Tagged Questions

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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What will be my data set in second level of cluster nodes

Each sensor node collected the 125 seawater temperature at 1m depth. SO my data at first level of cluster nodes is (125 * 7)i.e 125 days reading. I am compressing the data using Principal Component ...
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2answers
523 views

How to understand “nonlinear” as in “nonlinear dimensionality reduction”?

I am trying to understand the differences between the linear dimensionality reduction methods (e.g., PCA) and the nonlinear ones (e.g., Isomap). I cannot quite understand what the (non)linearity ...
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1answer
70 views

Meaningful inference about data structure based on components with low variance in PCA

A lot of microbiome (microbial ecology) papers that I have come across use either principal component analysis (PCA) or principal coordinate analysis (PCoA) to make conclusions about the data. A lot ...
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1answer
445 views

Confused about the visual explanation of eigenvectors: how can visually different datasets have the same eigenvectors?

A lot of statistics textbooks provide an intuitive illustration of what the eigenvectors of a covariance matrix are: The vectors u and z form the eigenvectors (well, eigenaxes). This makes sense. ...
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0answers
31 views

Non-decaying eigenvalues in Kernel PCA with small kernel width

I noticed that when I use a small width kernel (RBF) with PCA, I get my desired result (clustering in this case), but I do not get a decay in the eigenvalues (they stay about the same value). Is that ...
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13 views

Construct validity technique for small sample size

I have developed and pilot tested a quantitative survey instrument. I got only 40 respondents. No, I need to test its construct validity with the available data (N=40). What statistical analysis I can ...
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1answer
40 views

How to select a subsample of fixed size to maximize its total PCA variance?

I would like to use PCA to help design my genomics experiment. I can only afford to perform my experiment on a limited number of genotypes so would like to maximize the variation of the ones I ...
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1answer
22 views

Can nonlinear clustering produce 'fake' results?

I know that overfitting in classification is possible when using, for instance, an RBF kernel, due to its infinite dimension. But, is it possible to get (in a similar manner) fake clustering results ...
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1answer
40 views

How can I estimate a principal component from incomplete data?

I would like to know the best way to estimate a principal component's latest value, if I only have partial information about the latest variable data points: Assuming I have 5 variables: ...
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59 views

What is PCA doing with autocorrelated data?

Just because some correspondent posed an interesting question concerning methods of computation of autocorrelation, I began to play with it, nearly without any knowledge about time series and ...
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6 views

appling pca on spss with mixed type of variables (nominal-binary-ordinal-continuous)

I have a database, mixed type of variables (nominal-binary-ordinal and continuous) I want to apply pca with spss not R package , Can I ?? and how ?? many thanks..
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1answer
49 views

Why are there only $N-1$ principal axes for $N$ data points if the number of dimensions is larger than $N$?

In PCA, when the number of dimensions $d$ is much much greater than the number of samples $N$, why is it that you will have at most $N-1$ non-zero eigenvectors? In other words, the rank of the ...
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1answer
49 views

PCA clustering results 'ruined' by standartization

I have some data that I want to classify. As an initial measure, I did PCA for the data and I saw two distinct clusters of my data. However, when standardizing the data, the two clusters disappear. ...
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5answers
968 views

Is there any good reason to use PCA instead of EFA?

In some disciplines, PCA (principal component analysis) is systematically used without any justification, and PCA and EFA (exploratory factor analysis) are considered as synonyms. I therefore ...
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0answers
33 views

What's wrong with t-SNE vs PCA for dimensional reduction using R?

I have a matrix of 336x256 floating point numbers (336 bacterial genomes (columns) x 256 normalized tetranucleotide frequencies (rows), e.g. every column adds up to 1). I get nice results when I run ...
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1answer
61 views

How to know which feature mainly led to the prediction?

I have a classification problem where I use a model (say Logistic regression or SVM) to determine whether an instance belongs to class 0 or class 1. For a certain prediction on a test instance X, if ...
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1answer
60 views

Difference between svd() and prcomp() in R

Conceptually, aren't the eigenvalues of a correlation matrix and the singular values of the associated scaled data matrix supposed to be the same? The below illustration is saying that it isn't so. ...
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1answer
27 views

PCA or MCA for binarized data

I am working with bioinformatics and I have data that looks like the following: ...
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0answers
28 views

Principal components analysis on nested data

I'm working on a piece of analysis that requires identifying a small set of variables that summarize the variation found in a larger set of principal observations on teacher practice. Given the nature ...
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0answers
35 views

Understanding kernel PCA

Kernel SVMs are explained as follows: Apply kernel method to original data Check if we have a linear separator in the kernelized space. Map linear separator back to original space Is it fair to ...
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0answers
32 views

EFA versus PCA in SPSS

If I run a dimension reduction analysis in SPSS with Principal Components as extraction methods and Promax as rotation method, am I conducting an Exploratory Factor Analysis or a Principal Components ...
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0answers
30 views

Does it mean anything when all items load negatively on one factor when several factors are output?

So I am fairly familiar with factor analysis, and am aware of answers here and here that tangentially address my question. I believe I am right in my answer to the question I'm asking, but I wanted to ...
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2answers
60 views

Motive behind preserving variance

Dimensionality reduction techniques preserve some properties of the data. I was wondering how preserving variance (as PCA does) can be helpful? Precisely speaking, PCA takes the covariance matrix and ...
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2answers
56 views

How to transform test set to the training set transformed space with PCA?

I'm working on a text classification project, and I want to reduce the tf-idf matrix dimension with Principal Component Analysis (PCA) and then train my model with this, which is pretty ...
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12 views

Statistical arbitrage using eigen portfolios [migrated]

I was trying to understand below paper https://www.math.nyu.edu/faculty/avellane/AvellanedaLeeStatArb071108.pdf Page 20 explains about "Entering a trade". I wan't to know clearly what it means to ...
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1answer
333 views

Is there any advantage of SVD over PCA?

