Dimensionality Reduction by Low-Rank Embedding

Abstract

We consider the dimensionality reduction task under the scenario that data vectors lie on (or near by) multiple independent linear subspaces. We propose a robust dimensionality reduction algorithm, named as Low-Rank Embedding(LRE). In LRE, the affinity weights are calculated via low-rank representation and the embedding is yielded by spectral method. Owing to the affinity weight induced from low-rank model, LRE can reveal the subtle multiple subspace structure robustly. In the virtual of spectral method, LRE transforms the subtle multiple subspaces structure into multiple clusters in the low dimensional Euclidean space in which most of the ordinary algorithms can perform well. To demonstrate the advantage of the proposed LRE, we conducted comparative experiments on toy data sets and benchmark data sets. Experimental results confirmed that LRE is superior to other algorithms.