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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Can we apply PCA(principal Component Analysis) on Binary variables for computing significant variables? [duplicate]

I have a dataset that looks like- I want to know whether we can apply PCA on binary variables for computing most significant variables out of hell lot of variables. Among these variables I want to ...
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7 views

Sparse PCA using elasticnet package in R - How to know how many number of nonzero values in one PC?

Can someone help me on Sparse PCA? I am using the "elasticnet" package to perform sparse PCA. I am having a hard time in figuring out how many nonzero values should a component contain? For example, ...
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17 views

Facial recognition phase in Eigenfaces requires normalizing coefficients ???

I'm working on an assigment about Eigenfaces for facial recognition: http://courses.cs.washington.edu/courses/cse455/10wi/projects/p2/ . Here is the dataset: http://courses.cs.washington.edu/courses/...
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9 views

Scikit Learn Python PCA and Feature Agglomeration feature indices?

I am using Scikit learn to perform PCA and Feature Agglomeration of my survey data. I have done the following : ...
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12 views

Why rarely use Restricted Boltzmann machine as preprocessor and shallow learning as classifier?

Recently, I'm interested in feature learning. I know that PCA, RBM, Autoencoder...etc have used as preprocessor or feature representer for selecting more discriminative features. and also know that ...
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20 views

Dimensionality reduction of small vectors (image processing)

I have N small floating point vectors of length K (typically, N is in the millions and K=9). I need to compute a lot (millions and millions) of squared euclidean distances between those vectors. It ...
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69 views

What is the value of linear dimensionality reduction in the presence of nonlinear alternatives?

From the results I've seen, manifold learning methods seem to generally outperform PCA for complicated, very high-dimensional datasets like images or videos. This makes sense to me, since nonlinear ...
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18 views

Why can't I find a pure representation of a PCA loading in my dataset

Perhaps I don't fully understand the PCA principles...I am applying PCA to spectroscopic data. I get a nice loading that beautifully explains 1 component in my dataset, however I cannot find this pure ...
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70 views

A problem with interpretation of principal components as linear combinations of features

I often see the principal components of PCA described as "linear combinations of the original features". Say we want to compute the principal components of our $m \times n$ design matrix $A$ ($m$ ...
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32 views

The use of PCA index as a dependent variable

My question is a follow up one to the use of PCA as a dependent variable which was posed by Singh and answered by Sympa on May 22, 2016: Principal Components for dependent variable in a regression. ...
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2answers
77 views

Can I use PCA (or should I use regression) for testing the effect of multiple variables on one dependent variable?

I have 2000 soil property measures and 14 different variables like rainfall, temperature, slope, etc. I want to check the effect of those 14 variables on soil property measures, including which ...
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Can PCA help me in determining effect of multiple variables on other variable? [duplicate]

I have a dataset containing 2000 soil property measured values and other attributes like slope, TWI, aspect, rainfall etc for the same. I want to see how my soil property changes with the change in ...
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22 views

PCA with variables in different Likert scales

Can I run PCA (principal components analysis) if my Likert variables are measured differently? E.g. one Likert variable is in the range 0-6, another one is in the range 0-10 and yet another one is in ...
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1answer
47 views

Should outliers be removed from Principal Components Analysis?

I have calculated Hotelling's T2 statistic for detection of outliers in PCA analysis in Matlab. However, I am unsure as to whether or not it is a robust approach to remove these outliers? The output ...
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PCA result: How to convert data from zero-mean to a suitable format for percentage increase?

I am working on a project where I am trying to evaluate whether geographical areas have become better off - let's say between 2000 and 2010. I have found 5 variables: income, house prices, % with ...
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238 views

Why doesn't my code for extracting the first principal component work?

Following the Wikipedia article on PCA, I extract the weights of the first principal component by calculating $$\textbf{w}_1 = \mathrm{\arg\ max} \left\{ \frac{\textbf{w}^\intercal \textbf{X}^\...
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48 views

What is maximum likelihood PCA?

There are many papers on this topic, such as this one (pdf). However, I could not find out what exactly maximum likelihood PCA is, how it is applied and for which purpose. Can anyone explain it?
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88 views

How to manually compute PCA transformation as performed by predict() following pcrcomp() in R?

How to manually compute PCA transformation as performed by predict() following pcrcomp() in R? Example: ...
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76 views

Angles between variables on a PCA biplot and correlations between the variables

A friend or mine has performed a PCA and he asked me for help about interpretating a biplot. In that biplot I found that the vector representing a variable, say A, forms a very wide angle, perhaps ...
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33 views

Visible cluster separability better from PC score coefficients vs. eigenvector Z-score cross products

I am using about 20 features which were identified to best predict true class for a 4-class problem involving about 60 objects. It was noticed that, when using the $p \times p$ correlation matrix $\...
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“Regress on” - PC1 driven standardization

I have 450 individual fish each with 25 highly correlated measurements (body length, fin size, jaw length, etc). My dataset is made up of a relatively normal distribution of sizes. What I am curious ...
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Some variables represented well on 1st dimension, others on 2nd dimension in correspondence analysis output

I'm performing correspondence analysis on survey data (n~5000). My problem is that 3 groups of respondents (that I personally created) are well represented on one dimension (e.g., height) and the ...
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Recovering original data from projected PC rotations

I am interested in doing the following: 1) Perform PCA on dataset; 2) Take new data, project into PC space, then project back into original data's space with a truncated number of PCs. However, I ...
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Cross-validation scheme used in the Introduction to Statistical Learning, Chapter 6, Lab 3

