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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Is there a test for comparing principal components decompositions between samples?

Is there any test for comparing the directions, magnitudes, etc of PCA results for different samples? I'm leaving the nature of the test deliberately vague because I'd like to hear all the various ...
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20 views

How can Principal Component Analysis applied to logistic regression or binary dependent variables? [on hold]

How to establish logistic principal component analysis? Is it meaningful to apply PCA to binary dependent variables?
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0answers
36 views

Using principal component analysis to reduce dimensions of data in R [on hold]

I have a dataset which includes 4 separate measures of intelligence. To simplify my analysis, I wanted to express them as "g" a variable based on the shared variation of the 4 measures. A paper I read ...
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1answer
29 views

Why do we use only the first component scores to construct different indices?

I have seen that in constructing indices by PCA the scores of only the first component is used. Although the first principle component explains the most variation contained in the data, often the VAF ...
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14 views

Multiple Factor analysis and squared cosines

I am a bit confused on how to proceed using the MFA analysis from FactoMineR in my data set. I am currently working with activity results of 15 bacteria (b1, b2, b3, b4, b5,.., b15), divided into 3 ...
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2answers
61 views

PCA: which original variables are used to construct a new variable?

Consider a new variable that is linear combination of original variables (e.g. one of the principal components). How can we find out which original variables "product" the new variable?
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1answer
48 views

PCA vs SVD - understanding difference and preference of SVD over PCA [duplicate]

I understand that PCA and SVD are similar - PCA removes the mean and SVD doesn't? I think I have an understanding of PCA - you would use it to reduce dimensions of data and separate it out into ...
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1answer
23 views

R caret - how to combine principal components and non-principal-component predictors?

Consider the following example. Suppose I want to model x in DF2 using everything else. While it makes sense to do ...
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28 views

Are PCA axes from different analysis comparable?

My issue is: I conducted two independent principal component analysis, and I am interested in comparing the variation of the values between the two analysis. In other words, I want to know if the ...
2
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1answer
50 views

Log Scale on Scree Plot for PCA/ICA/FA

I always found the concept of determining the "ideal" number of components/factors for an ICA/PCA/FA via a scree plot useful and quick, but also a bit shaky. In an effort to try to make the scree ...
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19 views

Determine concrete important factors in pca

after using the R function pcromp () I get how many factors might be important. How to determine what are these factors? Which statistical tool could I use? I appreciate your reply!
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1answer
99 views

Some questions on Principal Component Analysis (PCA)

I am trying to understand some descriptions about PCA (the first 2 are from Wikipedia): 1) Principal components are guaranteed to be independent only if the data set is jointly normally distributed. ...
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30 views

PCA + L1 equivalent to elastic net?

I am performing a logistic regression on a rather big dataset (700k+ samples and 1k+ features). I suspect that a lot of these features will be highly correlated and multicollinearity can be an issue. ...
3
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1answer
53 views

Reference for dimension reduction techniques

This is a follow-up question to Is PCA appropriate for comparing subsets of panel data?. It turns out that, yes, PCA is appropriate. But there are also many other ways to reduce n-dimensional data to ...
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25 views

Minimizing the Training data

I have a grey-box model of the form Y= a + b X1 + c X2. Where a, b and c are the coefficients based on regression. The regression variables X1 and X2 are determined based on ...
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43 views

How to create a composite of several variables without throwing information away

I want to create an index as a composite of several variables. It was recommend to me to use PCA. However, PCA discards too much information - essentially throwing away several of the variables in ...
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0answers
17 views

how to handle occlusion for face recognition?

If there some occlusion on face (such as sunglasses, mask, scarf), the recognition rate will decrease steeply? How to handle this case? I have do a survey, the PCA reconstruction method have been ...
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10 views

calculation of composite scores from factor analysis

We're designing a survey where we ask students to indicate their level of agreement (likert scale 1 - Strongly agree....5 - Strongly disagree. We ran factor analysis on the data and obtained 4 ...
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2answers
62 views

Is PCA appropriate for comparing subsets of panel data?

I have a large panel (5000+ subjects, 4 variables over 182 periods), and I've identified particular Granger-causal relationship in a large subset of those subjects (30% or so). I would like to somehow ...
0
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1answer
13 views

variable reduction

I have a set of features and a score in my dataset. Score is defined based on these features. What technique is used to see which of the features is more effective in the total score? I used anova and ...
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31 views

Can PCA scores be used as dependent variable?

I am working on a research project where I have several questions from a survey data that measures the same underlying quantity (my dv), possibly each with some measurement error. I was thinking about ...
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2answers
31 views

Dimensionality reduction (PCA) for plotting text documents on a graph

I have 50 text documents There are 500 possible words, after a stop list has been applied My term/document sparse matrix is therefore 50x500 I'd like to cluster these documents. One easy way to do ...
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29 views

Using a PCA to reduce response variables or multivariate multiple regression?

Does it make sense to use a PCA (principal component analysis) on a set of response Y variables and then conduct a multiple regression, or carry out a multivariate multiple regression all response ...
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1answer
18 views

Multivariate regression or PCA to reduce response variables?

I hope the title is self-explanatory, but essentially I want to know which method is better: does it make sense to use a PCA to reduce a number of response Y variables and then conduct a univariate ...
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0answers
21 views

Predict/impute one cell of matrix using all other cells

The question: I want to predict/impute one missing cell of a matrix using the contents of all other cells. Anyone have ideas on how to do this? The context: The matrix is n people's responses to m ...
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37 views

Can Principal Component analyses be applied to a counting trait?