I know how to calculate PCA and SVD mathematically and I know that both can be applied to Linear Least Squares regression. The main advantage of SVD mathematically seems to be that it can be applied ...
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0answers
41 views

Imputation of missing values for doing PCA in R [duplicate]

I have a dataset with approximately 4000 rows and 150 columns. I want to predict the values of a single column (= target). The data is on cities (demography, social, economic, ... indicators). A lot ...
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0answers
70 views

Small loadings in all variables, PCA analysis is ok?

I'm performing a PCA analysis on a set of 5 variables, whose correlation matrix is: ...
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0answers
37 views

Using principal components to perform further PCA

I am working with principal component analysis for the first time. I have managed to extract the principal components of one set of data (say data1) using prcomp(). ...
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2answers
115 views

Why does my loading matrix following PCA with a varimax rotation contain only ones and zeros?

I'm running a PCA using the R function prcomp. This is the function: d2.pca <- prcomp(sel.d2, center=TRUE, scale.=TRUE) So ...
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1answer
29 views

Bi-normal separation feature selection (BNS) in R

I'm doing binary classification on highly dimensional text data, with a biased class distribution. After reading this paper, i found out about BNS feature selection. Is there any package that ...
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0answers
23 views

How to program automated shrinkage for a subset of terms in R?

I've got data from a randomized experiment that includes a lot of covariates. I'm interested $\delta$ from a model of the form $y = g(\delta T + X'\beta+ \epsilon)$, where $T$ is randomly assigned and ...
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0answers
34 views

PCA on spatial precipitation data time series

I have precipitation time series data stored in a 3D matrix called 'pre' (dim1/2=position (index), dim3=time). I want to do a principal component analysis in order to detect the main variance and thus ...
3
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2answers
213 views

2D projection to maximise separability

I have a set of 500 points in 5D. Each point belongs to one of five classes, and the class labels are known. I’d like to visualise the dataset in 2D such that the classes would be separated as much ...
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2answers
76 views

What're the differences between PCA and autoencoder?

Both PCA and autoencoder can do demension reduction, so what are the difference between them? In what situation I should use one over another?
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1answer
76 views

Which PCA (or kernel PCA) basis better describes a single test sample?

I have two PCA bases obtained by decomposition of two groups of training data. I also have some samples of test data. How can I decide which PCA basis fits better each test sample? I tried to ...
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1answer
169 views

What is the proper association measure of a variable with a PCA component?

I am using FactoMineR to reduce my data set of measurements to the latent variables. Now, the variable map is clear for me to interpret, but I am confused when ...
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0answers
31 views

PCA run on any 4 tenors of interest rate swaps results in identical or exact opposite zscores of the residuals

I'm stumped when I run PCA on 4 tenors on a yield curve, it can be any 4 tenors, any length of data, and it's always the same thing I observe. The z-scores of my residuals are identical to each ...
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2answers
78 views

How to interpret PCA for data reduction?

I have 19 currency pairs like USD.AUD, USD.CAD, etc. Also 82 cross currency pairs like ...
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2answers
61 views

Classifying by performing PCA for positive and negative datasets separately

I have a dataset with binary labels, and I try to figure out whether the data can be classified and yield the ground-truth labels. I thought to try PCA for the data with each of the labels, and see ...
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0answers
28 views

Selection of variables using principal component analysis

I have constructed four dummy variables for the source of drinking water as homewell drinking, tube well drinking, agro well drinking & tap water. From the principal component analysis, I found ...
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0answers
49 views

How to interpret component matrix scores in Principal Components Analysis

Following on from this question I'm currently using Principal Components Analysis in SPSS to investigate dimension reduction across n (33) binary variables. This is for dimension reduction and to ...
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1answer
71 views

Identifying the coefficients of a principal component

Suppose that a two-dimensional random variable $X$ has a covariance matrix given by $$ \Sigma = \pmatrix {1 & -2\\ -2 & 4}$$ One of the three linear combinations below corresponds ...
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0answers
24 views

Is there any characterization of the score matrix obtained with PCA on a very correlated dataset?

I have a dataset $X$ of very correlated variables. With Principal Component Analysis I have computed the matrix of component scores $Z$. Is there any particular property of $Z$ in this case? I am ...
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2answers
57 views

Why is the eigenvector in PCA taken to be unit norm?

In deriving the eigenvectors for PCA, the vector is subject to the condition that it should be of unit length. Why is this so?
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0answers
61 views

Relative weights in regression analysis in SPSS: Matrix-approach vs. factor and regression

I am trying to perfome a relative weight analysis as described by Johnson (2000). I have 13 predictors to a more general indicator. Initially, I started by: running a principal component analysis ...
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2answers
251 views

What is the difference between ZCA whitening and PCA whitening?

I am confused about ZCA whitening and normal whitening (which is obtained by dividing principal components by the square roots of PCA eigenvalues). As far as I know, $$\mathbf x_\mathrm{ZCAwhite} = ...
3
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0answers
39 views

Can you do a PCA on 3-point Likert to weigh items 20k responses

I am developing an inventory tool that has 21 items. I need to determine the weight of each of the items, as the presence of some may give a higher overall rating to a scenario than the presence of ...
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1answer
78 views

How can there be a linear correlation between two PCA components?

I perform principal component analysis (PCA) on a dataset, and then plot the first and the second principal components. I get the following phenomenon: one principal component appears to be a linear ...
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0answers
61 views

Bartlett's Sphericity Test for PCA Failure

I am using XLStat for a PCA of time-series water chemistry data. I have 23 analytes and 29 samples. I am using a correlation matrix for PCA as I find it more interpretable in the context of ...