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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133 views

How does “Fundamental Theorem of Factor Analysis” apply to PCA?

I'm currently going through a slide set I have for "factor analysis" (PCA as far as I can tell). In it, the "fundamental theorem of factor analysis" is derived which claims that the correlation ...
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0answers
11 views

How to reconstruct the data? [duplicate]

I have compressed the data( seven sensors are measuring 125 days temperature) using Principal Component Analysis . Then How to reconstruct the data ? What formula should i use?
4
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3answers
100 views

How to interpret PCA on time-series data?

I am trying to understand the use of PCA in a recent journal article titled "Mapping brain activity at scale with cluster computing" Freeman et al., 2014 (free pdf available on the lab website). They ...
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2answers
46 views

Multi-class Classification using SVM with PCA

I'm doing an image classification task and the number of features of each example image is pretty huge (3,072: # pixels in each image). I'm thinking of using PCA to reduce the # features of each image ...
0
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0answers
17 views

Can someone explain briefly application of PCA for estimating parameters in GMM

I am having some difficulty in seeing connection between PCA of second order moment and parameters of GMM ( mean components) . The claim is mean components are in the span of eigenvectors. Can some ...
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1answer
39 views

Combining pca and classification algorithms

For some classification algorithms, assuming independence of data helps reduce the number of parameters to estimate. Why then not just to apply a method like pca or ica to the original features to get ...
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2answers
29 views

Choosing the number of principal components to retain before training a neural network for classification

I am working on neural networks and I am currently creating a perceptron that will work as a classifier for a data set of images with faces. I am required to perform pca (principal component analysis) ...
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2answers
545 views

How to understand “nonlinear” as in “nonlinear dimensionality reduction”?

I am trying to understand the differences between the linear dimensionality reduction methods (e.g., PCA) and the nonlinear ones (e.g., Isomap). I cannot quite understand what the (non)linearity ...
5
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1answer
82 views

Meaningful inference about data structure based on components with low variance in PCA

A lot of microbiome (microbial ecology) papers that I have come across use either principal component analysis (PCA) or principal coordinate analysis (PCoA) to make conclusions about the data. A lot ...
7
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1answer
469 views

Confused about the visual explanation of eigenvectors: how can visually different datasets have the same eigenvectors?

A lot of statistics textbooks provide an intuitive illustration of what the eigenvectors of a covariance matrix are: The vectors u and z form the eigenvectors (well, eigenaxes). This makes sense. ...
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0answers
33 views

Non-decaying eigenvalues in Kernel PCA with small kernel width

I noticed that when I use a small width kernel (RBF) with PCA, I get my desired result (clustering in this case), but I do not get a decay in the eigenvalues (they stay about the same value). Is that ...
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0answers
17 views

Construct validity technique for small sample size

I have developed and pilot tested a quantitative survey instrument. I got only 40 respondents. No, I need to test its construct validity with the available data (N=40). What statistical analysis I can ...
2
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1answer
40 views

How to select a subsample of fixed size to maximize its total PCA variance?

I would like to use PCA to help design my genomics experiment. I can only afford to perform my experiment on a limited number of genotypes so would like to maximize the variation of the ones I ...
2
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1answer
24 views

Can nonlinear clustering produce 'fake' results?

I know that overfitting in classification is possible when using, for instance, an RBF kernel, due to its infinite dimension. But, is it possible to get (in a similar manner) fake clustering results ...
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1answer
40 views

How can I estimate a principal component from incomplete data?

I would like to know the best way to estimate a principal component's latest value, if I only have partial information about the latest variable data points: Assuming I have 5 variables: ...
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0answers
65 views

What is PCA doing with autocorrelated data?

