Subspace clustering via thresholding and spectral clustering

We consider the problem of clustering a set of high-dimensional data points into sets of low-dimensional linear subspaces. The number of subspaces, their dimensions, and their orientations are unknown. We propose a simple and low-complexity clustering algorithm based on thresholding the correlations...

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Bibliographic Details
Published inProceedings of the ... IEEE International Conference on Acoustics, Speech and Signal Processing (1998) pp. 3263 - 3267
Main Authors Heckel, Reinhard, Bolcskei, Helmut
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.05.2013
Subjects
Algorithm design and analysis
Clustering algorithms
Computer vision
Correlation
erasures
Heart
outlier detection
principal angles
Probabilistic logic
spectral clustering
subspace clustering
Vectors
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Summary:We consider the problem of clustering a set of high-dimensional data points into sets of low-dimensional linear subspaces. The number of subspaces, their dimensions, and their orientations are unknown. We propose a simple and low-complexity clustering algorithm based on thresholding the correlations between the data points followed by spectral clustering. A probabilistic performance analysis shows that this algorithm succeeds even when the subspaces intersect, and when the dimensions of the subspaces scale (up to a log-factor) linearly in the ambient dimension. Moreover, we prove that the algorithm also succeeds for data points that are subject to erasures with the number of erasures scaling (up to a log-factor) linearly in the ambient dimension. Finally, we propose a simple scheme that provably detects outliers.
ISSN:1520-6149
DOI:10.1109/ICASSP.2013.6638261