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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Data sets for which PCA can classify better than LDA (using a very small training set)

Can you provide an example of a dataset where PCA can find better discriminant directions than (LDA) Linear Discriminant Analysis? One example is UCI's wine data set. If you use only 2 observations ...
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30 views

PCA on count-based data

I'm looking to do a PCA analysis on count based data itself rather than averages. I'm hoping this will help for variable observation depths; for example, 3/4 reads is not really equivalent to 15/20. ...
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2answers
50 views

Why log-transforming the data before performing principal component analysis?

Im following a tutorial here: http://www.r-bloggers.com/computing-and-visualizing-pca-in-r/ to gain a better understanding of PCA. The tutorial uses the Iris dataset and applies a log transform prior ...
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21 views

Ranking Data through rank number

Suppose in my survey, through one question, 100 respondents are asked to rank all the 5 product-attribute options for buying a product by giving separate rank numbers (from 1 to 5) to each of 5 ...
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75 views

Is large scale PCA even possible?

The principal component analysis (PCA) algorithm assumes that columns of an input matrix have zero mean. This can be achieved easily, but when the input matrix is sparse, the centered matrix will now ...
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26 views

what does the scale within a PCA mean

I am searching for an explanation what the x and y axis within a PCA analysis really means? I could not find any explanation on this topic, can somebody help me with it? So, just as an example ...
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1answer
36 views

When there is only one dependent variable, is partial least squares regression the same as principal component regression?

When there is only one response (dependent) variable, what is the advantage of partial least squares (PLS) regression over principal component regression (PCR)? My understanding is that PLS is only ...
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1answer
42 views

PCA output of Matlab's pca() function doesn't match manual calculation

I try to calculate the PCA in my matrix and I use two ways for this: PCA function [coeff, score, eigenvalues] = pca(M); And for compare and understand the PCA ...
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1answer
38 views

SVD from Matrix formulation to objective function

I'm writing the question to try to complete the circle after reading the 2 other questions on Cross Validated and the link on the third bullet point: What is the objective function of PCA? What ...
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2answers
90 views

Why is linear regression different from PCA?

I am taking Andrew Ng's Machine Learning class on Coursera and in the below slide he distinguishes principal component analysis (PCA) from Linear Regression. He says that in Linear Regression, we ...
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42 views

Estimating a plane from a set of 3D points

I am trying to estimate a midplane of a 3D model using the midpoints of paired landmarks, in order to reconstruct missing data. I therefore need to estimate a midplane from 27 3D points. I have looked ...
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28 views

Kernel PCA wrong output [Edited]

Linear PCA and kPCA with linear kernel should produce exactly the same results ( good explanation is in this post ). As I am learning to use PCA family methods I try to write my own functions ...
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35 views

making sense of small eigenvalues

I have a huge dataset with about 1.000.000 matrix entries of size about 300.000 and ran a PCA on them, but the components and the eigenvalues are really small. I am unsure what this means. I ran an ...
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1answer
49 views

Evaluate output of different dimensionality reduction methods

I used PCA, ICA, and FA to perform dimensionality reduction on my data. How can I measure which method performed best? If I reduce my data to 3 dimensions and plot it, what type of trends would ...
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30 views

Definition of eigenvalues in PCA

I've been reading two (peer reviewed) papers that use Principal Component Analysis to solve a problem I'm interested in, they both state they find the eigenvalues for the correlation matrix using the ...
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30 views

Representing experimental data by unconstrained ordination: PCA, PCoA, or NMDS?

I have a dataset composed by presence of different bacterial families in function at different pesticide treatment. I need to find a good representation of my data but I don't know which method ...
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36 views

Principal Component of non-centered data and PCA-Transformation

I am reading a chapter about principal component analysis (PCA). It states that for any random varible $X \in \mathbb{R}^p$ with $n$ observations, $E[X] = \mu$ and $Cov[X] = \Sigma$ the i-th PC is ...
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23 views

How to organise an iterative manual rotation of n component pairs?

