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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How do you get the principal components of one matrix along the principal directions of another matrix?

I have a data matrix, A, on which I have performed principal component analysis (PCA) using the prcomp function in R. This gives me the ...
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18 views

Inconsistent Performance of PCA Results from SPSS

I've completed PCA with my dataset (16 variables) and extracted 3 factors. I then created an Excel spreadsheet where I can enter in user provided data and calculate the scores for each of the three ...
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15 views

Convert principal components based on covariance into principal components based on correlation

I am wondering if there is any way to mathematically express the change in direction of the principal components from the $2\times2$ covariance matrix to the correlation matrix. In other words, if ...
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29 views

Generalization error of PCA and kernel PCA

I've been recently reading Shawe-Taylor et al. 2005, On the Eigenspectrum of the Gram Matrix and the Generalization Error of Kernel PCA, where the authors analyze the squared residual of kernel ...
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20 views

Naive Bayes Binary Classification with Binary Features

I have a dataset with two classes $C_0$ and $C_1$. I have around $10$ to $20$ features that take binary values (either $0$ or $1$). My dataset has around $10000$ instances, with only a hundred of ...
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Is it possible to use PCA twice, first on several subsets of data, and then again on the main components of those subsets?

I am interested in understanding if it is possible to use PCA twice, first on several subsets of data, and then again on the main components of those data subsets. I'm not entirely sure if this will ...
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27 views

Does PCA of high-dimensional data yield inaccurate reconstruction?

I have a data $1600\times5000$ matrix $X$ containing 1600 datapoints in 5000-dimensional space. Using MATLAB's built-in pca function, I get the loadings in ...
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22 views

Application of PCA in clustering [on hold]

How can I use results of principal component analysis (PCA) from Matlab in a clustering algorithm written in Java? The results of the clustering algorithm are unsatisfactory at higher dimensions, so ...
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46 views

Is PCA still done via the eigendecomposition of the covariance matrix when dimensionality is larger than the number of observations?

Disclaimer: I understand that this question has been answered on CV, but I am asking about the particular implementation, which AFAIK, is not answered yet. I have a $20\times100$ matrix $X$, ...
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22 views

Nested PCA : is it the same to reduce dimension one time by m and to reduce m times by 1?

My data is initially represented in a vector space $E$ of dimension $n$. I want to reduce the dimension by $m$, so I apply a PCA process to obtain a vector space $E'$ of dimension $n-m$. If I had ...
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35 views

Interpretation of biplot in PCA

Blue points all appear in the lower right-hand quadrant in the plane formed by the first two principal components. Is it a good interpretation of the biplot (right panel) to say that blue points ...
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Are composite factor scores produced by PCA are automatically standardize?

I have done a Principal Component Analysis (rotated factors, varimax, etc.) which gave me 6 factors (F1, F2, F3, F4, F5, and F6). From this PCA, I saved the factor scores for regression (In SPSS, I ...
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21 views

How to reconstruct the observed data using weighted-PCA in Matlab?

Calling pca function in Matlab using the inverse of variances as variable weights: ...
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33 views

How to figure out whether PCA can be performed on a data set or not?

I do have idea on the way PCA works but I do not know how to figure out whether a high dimensional data set is suited for PCA compression. I googled for some algorithms but could find any. Are there ...
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56 views
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Controling segmentation process in order to get usable segments

My aim is to create segments based on survey data. This in it self is quite straight forward: I use PCA to extract information from the survey answers, and then ...
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Line that separates data partitioned by the first principal component of PCA

I want to partition some 2d points into 2 groups (clustering). The way that I need to do it is by using PCA to find the first principle component. Then I project the data to find 1d projections. Then ...
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9 views

Weka Ranker principal component analysis

I'm using the software WEKA to perform principal component analysis on a dataset, using the attribute evaluator "principal components" with the search method "ranker". Everything works fine but I was ...
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55 views

Structure of semantic relationships using Latent Semantic Analysis

I am struggling to answer the below question: How would you describe the structure of semantic relationships among the terms from a document collection using principles of Latest Semantic Analysis? ...
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16 views

First factor in Exploratory Factor Analysis and Principal Component Analysis

I am conducting an Exploratory Factor Analysis (EFA) and I was wondering if it is common or appropriate to say that the first factor is the strongest or most important of the model as it is explaining ...
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37 views

PCA on fixed effects variables

I would like to run a panel logit model with fixed-effects on three indices, i.e. company, industry and time. The data set comprises around 1000 companies (index i) and 15 industries (j) over 6 years ...
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Reference for this claim: important features in data can be “hidden” in the higher PCA axes that are typically thrown out [duplicate]

I remember reading a paper a while ago that demonstrated some cases in which PCA would fail to capture important features of a data set in the first few principal components, but where those features ...
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21 views

Reproducing levels when PCA has been done on changes

I'm trying to do PCA on a time series which is not stationary. So I did the PCA on its daily differences, which are indeed stationary. I can then reproduce the daily changes using selected eigen ...
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11 views

Can I perform a PCA on species count differences instead on the species counts themselves?

I'm busy with the analysis of bird community change through time on a couple of sites and want to relate it to environmental covariates. I use the R-package vegan ...
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9 views

Using Princomp() in R [migrated]

After running Principal Component Analysis in R using princomp() and running summary() on the results I got a list of ...
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60 views

How to compute component or factor scores when the analysis is based on polychoric/tetrachoric correlations?

