this one, this one, and this one). The geometric problem that PCA is trying to optimize is clear to me: PCA tries to ...
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54 views
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Principal Component Analysis handled multicolinearity in data [duplicate]

How principal component analysis handled high multicolinearity in data set?
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1answer
70 views

Does PCA do something else apart from selecting features with the most variance?

While experimenting with Spark library MlLib, I questioned myself if I understood well the mechanism of PCA algorithm, because output of MlLib algorithm was not what I expected to get. so for given ...
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1answer
36 views

How to calculate the information loss of PCA?

How would we calculate the information loss of reducing dimensions using PCA ? Would it be the amount of variance loss if we skip certain eigenvectors after the PCA ?
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Agreement Measure

The Situation We have a set of audio transformations each described by their position in an 80 dimensional feature space, each dimension corresponding to a particular feature of the transformation or ...
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Categorical PCA: Merge categories based on Transformation Plots?

A tutorial on categorical pca (CATPCA) (Linting et al. 2012) explains that a decision to merge categories of an ordinal variable can be made based on the category quantification ("none of the ...
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Is the data visualization a sufficient indication for the separability of the data? What are the other indications of the data separation?

In other words, let's say we have a data representation as in the image below, which is generated from the PCA, the projection of the data onto the first two PCs. As it's shown in the 2-D space, the ...
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35 views

Options for PCA for ordinal data (in addition to CATPCA)?

When developing an instrument involving ordinal data (likert scale with 5-6 response levels), how does one reduce the initial item pool before completing the exploratory factor analysis? I have seen ...
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1answer
253 views

Is there Factor analysis or PCA for ordinal or binary data?

I have completed the principal component analysis (PCA), exploratory factor analysis (EFA), and confirmatory factor analysis (CFA), treating data with likert scale (5-level responses: none, a little, ...
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prediction using PCA in R

I'm calculating a PCA using the prcomp function in R and I have a short question about the prediction capabilities within this ...
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Can one use dimension reduction algorithms like PCA for categorical variables? [duplicate]

I am in doubt the best test to be chosen. I want to investigate the relationship between the type of mutation in a protein (binary categorical data) with the type of protein structure (three types, ...
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34 views

Can Factor Analysis on Mixed Data be treated like a PCA?

I wanted to do something equivalent to a PCA on a mixed data set containing categorical variables and continuous numerical predictor variables which are normally distributed but measured in very ...
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2answers
325 views

I did PCA of my dataset with two classes and here is the scatterplot; how can I tell if my dataset is learnable?

What should I look for in my PCA? I'm doing supervised learning with (unfortunately only) 2000 examples, evenly split into 1000 yes and 1000 no. Each vector is a 1000 dimensional boolean vector. I ...
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24 views

Hierarchical Cluster Analysis validation

I have never used Hierarchical Cluster Analysis for inferential statistics before, but the dendrogram it produces provides a nice way to visualise my data. I applied the HCA to my variables with the <...
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Principal Component Analysis: Scale reliability and validity

I'm using a popular psychometric scale, the Domain Specific Risk Taking (DoSpeRT) scale, that contains 30 items that measure an individual's risk taking capacity across five different dimensions: ...
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57 views

2 features and 2 principal components

Whats the difference between 2 features and 2 principal components? I know what a PCA is, I just have the following problem: If my data has 2 features, the PCA will produce 2 components. So why does ...
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Interpreting PCA results on gene expression data

I'm working on a gene expression dataset from patients who either have systemic sclerosis or not. I normalized the data with housekeeping gene values and scaled the expression values for each DNA ...