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Subspace clustering with a learned dimensionality reduction projection

Subspace clustering aims to separate data from a union of low dimensional linear subspaces. Many recent subspace clustering methods based on self-representation are popular and achieve state-of-art performance. Dimensionality reduction is a common preprocessing procedure before applying these clustering methods. In this paper, we present an algorithm to segment subspaces with a learned dimensionality reduction projection instead of simply using PCA (Principal Component Analysis). We propose an objective function which simultaneously learns the dimensionality reduction projection and self-representation coefficients. We integrate SMR (Smooth Representation subspace clustering) into this framework and propose SMR_LP (Smooth Representation clustering with Learned Projection). We also propose an efficient method to optimize the cost function. A well learned projection helps preserving the data structure and improves the clustering performance. Experimental results demonstrate the effectiveness of our proposed method.