Linked Questions

131 votes
6 answers
23k 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 ...
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  • 2,255
39 votes
2 answers
19k views

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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  • 3,145
38 votes
1 answer
53k 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 ...
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  • 381
11 votes
2 answers
6k views

Difference between PCA and spectral clustering for a small sample set of Boolean features

I have a dataset of 50 samples. Each sample is composed of 11 (possibly correlated) Boolean features. I would like to some how visualize these samples on a 2D plot and examine if there are clusters/...
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2 votes
1 answer
12k views

PCA on Binary Data [duplicate]

I having binary data set (yes/no), so can I apply PCA on that. Is it mathematically correct to do that. In my opinion Binary variable can only be subjected to logical operations, so how it can be ...
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  • 315
4 votes
1 answer
3k views

Is continuous inputs an assumption of factor analysis?

Should we use only continuous inputs for factor analysis (FA)? My data is a mix of continuous and categorical inputs: one of the inputs has only 600, 700 and 1000 as values. I found that principal ...
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  • 3,731
4 votes
1 answer
2k views

Is it acceptable to rotate factors with PCA for binary data?

What issues, if any, might there be in rotating factors in order to obtain factor/component loadings of binary data? Is it acceptable to rotate the factors when doing a traditional PCA? (Assuming I’m ...
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5 votes
0 answers
3k views

Is MCA equivalent to PCA when all variables are binary?

I am looking to apply principal component analysis on binary (true/false) data, and I have come across the "equivalence between PCA and MCA" (Multiple Correspondense Analysis) for binary data, but ...
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  • 51
1 vote
1 answer
325 views

Factor analysis for ordinal data converted from binary ordinal data [closed]

Let’s begin with simple visualization: ...
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0 votes
1 answer
259 views

Should I remove ID variable before PCA?

My data has 50 features like... 1. student_num 2. sub1 3. sub2 4. sub3 .. .. 50. hasFailed There's one row for each student. I have 12000 students so 12000 records. My goal is to reduce dimensional. ...
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  • 103