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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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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Maximum important variable using PCA [on hold]

In the following figure of biplot for PCA, can I say that petal.length and petal.width are most important variable in iris dataset because they are explaining most of the variance of the whole ...
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Kernel PCA wrong output

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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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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43 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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28 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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26 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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32 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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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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46 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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58 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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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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48 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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21 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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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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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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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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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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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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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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45 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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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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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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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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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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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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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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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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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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24 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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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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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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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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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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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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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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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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59 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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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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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 ...
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51 views

K-means cluster significance after PCA and hierarchical clusters in R with FactoMineR

I am using FactomineR to explore a set of continuous variables in a large set of sites (ecological data). I did a PCA and found the relevant principal components and their scores and such. Afterwards ...
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What to do in PCA when one variable has similar values in several principal component eigenvectors?

I'm performing a principal component analysis (PCA) using some economic variables of a region. I have six variables and I want to reduce them to two principal components. Most of the variables have ...
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Given that principal components are orthogonal, can one say that they show opposite patterns?

I've conducted principal component analysis (PCA) with FactoMineR R package on my data set. I have a general question: Given that the first and the second ...
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1answer
46 views

How to identify variables with significant loadings in principal component anlaysis

I have following example of principal component analysis using first 4 variables of iris data set (code in R): ...
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167 views

What is the “horseshoe effect” and/or the “arch effect” in PCA / correspondence analysis?

There are many techniques in ecological statistics for exploratory data analysis of multidimensional data. These are called 'ordination' techniques. Many are the same or closely related to common ...
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All samples are concentrated in one part of the PCA scatter plot, how is that possible?

I have an unusual result of a principal component analysis (PCA) that I am unsure how to explain or rationalise. I seem to have component #1 sending all the samples in one direction of the plot ...
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How to understand PCA output in R? [duplicate]

I have problem on understanding the PCA output. I found two ways of doing PCA: 1) pca <- prcomp(inputdata); 2) do it myself: ...
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How do random data eigenvalues change, as random variables are added?

I am using parallel analysis (Horn 1965) to determine how many principal components I can extract from my data. I can add more variables to my dataset, but I cannot add more cases (I know, that's ...
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65 views

Can PCA be applied for time series data?

I understand that Principal Component Analysis (PCA) can be applied basically for cross sectional data. Can PCA be used for time series data effectively by specifying year as time series variable and ...