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Low-Rank Representation (LRR) is arguably one of the most powerful paradigmsfor Multi-view spectral clustering, which elegantly encodes the multi-viewlocal graph/manifold structures into an intrinsic low-rank self-expressive datasimilarity embedded in high-dimensional space, to yield a better graphpartition than their single-view counterparts. In this paper we revisit it witha fundamentally different perspective by discovering LRR as essentially alatent clustered orthogonal projection based representation winged with anoptimized local graph structure for spectral clustering; each column of therepresentation is fundamentally a cluster basis orthogonal to others toindicate its members, which intuitively projects the view-specific featurerepresentation to be the one spanned by all orthogonal basis to characterizethe cluster structures. Upon this finding, we propose our technique with thefollowings: (1) We decompose LRR into latent clustered orthogonalrepresentation via low-rank matrix factorization, to encode the more flexiblecluster structures than LRR over primal data objects; (2) We convert theproblem of LRR into that of simultaneously learning orthogonal clusteredrepresentation and optimized local graph structure for each view; (3) Thelearned orthogonal clustered representations and local graph structures enjoythe same magnitude for multi-view, so that the ideal multi-view consensus canbe readily achieved. The experiments over multi-view datasets validate itssuperiority.

Beyond Low-Rank Representations: Orthogonal Clustering Basis Reconstruction with Optimized Graph Structure for Multi-view Spectral Clustering