Learning idempotent representation for subspace clustering
The critical point for the successes of spectral-type subspace clustering algorithms is to seek reconstruction coefficient matrices which can faithfully reveal the subspace structures of data sets. An ideal reconstruction coefficient matrix should have two properties: 1) it is block diagonal with ea...
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Main Authors | , , , |
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Format | Journal Article |
Language | English |
Published |
28.07.2022
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Subjects | |
Online Access | Get full text |
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Summary: | The critical point for the successes of spectral-type subspace clustering
algorithms is to seek reconstruction coefficient matrices which can faithfully
reveal the subspace structures of data sets. An ideal reconstruction
coefficient matrix should have two properties: 1) it is block diagonal with
each block indicating a subspace; 2) each block is fully connected. Though
there are various spectral-type subspace clustering algorithms have been
proposed, some defects still exist in the reconstruction coefficient matrices
constructed by these algorithms. We find that a normalized membership matrix
naturally satisfies the above two conditions. Therefore, in this paper, we
devise an idempotent representation (IDR) algorithm to pursue reconstruction
coefficient matrices approximating normalized membership matrices. IDR designs
a new idempotent constraint for reconstruction coefficient matrices. And by
combining the doubly stochastic constraints, the coefficient matrices which are
closed to normalized membership matrices could be directly achieved. We present
the optimization algorithm for solving IDR problem and analyze its computation
burden as well as convergence. The comparisons between IDR and related
algorithms show the superiority of IDR. Plentiful experiments conducted on both
synthetic and real world datasets prove that IDR is an effective and efficient
subspace clustering algorithm. |
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DOI: | 10.48550/arxiv.2207.14431 |