I am currently building a q.rotate() function for the qmethod R package for Q Methodology. As is desirable for Q, I'd like users to be able to iteratively rotate ...
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1answer
48 views

What is a “principal component factor analysis”?

I am currently researching silence in the social sciences and am reviewing surveys and statistical methods implemented by researchers to get an idea methods in both survey design and the analysis ...
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1answer
75 views

Naming PCA Factors - Is it a Minor Art?

QUESTION: What is a good, structured and reproducible method to name selected components or factors in principal component analysis (PCA)? Clearly, the sign and magnitude of the entries in the ...
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38 views

Does the order of rotations matter in rotating PCA loadings (by-hand)?

Suppose I have retained 3 principal components, and I want to rotate their loadings by hand (yeah, that's rare, but it is commonly used in Q Methodology). Does it matter in which order I rotate the ...
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2answers
52 views

Is it correct to use the scores of PC1 as a composite index?

I have three correlated variables for 18 cases. I would like to construct a composite index using PCA, where each case has a score. Basically to reduce three dimensions to one, and use that dimension ...
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1answer
22 views

How to see from the PCA results if two original variables were correlated? [closed]

I perform principal component analysis (PCA) on a dataset with 120 variables. If I want to know if two variables A and B from my original dataset are correlated, how could I answer this question ...
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22 views

Techniques for plotting PCA projections in more than three dimensions

After running PCA on my data set, I noticed that using the three first eigenvectors, a separation between two different classes is still achievable (doing PCA on data from two classes). Unfortunately, ...
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2answers
75 views

Does each eigenvalue in PCA correspond to one particular original variable?

I have a matrix of let's say 120 variables and 50 subjects (rows). Before computing correlation between the 120 variables, I want to perform principal copmonent analysis (PCA) on this matrix. I will ...
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7 views

Principant Component Analysis being too slow (MLPY Python) [migrated]

I am using the PCAFast method from the MLPY API in python (http://mlpy.sourceforge.net/docs/3.2/dim_red.html) The method is executed pretty fast when it learns a feature matrix generated as follows: ...
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21 views

Uniformly sampling principal component scores to explore response surface

New simpler version of the question Consider a sample $\mathbf{X} \in \mathbb{R}^{n\times p}$ of $n$ points in $\mathbb{R}^p$ with $p$ small, say $p=5$, and $n$ large, say $n=3000$. Because they are ...
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19 views

Is it valid/relevant to do PCA on data which has multiple independent variables?

I have lots of data on the effects of different drugs on ~100 cell variables, and want to perform PCA on the data to reduce its dimensionality so the effects can be more easily visualised. The thing ...
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1answer
66 views

Significance/confidence intervals for PCA or factor loadings - how can such be defined?

Current discussions here in SSE made me to reconsider the PCA and FA models and procedures. I got curious how one would determine confidence intervals for the components/factor loadings by assuming ...
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1answer
44 views

PCA dataset to test my implementation

I'm trying to find a dataset with examples of data matrices and their principal components. I know that I could construct my own dataset using standard implementations found in python, or octave ...
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1answer
51 views

Supervised dimensionality reduction

I have a data set consisting of 15K labeled samples (of 10 groups). I want to apply dimensionality reduction into 2 dimensions, that would take into consideration the knowledge of the labels. When I ...
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2answers
31 views

PLS identify only peaks not troughs, and ignore certain region

I recorded a few Raman spectra for varying concentration of a substance. I processed the data in R and these are my steps: Remove baseline using baseline.corr with lambda=1e3 and p=0.01 Run PLSR on ...
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34 views

Why do auto-encoders with 1 hidden layer usually use the output weights/filter as $W=W^T$?

