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

arXiv: https://arxiv.org/abs/1708.02288 · HTML: https://mlsanity.com/paper/1708.02288/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Aug 2017.

## Built on by (most cited first, 6 of 6)

- [Non-Linear Fusion for Self-Paced Multi-View Clustering](https://mlsanity.com/paper/2104.09255/) (2021)
- [Graph-Collaborated Auto-Encoder Hashing for Multi-view Binary Clustering](https://mlsanity.com/paper/2301.02484/) (2023)
- [Self-Learning Symmetric Multi-view Probabilistic Clustering](https://mlsanity.com/paper/2305.07307/) (2023)
- [GPS: Graph Contrastive Learning via Multi-scale Augmented Views from Adversarial Pooling](https://mlsanity.com/paper/2401.16011/) (2024)
- [Tensor Laplacian Regularized Low-Rank Representation for Non-uniformly Distributed Data Subspace Clustering](https://mlsanity.com/paper/2103.04064/) (2021)
- [Towards Generalized Multi-stage Clustering: Multi-view Self-distillation](https://mlsanity.com/paper/2310.18890/) (2023)

## Abstract (arXiv)

Low-Rank Representation (LRR) is arguably one of the most powerful paradigms for Multi-view spectral clustering, which elegantly encodes the multi-view local graph/manifold structures into an intrinsic low-rank self-expressive data similarity embedded in high-dimensional space, to yield a better graph partition than their single-view counterparts. In this paper we revisit it with a fundamentally different perspective by discovering LRR as essentially a latent clustered orthogonal projection based representation winged with an optimized local graph structure for spectral clustering; each column of the representation is fundamentally a cluster basis orthogonal to others to indicate its members, which intuitively projects the view-specific feature representation to be the one spanned by all orthogonal basis to characterize the cluster structures. Upon this finding, we propose our technique with the followings: (1) We decompose LRR into latent clustered orthogonal representation via low-rank matrix factorization, to encode the more flexible cluster structures than LRR over primal data objects; (2) We convert the problem of LRR into that of simultaneously learning orthogonal clustered representation and optimized local graph structure for each view; (3) The learned orthogonal clustered representations and local graph structures enjoy the same magnitude for multi-view, so that the ideal multi-view consensus can be readily achieved. The experiments over multi-view datasets validate its superiority.