Linked Questions

0
votes
0answers
83 views

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 ...
328
votes
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 ...
103
votes
6answers
11k views

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 ...
88
votes
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 ...
68
votes
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 – ...
73
votes
2answers
19k views

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.
20
votes
2answers
9k 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 ...
12
votes
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: ...
12
votes
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 ...
9
votes
1answer
3k views

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....
8
votes
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 ...
9
votes
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 ...
2
votes
1answer
4k views

Princomp() outputs seemingly wrong PCA scores with cor=TRUE input argument

Given a 2D data frame d that is centered and scaled: ...
5
votes
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: ...
3
votes
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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