Theoretical Analysis of Sparse Subspace Clustering with Missing Entries
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Sparse Subspace Clustering (SSC) is a popular unsupervised machine learning method for clustering data lying close to a union of low-dimensional linear subspaces; a problem with numerous applications in pattern recognition and computer vision. Even though the behavior of SSC for uncorrupted data is by now well-understood, little is known about its theoretical properties when applied to data with missing entries. In this paper we give the first interpretable theoretical guarantees for SSC with incomplete data, and analytically establish that projecting the zero-filled data onto the observation patten of the point being expressed leads to a substantial improvement in performance. Since the projection induces further missing entries, this is a remarkable phenomenon, whose significance potentially extends to the entire class of self-expressive methods.
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