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### How does Factor Analysis explain the covariance while PCA explains the variance?

Here is a quote from Bishop's "Pattern Recognition and Machine Learning" book, section 12.2.4 "Factor analysis": According to the highlighted part, factor analysis captures the covariance between ...
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### What are the assumptions of factor analysis?

I want to check if I really understood [classic, linear] factor analysis (FA), especially assumptions that are made before (and possibly after) FA. Some of the data should be initially correlated and ...
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### When can we speak of collinearity

In linear models we need to check if a relationship exists among the explanatory variables. If they correlate too much then there is collinearity (i.e., the variables partly explain each other). I am ...
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### Do I need to drop variables that are correlated/collinear before running kmeans?

I am running kmeans to identify clusters of customers. I have approximately 100 variables to identify clusters. Each of these variables represent the % of spend by a customer on a category. So, if I ...
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### Can the scaling values in a linear discriminant analysis (LDA) be used to plot explanatory variables on the linear discriminants?

Using a biplot of values obtained through principal component analysis, it is possible to explore the explanatory variables that make up each principle component. Is this also possible with Linear ...
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I am often disappointed with PCA plots in the scientific literature. Typically PCA plots do not provide a breakdown of the variables and their weights, just something like PCA1 (70% variance explained)...
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### How to interpret this PCA biplot coming from a survey of what areas people are interested in?

Background: I asked hundreds of participants in my survey how much they are interested in selected areas (by five point Likert scales with 1 indicating "not interested" and 5 indicating "interested"). ...
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### What are the units in this PCA biplot? [duplicate]

This is a plot of my data These are the values: ...
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### Can PCA allow to identify redundant variables that can be removed before doing cluster analysis?

I hope this is suitable for this forum: I am new to PCA and what I ultimately want to do is perform cluster analysis on my dataset. I have 20 physical descriptor variables for organisms, each with 300 ...
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### PCA, dimensionality, and k-means results: reaction to duplicating of variables

There are many excellent conversations on CV about the curse of dimensionality when applied to methods like k-means. The answer in the same post and other research (e.g., the paper titled "When Is ‘...
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### Which font to use in a plot to maximize clarity?

I was reading the Wikipedia page of the Bitstream Vera font (used by default by matplotlib), which says: The Bitstream Vera Sans Mono typeface in particular is suitable for technical work, as it ...
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### Geometric understanding of PCA in the subject (dual) space

I am trying to get an intuitive understanding of how principal component analysis (PCA) works in subject (dual) space. Consider 2D dataset with two variables, $x_1$ and $x_2$, and $n$ data points (...
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### What can be the reason to do feature selection based on variance before doing PCA?

I have noticed that when applying PCA to large datasets, people often will first subset the data considerably. Sometimes people just randomly take a subset of the features/variables, but often they ...
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### Interpreting overlapping arrows on a PCA biplot: does it mean that the variables are redundant?

I'm new in principal component analysis (PCA) and I don't really understand the biplot representation of its results, so I would really appreciate some guidance. Having the example of the illustration ...
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I'm running a PCA over a data set of $N \times p$ size ($N\approx 1000$ being the number of measurements and $p\approx 200$ being the number of dimensions/predictors). I expect many of the predictors ...