Linked Questions

2
votes
1answer
4k views

PCA demeaning the data [duplicate]

What is the motivation for demeaning the data when doing PCA. I've been told to do it, but I've never heard a good and/or intuitive reason for it. Is this a case where doing it just makes the math ...
5
votes
1answer
11k views

PCA on non-centered data [duplicate]

How does the mean influence PCA? What happens if I use PCA on data with a mean $\ne0$?
2
votes
1answer
162 views

Is mean centering required in regression? if so, what does it do? [duplicate]

Let say we have a dataset, $\mathbf{X}$ of $m$ instances, and $n$ features, and a target scalar variable $\mathbf{y}$ ($m$ instances). Now I want to do a regression so, I try to fit a hyperplane $ y =...
3
votes
0answers
255 views

What does it mean to compute eigenvectors of a covariance matrix if the data were not centered first? [duplicate]

Say $\mathbf{X} \in \mathbb{R}^{n \times p}$ and $\boldsymbol{\Sigma} = \frac{1}{n}\mathbf{X}'\mathbf{X}$. The eigenvector decomposition of $\boldsymbol{\Sigma}$ gives $\boldsymbol{\Sigma} = \mathbf{P}...
0
votes
0answers
89 views

Centering variables before running PCA [duplicate]

I am learning about PCA, regarding PCA I need to know that given a dataset is it always necessary to use centering? what if I don't center the variables used in PCA?
1
vote
0answers
87 views

PCA Why covariance matrix? [duplicate]

At PCA why we find the Eigenvalues of the covariance matrix and not the eigenvalues of the matrix $A\times A^T$, where $A$ is the data matrix and $A^T$ its transpose? I saw a professor at YouTube who ...
151
votes
5answers
201k views

How exactly does one “control for other variables”?

Here is the article that motivated this question: Does impatience make us fat? I liked this article, and it nicely demonstrates the concept of “controlling for other variables” (IQ, career, income, ...
32
votes
3answers
49k views

PCA on correlation or covariance: does PCA on correlation ever make sense? [closed]

In principal component analysis (PCA), one can choose either the covariance matrix or the correlation matrix to find the components (from their respective eigenvectors). These give different results (...
30
votes
1answer
41k views

Doing principal component analysis or factor analysis on binary data

I have a dataset with a large number of Yes/No responses. Can I use principal components (PCA) or any other data reduction analyses (such as factor analysis) for this type of data? Please advise how I ...
31
votes
1answer
32k views

How does centering make a difference in PCA (for SVD and eigen decomposition)?

What difference does centering (or de-meaning) your data make for PCA? I've heard that it makes the maths easier or that it prevents the first PC from being dominated by the variables' means, but I ...
10
votes
1answer
11k views

Questions on PCA: when are PCs independent? why is PCA sensitive to scaling? why are PCs constrained to be orthogonal?

I am trying to understand some descriptions of PCA (the first two are from Wikipedia), emphasis added: Principal components are guaranteed to be independent only if the data set is jointly normally ...
16
votes
1answer
14k views

Need for centering and standardizing data in regression

Consider linear regression with some regularization: E.g. Find $x$ that minimizes $||Ax - b||^2+\lambda||x||_1$ Usually, columns of A are standardized to have zero mean and unit norm, while $b$ is ...
4
votes
1answer
7k views

User segmentation by clustering with sparse data

Imagine that I have 100k users and 1k categories. For each user, up to 5 categories, I know how much money they have spent. Obviously my data is very sparse. Now I want to group users by the money ...
2
votes
2answers
4k views

How can one interpret the Stata output for Multiple Correspondence Analysis?

As an alternative to conducting exploratory factor analysis on a set of data, with binary responses, I have been suggested to use Multiple Correspondence Analysis (MCA). Following is a curtailed and ...
8
votes
2answers
910 views

Why does the first eigenvector in PCA resemble the derivative of an underlying trend?

I am using PCA to analyze several spatially related time series, and it appears that the first eigenvector corresponds to the derivative of the mean trend of the series (example illustrated below). I ...

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