I am analyzing a segregating population of plants coming from an hybridization process. The experiment consists in several field plots (according to an augmented design). In each plot a segregating ...
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1answer
108 views

Pull out most important variables from PCA

I would like to get the most important variables from a PCA result. I see two clusters in the plot. I now that is possible that there is no only one variable causing this, so maybe I would have to get ...
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21 views

Rotation of Mean Centred Variables in Principle Components Analysis

I'm looking to manually (Excel) perform PCA without any statistical packages such as R, but having trouble understanding how to rotate the original variables to find the maximum variance for the new ...
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25 views

Can I use non-linear PCA (CATPCA?) on my multivariate dataset that contains nominal AND ordinal data?

In my multivariate dataset I have over 100 objects/cases that have been coded on 20 different variables. Several variables are ordinal and several variables are nominal. Is it possible to use ...
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1answer
46 views

Principal components using correlation matrix in R

My understanding is that prcomp and princomp work off the dataset itself (row of observations, across variables in the columns). ...
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22 views

Intuition behind which eigenvectors to use in PCA for orthogonal regression

I am learning PCA, and while this seems like an obvious question, I can't seem to understand some of the ideas behind which eigenvectors to use when performing orthogonal regression with PCA. My code ...
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32 views

Can seasonality be detected / explored with principal components analysis?

I have a rainfall data consisting of around 95 years for the rows and twelve months of the year for columns. So this is a 95x12 matrix, not a column vector. Can I derive any idea about the months to ...
3
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1answer
47 views

When is it appropriate to use PCA as a preprocessing step?

I understand that PCA is used for dimensionality reduction to be able to plot datasets in 2D or 3D. But I have also seen people applying PCA as a preprocessing step in classification scenarios where ...
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17 views

Is subtracting the mean from PCA necessary when using an SVD result that is feature scaled?

I've applied SVD to the original data matrix and eliminated insignificant columns and rows from U and V^T respectively using the Sigma values. I multiplied together my optimized U, Sigma, and V^T ...
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2answers
51 views

Is it important to convert “integer” variables (with 0 or 1 values) to factors?

I am working on a high-dimensional dataset (1776 variables). When I read the csv file, R loads variables (with 0 or 1 values) as class of "integer". Is it important to convert these variables to ...
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1answer
19 views

What is the range of values that can be expected in the result of Principal Component Analysis (PCA)?

I want to normalize all of my preprocessing techniques between 0 and 1 so I want to know what the PCA range of values is so that I can apply a proper normalization to it. I applied PCA by using the ...
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16 views

Reconstructing a vector after projection

Suppose one has a matrix of data $X$, which is $n$ observations by $p$ dimensions. Let $P_\perp$ be a projection onto some $k<p$ dimensional subspace. Suppose one computes the principal direction ...
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19 views

Feature selection from wavelet transformation in R

I am new to wavelets. Currently, I am developing a prediction model using time series data. I am using the wavelets package in R. I am taking part of the time ...
3
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2answers
134 views

Best practice for dimensionality reduction using Principal Component Analysis (PCA) and/or Linear Discriminant Analysis (LDA)

Assume I have a dataset for a supervised statistical classification task, e.g., via a Bayes' classifier. This dataset consists of 20 features and I want to boil it down to 2 features via ...
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23 views

Is there an ideal number of measures in PCA ?

Working on a problem of extracting a minimal sub-set of criteria in a siting problem, I resorted to PCA, I have only 26 individuals (measures), I naturally thought it would be wise to ask whether that ...
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32 views

Correlation tests – multivariate correlation matrix?

I just got comments from a reviewer to a submitted article and didn't understand what I should do very well. Here are the tests I performed: We first used principal components analysis (PCA) to ...
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4answers
245 views

Clustering binary categorical data

I have some data where I have certain classes (c1, c2, c3, c4 ...) and the data comprises of binary vectors where 1 and 0 denote that an entry belongs to a class or not. The number of classes will be ...
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4answers
70 views

Impractically long running time PCA command in R RStudio

I am using R in RStudio on OS X ver. 10.9.2 on 1.7 GHz Intel Core i7 with 8 GB RAM. I am trying to run a PCA command (prcomp) and plots on a dataset with ...
3
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1answer
92 views

Not normalizing data before PCA gives better explained variance ratio

I normalized my dataset then ran 3 component PCA to get small explained variance ratios ([0.50, 0.1, 0.05]). When I didn't normalize but whitened my dataset then ran 3 component PCA, I got high ...
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0answers
26 views

Representing a distance matrix in the plane [duplicate]

I've worked with observations as vectors with both continuous and categorical variables. In both cases one can use dimensionality reduction techniques such as PCA (in the latter case through ...
0
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0answers
33 views

PCA proof needed for proportion of variance explained by L PCs = mean R-square from regression on PC scores

I observed the following relation and would like to know where I can find a general proof for this: Assume a data matrix $A = [a_{ij}]_{t x k}$. 1) Perform principal component analysis (PCA) using ...
2
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0answers
57 views

Factor analysis - CATPCA combined with conventional PCA

I have some concerns regarding factor analysis and especially about combining the factor analysis for an ordinal scale (categorical data) - CATPCA with conventional PCA. Basically, I need to enter my ...
0
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0answers
30 views

Principal component analysis, psychometrics, and number of items required

I saw that questions regarding sample sizes and PCA are asked here quite frequently. However, I was not able to find exactly the information I need. I plan to do a psychometric study and conduct a ...
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0answers
30 views

Effect sizes from regression analysis and factor loadings

To do a meta analysis, I try to calculate effect sizes. In an article by Shah and Ward, the authors do a regression analysis after combining various factors by a CPA to four factors. The factor ...
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2answers
83 views

R and SPSS differences in pca loadings

I performed two principal components analyses: in R and in SPSS - using the same dataset and the same variables. I got the same results - at least to some point. The eigenvalues are the same (I used ...