[This question is modified based on suggestion from @ttnphns] I am doing linear principal component analysis (PCA) based on polychoric correlations between the variables (rather than on native ...
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26 views

minimization of weighted frobenius norm for pca

So my problem is i like to derive pca solution as the maximum likelihood estimate for the true data.So basically i am assuming that my measured data has two component one is low rank component and ...
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26 views

Justification for variable reduction by removing predictors with near zero variance

I have a large number of variables that I'm trying to reduce, and I've stumbled on Kuhn's (2008) suggestion that I eliminate variables with zero or near-zero variance. This makes sense to me, it's ...
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7 views

Computing statistical significance for correlations between PCA scores

What would be the best way to statistically compare difference between component scores in PCA between different days? I used PCA for 10 days of my experiment. Since I have 5 principal components for ...
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25 views

PCA on nominal-ordinal data

I am trying to "decorrelate" two variables: one is binary categorical (cluster assignments) and the other one is ordinal (0 to 4 ratings). I have browsed around and came across Nonlinear principal ...
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40 views

PCA/MFA for (graphical) dimension reduction: what to do with very small explained variance?

I ran a Multiple Factor Analysis on a data set with 3,924 rows and 96 columns, of which six are (unordered) categorical, with 12-14 categories in each, and the rest are numeric, mean-centered and ...
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10 views

Minimum sample size required for sparse PCA

What is the minimum sample size that we need for filtering variables using sparse principal component analysis (sparse PCA, SPCA)?
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20 views

can we do pca analysis by binary characters? [duplicate]

I have a question about pca analysis. can we do it for binary characters? (for example for morphological characters). it seems that multistate characters are more appropriate for pca.could you please ...
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2answers
44 views

Why do we need PCA whitening before feeding into autoencoder?

In the UFLDL tutorial, we saw that autoencoder can not compress data with uncorrelated random variables. 'If the input were completely random---say, each variable comes from an IID Gaussian ...
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How to choose the regularization parameter in ZCA whitening?

ZCA whitening can use regularization, as in $$ \tilde{X} = L\sqrt{(D + \epsilon)^{-1}}L^{-1}X, $$ where $LDL^\top$ is an eigendecomposition of the sample covariance matrix. What's a good choice for ...
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47 views

What does “varimax” mean in SPSS factor analysis?

In the rotation options of SPSS Factor Analysis, there is a rotation method named "Varimax". If I choose this option, does it mean the same orthogonal rotation techniques of Principal Component ...
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Estimating the opinion of a user by looking at opinions of other users

First of all, a bit of background: i am not a statistics expert but i am an enthusiast about data analysis. I have this list of "items" and for each item i have a list of "users" and the vote that ...
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16 views

Finding redundant variables

I have data of several variables (all numeric or continuous) on different subjects. I want to find out if some of these variables are highly correlated so that not all need to be determined. This will ...
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1answer
37 views

factor analysis with missing values

I have data on about 25 subjects and 30 variables with about 20 missing values. The data is missing at random. What will be the best approach to perform factor analysis. How is factor analysis versus ...
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19 views

Does biplot() function in R use rotations or loadings to plot arrows? [duplicate]

For following code performing principal component analysis: ...
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33 views

Establishing an empirical relationship among environmental properties using PCA and Multiple Regression

So, this post is a follow-up to a previous question of mine asked recently (Percentage of contribution of multiple factors to a single dependent variable), with more details on what I am trying to ...
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31 views

How to interpret this PCA biplot to determine which attributes to pick? [duplicate]

I'm running PCA on my dataset which can be found here. There are 6497 instances and 12 attributes with 13th column is the class (ranging from 3 - 9) for wine quality. I've read what PCA is supposed ...
3
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1answer
39 views

Interpreting standard deviation for PCA

I'm running PCA on my dataset using r and need some help interpreting the standard deviation results. Here are the results ...
2
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1answer
26 views

How to use factor analysis / PCA / regression for data having serial IV and DV?

I have data regarding effect of a food chemical on blood and urine levels as well as effect on blood sugar and cholesterol. So I have following variables: ...
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37 views

How to interpret PCA plots made using R [duplicate]

I'm using PCA for the first time and just experimenting with it. I used PCA on my dataset that can be found here ...
3
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1answer
81 views

Conclusions from output of a principal component analysis

I am trying to understand output of principal component analysis performed as follows: ...
2
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2answers
158 views

Applying PCA to test data for classification purposes

I've recently learned about the wonderful PCA and I've done the example outlined in scikit-learn documentation. I am interested to know how I can apply PCA to new data points for classification ...
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28 views

Condensing spatial time series data and spatial interpolation

I have spatio-temporal albedo (roughly, the 'reflectivity' of earth's surface) dataset, from NASA's MODIS satellite, for a 130 square kilometer area. The dataset contains raster files in the NetCDF ...
2
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1answer
72 views

Method for constructing large data set from smaller data set?

Is there a method for creating a large data set from a smaller one? I have a data set of anthropometric variables (e.g. stature, leg length, arm length and so on) So I have 7 variables and 1774 ...
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150 views

Loadings vs eigenvectors in PCA: when to use one or another?

In principal component analysis (PCA), we get eigenvectors (unit vectors) and eigenvalues. Now, let us define loadings as $$\text{Loadings} = \text{Eigenvectors} \cdot \sqrt{\text{Eigenvalues}}.$$ I ...
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19 views

Why is feature normalization important in PCA? [duplicate]

If feature normalization is not performed, does the algorithm give incorrect results or is it it inefficient or both?