I've been really enjoying the Introduction to Statistical Learning textbook so far, and I'm currently working my way through chapter 6. I realize that I am very confused by the process used in lab 3 ...
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Cluster analysis with PC scores (Multivariate Morphometrics)

I have a morphometric dataset of 430 fish, with 27 various "shape" measurements, for example: total length, head length, fin distances, etc. My goal is multi-fold: (BIG GOAL: cluster by "shape") ...
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25 views

Number of neighbors as a function of dimension

I apologize in advance for perhaps an imprecise formulation of the question. If I have a point in 1D, it has precisely 2 nearest neighbors independent of choices. In 2D, if I allow arbitrary ...
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27 views

PCA for stand-alone VaR

I am trying to compute the VaR on an international equity portfolio (40 stocks in 4 different countries) and, in addition to the total VaR, I need to find equity VaR and forex VaR. Alexander (2008) ...
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1answer
44 views

Scaling after Principal Component Analysis

I am attempting to model the yield of various crops as a function of weather data, namely one temperature variable and 7 moisture-related variables (measuring different aspects of moisture content). ...
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1answer
45 views

Best way to analyse percentage data

I have percentage data and would like to see if these different variables have an affect on certain factors; i.e., I have different habitats of an area e.g., improved grassland: 40%, arable: 15%, ...
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Is there a way to extract the topics and/or get the SVD matricies after using PCA on a document matrix?

I'm comparing various topic modeling algorithms on a data set and I'm hoping to compare them via looking at the log-likelihood of held out documents. I'm using SKLearn and I can see that PCA allows ...
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PCA & Cluster analysis for Typology with missing data - Choosing right approach

I am an ecology graduate with a decent practical familiarity with statistics in R, but limited experience of approaches such as PCA, and Cluster Analysis. I am currently faced with the challenge of ...
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23 views

What is meant with “decision level of factor loading”?

I have performed a PCA with some data sets. Prior to performing PCA, I tested the applicability of PCA with KMO and Bartlett's Sphericity tests. I got some critics stating that I have to add "my ...
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24 views
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why Matrix Factorization map the two spaces into same space?

It's a common sense that Matrix Factorization map the two space(e.g. user and item) into same factor space. But is there any more formal way to explain the fact they are the same ? Say, I have $$\...
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Why does executing a PCA on my unbalanced dataset change the prediction distribution of my test so much?

I'm using prtools to try and solve a machine learning problem and trying to use a PCA to help me with this. Now I have a dataset with 13 features (columns), 10000 ...
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How to determine parameters for t-SNE for reducing dimensions?

I am very new to word embeddings. I want to visualize how the documents are looking after learning. I read that t-SNE is the approach to do it. I have 100K documents with 250 dimensions as size of the ...
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1answer
53 views

Eigenvalue equation for kernel PCA

In Nonlinear component analysis as a kernel eigenvalue problem, Schölkopf et al start by describing PCA. Given a set of data instances $x_1, \dots, x_M$, with $x_k \in \mathbb{R}^N, k=1,\dots,M$, and ...
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How does Principal Coordinate Analysis (PCoA) work, as compared to PCA? [duplicate]

I am familiar with PCA from Making sense of principal component analysis, eigenvectors & eigenvalues where you either normalize the data (to standard normal or ...
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2answers
82 views

Projecting data on a sphere

I am used to working with PCA, tSNE, LLEs... They all do a great job projecting the data on a plane (or on linear subspaces of $\mathbb{R}^n$). Is there any other embedding technique that projects the ...
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93 views

In PCA, do the principal components beyond the first optimize any expression?

Given a covariance matrix $\mathbf\Sigma$, the first principal component $u_1$ is the unit vector that maximizes variance $u_1'\mathbf\Sigma u_1$. Do there exist similar expressions that the first $k$ ...
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Using PCA to model highly correlated variables

Specifically, Andrew Ng states that PCA should be used to speed up algorithms or to visualize data. He also states that using PCA as a way to prevent overfitting is an incorrect application of PCA. ...
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28 views

PLS regression in Octave

I'm doing a PLS regression in Octave, using the following function: [XLOADINGS,YLOADINGS,XSCORES,YSCORES,coefficients,fitted] = plsregress(X, Y, NCOMP); From ...
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1answer
43 views

covariate selection in inference problems in logistic regression

For my specific problem, but a common situation in the medical field, I have several hundred patients, and about 10-20 exaplnatory variables. the goal is to examine a specific predictor("treatment") ...
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PCA for questionnaire reduction

I'd like to have some opinion regarding if I'm in the right way with my questionnaire reduction. I have a questionnaire with 275 questions and 34 issues (so a couple of questions are related to each ...
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How to calculate regression coefficients in terms of original variables when I already have regression coefficients in terms of PCs? [duplicate]

While doing principal component regression I take the input data, standardize it, calculate PCA, and use the score matrix to solve the equation Y=score*B where Y is my mean-centered known output and B ...
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27 views

Interpreting the regression coefficient when the regressor is polychoric-based principal component

I have a regression where I am trying to interpret the regression coefficient of the first principal component on some outcome variable. The component scores variable was obtained in a polychoric ...
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2answers
68 views

Linear “self” regression, terminology and references?

Suppose that $X_i, i=1,\ldots,n$ are some random variables. I'd like to do multiple linear regression to learn to predict any of these variables from the others. My model for the reconstructed ...
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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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1answer
89 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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33 views

How do I predict original components from PCA analysis?

I have the following dataframe ...
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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 <...