# 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

## 1 Answer

In data augmentation (in vision) people generate additional images for training their model. A proper data augmentation is the one which gives reasonable set of images (usually) similar to the already existing images in the training set, but slightly different (say by patching, rotation, etc). Another way is to augment images by adding slight variations to images, which can be done by adding eigen images on top of different color channels. This way you wouldn't get very different images from the original images, but slightly different ones, which might help you in learning the task (depending on the type of the task). Section 4.1 comprehensively elaborates on this: http://www.cs.toronto.edu/~fritz/absps/imagenet.pdf