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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Explained variance in dimensionality reduction

I am new to dimensionality reduction and I am trying to learn different techniques about it. I am noticing that, unlike PCA, many other algorithms do not provide the explained variance of each feature ...
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23 views

Determining the PC scores for a new data point

so I have done a PCA analysis on a dataset (using prcomp in R) and I now want to determine what the principle components scores would be for a new sample(s). How can I do this? I'm sure the ...
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32 views

How LDA, a classification technique, also serves as dimensionality reduction technique like PCA

In this article , the author links linear discriminant analysis (LDA) to principal component analysis (PCA). With my limited knowledge, I am not able to follow how LDA can be somewhat similar to PCA. ...
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30 views

Interpretation of PCA eigenvectors

I have done a PCA analysis on genes expressed in cells under different stimulations, and retrieved the eigenvectors for a number of components. My question is can I use the value of these to ...
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16 views

Finding most relevant variables for components in PCA / MCA [on hold]

I am conducting PCA and MCA analyses in datasets with 150+ variables using Factominer in R. My main goal is to create 2-dimensional views of these datasets. After doing so, I would like to explain the ...
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18 views

Preprocessing via PCA in Caret, then fitting PLS

I am dealing with quite highly-dimensional data, and am using (in R) Caret's preprocessing 'pca' method to reduce the dimensionality. However, dependent on the number of components I choose, I seem to ...
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19 views

PLS with more variables than data points

Does it make sense to run partial least squares (PLS) on a data set that has many more columns (variables) than it has rows (data points)? I am using plsr in R. I ...
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21 views

Comparing regression coefficients using F-test to assess for batch effects

Here's what I have: two datasets with ~27,000 variables (same variables for each dataset). I'm trying to test whether or not dataset1 and dataset2 display batch effects. Namely, I want to do PCA and ...
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29 views

Importance and effect of mean normalization and feature scaling for PCA [duplicate]

What is the importance of mean normalization and feature scaling as a pre-processing step for principal component analysis (PCA)? What will be the result if I don't follow these pre-processing steps ...
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Miss Forest & Iterative PCA : How to handle very sparse matrix imputation?

I am currently benchmarking matrix completion methods (k-NN, RandomForest and iterative PCA) on multivariate normal data in which I introduce a certain proportion of NA (5 to 95%). My performance ...
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Anomaly detection using principal component classifier, cutoffs selection

I am trying to implement anomaly detection using principal component classifier proposed in "A novel anomaly detection scheme based on principal component classifier" by Shyu et al. It proposes that ...
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43 views

Is there an alternative to PCA that produces a unique representation?

PCA produces solutions that are not unique i.e. the resulting representation could be recreated using a different set of points. This is where my problem lies. I was wondering whether anyone is aware ...
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Fusion of two model reduced sensing systems / Comparison of two models

General context: I have a computer vision problem where I take an image sample then: Analyse* it (details omitted) to obtain a vector of values Run PCA (Principle Component Analysis) on it to ...
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23 views

How do I know if I adequately/correctly preprocessed my PCA/PCR data?

I'm an engineer with an interest in statistics, and my company sent me to a 1 week training in PCA/PCR (principal component analysis/regression) using The Unscrambler. I'm starting to apply these ...
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42 views

PCA to reduce dimensionality then classifier of choice?

I read about PCA online and the way it computes a covariance matrix, computes eigenvalues, and then transforms the matrix to reduce the dimensionality of the matrix to a certain number k <= p. ...
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25 views

Calculating Absolute Principal Component Scores from varimax-rotated principal components scores

In many receptor- modelling studies, after performing the PCA analysis, they often "rescale" their varimax-rotated PC scores (which are standardized with mean zero and standard deviaiton of 1) to ...
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15 views

Meaning of SVD plot of $U$ and $V^T$

I am using SVD/PCA for text mining purposes. Having a $(|terms|,|documents|)$ normalized matrix $M$, by applying SVD, I should be able to reduce the dimensionality and just keep the most meaningful ...
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23 views

Does it make sense to do PCA after robust PCA?

I was wondering whether it makes sense to do PCA after robust PCA. Suppose I have a matrix $X$ and if I do robust PCA I would get: $$X=A+E$$ And if I do PCA over $A$ would this make sense as a ...
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26 views

Can I use PCA to study how variables affect each other?

I'd like to know what PCA tells me about how the variables affect each other. For example, let's say I've three variables Cholesterol, Exercise, Calorie Intake and Sleep. I want to know how Exercise, ...
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198 views

Which matrix should be interpreted in factor analysis: pattern matrix or structure matrix?

When doing a factor analysis (by principal axis factoring, for example) or a principal component analysis as factor analysis, and having performed an oblique rotation of the loadings, - which matrix ...
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35 views

Kernel PCA for feature selection for various machine learning algorithms [duplicate]

I would like to forecast stock index returns with SVM, k-NN, and Neural Networks. In advance I want to select my inputs via kernel PCA (kPCA). Everything is performed in R. For the KPCA I use ...
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139 views

Is Mahalanobis distance equivalent to the Euclidean one on the PCA-rotated data?

I've been led to believe (see here and here) that Mahalanobis distance is the same as the Euclidean distance on the PCA-rotated data. In other words, taking multivariate normal data $X$, the ...
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42 views

Normalisation before and after PCA

Is it valid to normalise a dataset, reduce dimensionality with PCA and then to normalise the reduced dimension data? Assuming this is performed on training data, should the same PCA coefficients be ...
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17 views

Assessing the impact of the European sovereign debt crisis on the EURUSD

As the title suggests, I am trying to estimate the impact of developments in the European sovereign debt crisis on the EURUSD (the spot price of exchanging X dollars into 1 Euro). I am a little rusty ...
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14 views

Multivariate technique to determine whether an effect is intermediate to two or more other effects?

Let’s say I am looking at soil microbial community structure. I have a multivariate dataset with 20 dependent variables indicating various soil microbial biomarkers in the soil. My treatments include ...
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24 views

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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43 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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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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24 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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183 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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32 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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45 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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59 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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41 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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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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87 views

Fitting a plane to a set of points in 3D using PCA

I am trying to estimate a midplane of a 3D model using the midpoints of paired landmarks, in order to reconstruct missing data (midplane refers here to the middle/saggital plane of the cranium which ...
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34 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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38 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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55 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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40 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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40 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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28 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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57 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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88 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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45 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
53 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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25 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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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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82 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 ...