pca

Solved – Mahalanobis distance via PCA when $n<p$

by

I have an $ntimes p$ matrix, where $p$ is the number of genes and $n$ is the number of patients. Anyone whose worked with such data knows that $p$ is always larger than $n$. Using feature selection I have gotten $p$ down to a more reasonable number, however $p$ is still greater than $n$. I … Read more

Solved – PCA: Eigenvectors of opposite sign and not being able to compute eigenvectors with `solve` in R

by

I'm learning PCA in R language. I met two problems right now that I don't understand. I am performing a PCA analysis in R on a 318×17 dataset using some custom code. I take eigen function in R to find eigenvalues and eigenvectors. But my 1st and 3rd eigenvectors are of the opposite sign to … Read more

Solved – PCA: Eigenvectors of opposite sign and not being able to compute eigenvectors with `solve` in R

by

I'm learning PCA in R language. I met two problems right now that I don't understand. I am performing a PCA analysis in R on a 318×17 dataset using some custom code. I take eigen function in R to find eigenvalues and eigenvectors. But my 1st and 3rd eigenvectors are of the opposite sign to … Read more

Solved – Reconstruction of original dataset through loadings in PCA

by

This question already has an answer here: How to reverse PCA and reconstruct original variables from several principal components? (1 answer) Closed 5 years ago. I am very new to PCA and I was trying, just as excercize, to reconstruct original dataset from loadings. Let's suppose I have a matrix A corresponding to the original … Read more

Solved – Reconstruction of original dataset through loadings in PCA

by

This question already has an answer here: How to reverse PCA and reconstruct original variables from several principal components? (1 answer) Closed 5 years ago. I am very new to PCA and I was trying, just as excercize, to reconstruct original dataset from loadings. Let's suppose I have a matrix A corresponding to the original … Read more

Solved – Fundamental difference between PCA and FA

by

According to this, the fundamental difference between PCA and FA can be illustrated via the following image: So, the direction of arrows changes. According to this answer and a few others: Loadings are coefficients in linear combination predicting a variable by the (standardized) components. Also, according to this, loadings are: correlation between a component and … Read more

Solved – Fundamental difference between PCA and FA

by

According to this, the fundamental difference between PCA and FA can be illustrated via the following image: So, the direction of arrows changes. According to this answer and a few others: Loadings are coefficients in linear combination predicting a variable by the (standardized) components. Also, according to this, loadings are: correlation between a component and … Read more

Solved – Beginner references to understand probabilistic principal component analysis (PPCA)

by

I am totally new to machine learning. I started studying PCA from Jonathan Shlens, 2005, A Tutorial on Principal Component Analysis. The paper provides some concrete examples, and background mathematics so anyone can take the paper and understand PCA thoroughly. This paper is simply amazing. I am interested in understanding probabilistic model used for getting … Read more