Reduction and Null Space Algorithms for the Subspace Clustering Problem

Details Reduction and Null Space Algorithms for the Subspace Clustering Problem Reduction and Null Space Algorithms for the Subspace Clustering Problem

2010-10-11

arxiv.org/abs/1010.2198v1

Computer Science

Information Theory

Scientific paper

This paper presents two algorithms for clustering high-dimensional data points that are drawn from a union of lower dimensional subspaces. The first algorithm is based on binary reduced row echelon form of a data matrix. It can solve the subspace segmentation problem perfectly for noise free data, however, it is not reliable for noisy cases. The second algorithm is based on Null Space representation of data. It is devised for the cases when the subspace dimensions are equal. Such cases occur in applications such as motion segmentation and face recognition. This algorithm is reliable in the presence of noise, and applied to the Hopkins 155 Dataset it generates the best results to date for motion segmentation. The recognition rates for two and three motion video sequences are 99.15% and 98.85%, respectively.

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