I was trying to understand why for auto-encoders with 1 hidden layer, we usually use the output weights/filter as $W=W^T$. Is there any theoretical justification to use $W=W^T$? Or maybe any way to ...
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11 views

Singular value decomposition for complex Hermitian matrix [migrated]

I am computing singular value decomposition on a covariance matrix with complex values (goal: principal component analysis). I read here that it is possible to use svd algorithms for real values using ...
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23 views

How to calculate accuracy of PCA? [duplicate]

I want to compare different methods such as SVM and PCA to classify the data correctly. But I don't know how to calculate accuracy of PCA in R. Following the article "Genetic classification of ...
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19 views

Minimum sample size for Factor Analysis? [duplicate]

What is minimum sample size required for using Factor Analysis? I have a data-set with 22 cases and 12 features. Is this sufficient? (I can't increase number of cases in my research, it is restricted ...
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1answer
72 views

What are “unrotated” and “rotated” principal components, given that PCA always rotates the coordinates axes?

As far as I understand, principal components are obtained by rotating the coordinate axes to align them with the directions of maximum variance. Nevertheless, I keep reading about "unrotated ...
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1answer
28 views

Can I use Principal Component Regression/Analysis to identify Raman peaks in varying concentrations?

I have data of varying concentrations of a particular substance in water. I recorded its Raman signals between 1 ppt to 1 ppb using identical parameters. I would be using Savitzky-Golay filtering to ...
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35 views

Principal component regression loadings show nothing

In my experiment, I diluted a chemical in water and recorded its Raman spectra. Then I repeated this with different concentrations. As I can clearly see some peaks decreasing in intensity when I ...
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25 views

How can you detect outliers in a group of face images?

I'm trying to filter an image database which contains some irrelevant pictures. All the faces are labeled with points around the face contour, eyes, mouth, eyebrows, have age and gender. The faces are ...
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3answers
126 views

Would PCA work for boolean (binary) data types?

I want to reduce the dimensionality of higher order systems and capture most of the covariance on a preferably 2 dimensional or 1 dimensional field. I understand this can be done via principal ...
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14 views

Principal component analysis on neural datasets

I have dataset file contains binary bits (0s and 1s) for all attributes Do i still need to apply the Principal component analysis to my dataset to train an autoencoder neural network and when is PCA ...
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23 views

Is it essential to use a correlation matrix when the scales of variables are different in PCA?

I am doing PCA on two variables which have completely different units and scale. More exactly, I am doing multivariate-EOF analysis as the columns of the data matrix represent 12 grid points of the ...
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1answer
86 views

Combining principal component regression and stepwise regression

I want to use a combination of principal component analysis (PCA) and stepwise regression to develop a predictor model. I have 5 independent variables (which are correlated among each other to ...
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12 views

Detecting linear connection between only several measurements in PCA (or any orther method)

$X$ is an $n\times p$ data matrix that has $n-d$ random measurements and $d$ highly correlated measurements, i.e. $X_{n-d+1+i}=b_i+a_iX_{n-d+1}+W_n$ for $i=1,2,...,d-1$, $a_i,b_i$ are unknown ...
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49 views

Next step after principal component analysis to model a relation with an independent variable

I have a data set that consists of different characteristics of communities. What I want to do is to see how those characteristics influence each other. As in, for example I have the income and ...
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55 views

Can I create an Index score using factor scores as weights?

I am creating an Overall Customer Satisfaction Index score based off of 4 factors that comprise satisfaction for callers to a call center: A representatives concern for your needs; ease of navigating ...
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1answer
62 views

How to compute classification accuracy of PCA?

How to check classification accuracy for principal component analysis (PCA)? In order to compare it with different methods, for example with random forest classification, how can I compute accuracy? ...
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25 views

Difference in the interpretation of PCA and CA biplots

I would be grateful if someone could please explain the potential differences (if any) in the interpretation of a biplot acquired from PCA and Correspondence Analysis (CA) please.
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19 views

Can PCA explained variance be computed from the components (or from SVD matrices)?

I'm looking to use Spark to calculate PCAs. However I need to get the explained variance for each component and the PCAModel class doesn't appear to provide that. Is there a way to calculated the ...