Parallel Framework for Dimensionality Reduction of Large-Scale Datasets

Algorithm 1

Spectral dimensionality reduction.

Input: Set , , and the target dimension .

Output: Set , .

(1)  For each find its nearest neighbors.

(2) Define directed weighted graph ,

   where iff is a neighbor of ,

   and is a distance measure,

   usually .

(3) Let , where extracts specific property

   from graph .

(4) Normalize to obtain matrix .

(5) Find eigenvectors of , .

(6) Identify latent dimensionality .

(7) is represented by the first rows of .