Linked Questions

129
votes
6answers
22k 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 ...
39
votes
2answers
18k 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 ...
38
votes
1answer
51k 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 ...
10
votes
2answers
5k 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/...
1
vote
1answer
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 ...
4
votes
1answer
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 ...
4
votes
1answer
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 ...
5
votes
0answers
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 ...
1
vote
1answer
316 views

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

Let’s begin with simple visualization: ...
0
votes
1answer
179 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. ...