Just because some correspondent posed an interesting question concerning methods of computation of autocorrelation, I began to play with it, nearly without any knowledge about time series and ...
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0answers
7 views

appling pca on spss with mixed type of variables (nominal-binary-ordinal-continuous)

I have a database, mixed type of variables (nominal-binary-ordinal and continuous) I want to apply pca with spss not R package , Can I ?? and how ?? many thanks..
2
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1answer
50 views

Why are there only $N-1$ principal axes for $N$ data points if the number of dimensions is larger than $N$?

In PCA, when the number of dimensions $d$ is much much greater than the number of samples $N$, why is it that you will have at most $N-1$ non-zero eigenvectors? In other words, the rank of the ...
1
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1answer
51 views

PCA clustering results 'ruined' by standartization

I have some data that I want to classify. As an initial measure, I did PCA for the data and I saw two distinct clusters of my data. However, when standardizing the data, the two clusters disappear. ...
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5answers
1k views

Is there any good reason to use PCA instead of EFA?

In some disciplines, PCA (principal component analysis) is systematically used without any justification, and PCA and EFA (exploratory factor analysis) are considered as synonyms. I therefore ...
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0answers
37 views

What's wrong with t-SNE vs PCA for dimensional reduction using R?

I have a matrix of 336x256 floating point numbers (336 bacterial genomes (columns) x 256 normalized tetranucleotide frequencies (rows), e.g. every column adds up to 1). I get nice results when I run ...
0
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1answer
61 views

How to know which feature mainly led to the prediction?

I have a classification problem where I use a model (say Logistic regression or SVM) to determine whether an instance belongs to class 0 or class 1. For a certain prediction on a test instance X, if ...
2
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1answer
60 views

Difference between svd() and prcomp() in R

Conceptually, aren't the eigenvalues of a correlation matrix and the singular values of the associated scaled data matrix supposed to be the same? The below illustration is saying that it isn't so. ...
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1answer
29 views

PCA or MCA for binarized data

I am working with bioinformatics and I have data that looks like the following: ...
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0answers
30 views

Principal components analysis on nested data

I'm working on a piece of analysis that requires identifying a small set of variables that summarize the variation found in a larger set of principal observations on teacher practice. Given the nature ...
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0answers
36 views

Understanding kernel PCA

Kernel SVMs are explained as follows: Apply kernel method to original data Check if we have a linear separator in the kernelized space. Map linear separator back to original space Is it fair to ...
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0answers
33 views

EFA versus PCA in SPSS

If I run a dimension reduction analysis in SPSS with Principal Components as extraction methods and Promax as rotation method, am I conducting an Exploratory Factor Analysis or a Principal Components ...
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0answers
30 views

Does it mean anything when all items load negatively on one factor when several factors are output?

So I am fairly familiar with factor analysis, and am aware of answers here and here that tangentially address my question. I believe I am right in my answer to the question I'm asking, but I wanted to ...
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2answers
60 views

Motive behind preserving variance

Dimensionality reduction techniques preserve some properties of the data. I was wondering how preserving variance (as PCA does) can be helpful? Precisely speaking, PCA takes the covariance matrix and ...
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2answers
59 views

How to transform test set to the training set transformed space with PCA?

I'm working on a text classification project, and I want to reduce the tf-idf matrix dimension with Principal Component Analysis (PCA) and then train my model with this, which is pretty ...
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0answers
12 views

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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1answer
336 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 ...
2
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0answers
41 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 ...
0
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0answers
73 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: ...
0
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0answers
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(). ...
3
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2answers
121 views

Why does my loading matrix following PCA with a varimax rotation contain only ones and zeros?

I'm running a PCA using the R function prcomp. This is the function: d2.pca <- prcomp(sel.d2, center=TRUE, scale.=TRUE) So ...
0
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1answer
35 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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0answers
23 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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0answers
35 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 ...
3
votes
2answers
215 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
82 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?
1
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1answer
76 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 ...
4
votes
1answer
170 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 ...
0
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0answers
33 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
78 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 ...
3
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2answers
63 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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0answers
28 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 ...
0
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0answers
52 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
votes
1answer
73 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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0answers
24 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 ...