# Linked Questions

25 questions linked to/from Why PCA of data by means of SVD of the data?
0answers
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### PCA: When using eigendecompostion instead of single value decompostion [duplicate]

If you want to perform a PCA, I guess that using SVD will always work. Eigendecomposition on the covariance matrix only works when your data is not high dimensional(so n > p). But I'm wonder if there ...
3answers
199k views

### Relationship between SVD and PCA. How to use SVD to perform PCA?

Principal component analysis (PCA) is usually explained via an eigen-decomposition of the covariance matrix. However, it can also be performed via singular value decomposition (SVD) of the data matrix ...
6answers
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### Is there an intuitive interpretation of $A^TA$ for a data matrix $A$?

For a given data matrix $A$ (with variables in columns and data points in rows), it seems like $A^TA$ plays an important role in statistics. For example, it is an important part of the analytical ...
4answers
100k views

### PCA and proportion of variance explained

In general, what is meant by saying that the fraction $x$ of the variance in an analysis like PCA is explained by the first principal component? Can someone explain this intuitively but also give a ...
4answers
38k views

### What is the difference between R functions prcomp and princomp?

I compared ?prcomp and ?princomp and found something about Q-mode and R-mode principal component analysis (PCA). But honestly – ...
2answers
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### What is a “kernel” in plain English?

There are several distinct usages: kernel density estimation kernel trick kernel smoothing Please explain what the "kernel" in them means, in plain English, in your own words.
2answers
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### 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 ...
1answer
16k views

### Steps done in factor analysis compared to steps done in PCA

I know how to perform PCA (principal component analysis), but I would like to know steps that should be used for factor analysis. To perform PCA, let us consider some matrix $A$, for instance: ...
3answers
8k views

### What fast algorithms exist for computing truncated SVD?

Possibly off topic here, but there exist several (one, two) related questions already. Poking around in the literature (or a google search for Truncated SVD Algorithms) turns up a lot of papers that ...
1answer
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### Is PCA still done via the eigendecomposition of the covariance matrix when dimensionality is larger than the number of observations?

I have a $20\times100$ matrix $X$, containing my $N=20$ samples in the $D=100$-dimensional space. I now wish to code up my own principal component analysis (PCA) in Matlab. I demean $X$ to $X_0$ first....
3answers
16k views

### Understanding the output of SVD when used for PCA [duplicate]

I'm doing principal components analysis (PCA) on quite a bit of data (3000 variables, 100079 data points). I'm doing this mostly for fun; data analysis is not my day job. Normally, to do a PCA I ...
1answer
8k views

### Difference between scikit-learn implementations of PCA and TruncatedSVD

I understand the relation between Principal Component Analysis and Singular Value Decomposition at an algebraic/exact level. My question is about the scikit-learn implementation. The documentation ...
1answer
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### Princomp() outputs seemingly wrong PCA scores with cor=TRUE input argument

Given a 2D data frame d that is centered and scaled: ...
4answers
718 views

### When you do PCA (or any dimensionality reduction), what is “the number of dimensions”?

Fundamental question When you do PCA (or any dimensionality reduction), what is "the number of dimensions"? I always thought that the thing you measure (ie, the variable) is the number of dimensions: ...
2answers
636 views

### Is there any situation where PCA performs better than SVD?

It's for a text clustering application. There are around 25 documents and 50k features (from TF-IDF), so I was expecting SVD to be a better choice. I am using sklearn's PCA and TruncatedSVD functions ...

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