Random Projection for Dimensionality Reduction – Passion is like genius; a miracle.

Random projection in dimensionality reduction: Applications to image and text data

This is really easy way of dimensionality reduction. Simply, multiply data with random matrix $R$ where $r_{i,j}$ is a random number from $N(0, 1)$ .

If $X$ is a dxN dimension where d is very high dimension and N is the number of data and $R$ is a kxd dimension where k << d, then [latex]R \times X[/latex] is kxN dimension which is lower than original d. R code sample: [code lang="R"] > R = matrix(nrow=100, ncol=1000000) > set.seed(12345) > R[,] = rnorm(1000000*100) > R %*% X [/code]