# Data Augmentation using Eigenvalues and Eigenvectors

Recently, I have come across a paper which has used a unique way of augmenting the data. If the data has multiple channels say we have a $x_i , i=1...N$ as a column feature vector. If we compute the the eigenvalues and eigenvector of the whole samples $x$, the following is a method of augmenting the data to increase the number of samples:

$x_{aug}=x+\alpha_1\lambda_1\boldsymbol{p_1}+\alpha_1\lambda_1\boldsymbol{p_1}+\ldots$

In which $\alpha$ is a random number, usually from a normal distribution, $\lambda_i$ is a eigenvalue and $p_i$ is a eigenvector.

I couldn't find any sources for this. Can anyone elaborate?

• I came across some papers which referred to "eigenvalue noise". is this the same concept? – Siavash S Nov 11 '14 at 2:39
• So are the using this process to generate more data to add to their sample... or what exactly? – gung Nov 11 '14 at 2:42
• @gung Yes, I wanted to see what is the rationale behind it – Siavash S Nov 11 '14 at 2:51
• It sounds flatly invalid to me. Why not just copy your data and add it to the end of your data file? To generate data this way assumes that the means (& SDs etc) in your data exactly match the population. – gung Nov 11 '14 at 2:56
• you can do so but the the data will be the same. I want to use this data for classification. This method of data augmentation can be used to make the classifier more robust. – Siavash S Nov 11 '14 at 3:12