# Tucker-O-Minus Decomposition for Multi-view Tensor Subspace Clustering

arXiv: https://arxiv.org/abs/2210.12638 · HTML: https://mlsanity.com/paper/2210.12638/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 61 references that are in the map.
- First posted on arXiv 23 Oct 2022.

## Builds on (most cited first, 13 of 13)

- [Tensor Ring Decomposition](https://mlsanity.com/paper/1606.05535/) (2016)
- [Efficient tensor completion for color image and video recovery: Low-rank tensor train](https://mlsanity.com/paper/1606.01500/) (2016)
- [Ultra-Scalable Spectral Clustering and Ensemble Clustering](https://mlsanity.com/paper/1903.01057/) (2019)
- [Generalizing Tensor Decomposition for N-ary Relational Knowledge Bases](https://mlsanity.com/paper/2007.03988/) (2020)
- [Robust Graph Learning from Noisy Data](https://mlsanity.com/paper/1812.06673/) (2018)
- [Essential Tensor Learning for Multi-view Spectral Clustering](https://mlsanity.com/paper/1807.03602/) (2018)
- [Effective and Efficient Graph Learning for Multi-view Clustering](https://mlsanity.com/paper/2108.06734/) (2021)
- [Multi-graph Fusion for Multi-view Spectral Clustering](https://mlsanity.com/paper/1909.06940/) (2019)
- [On Unifying Multi-View Self-Representations for Clustering by Tensor Multi-Rank Minimization](https://mlsanity.com/paper/1610.07126/) (2016)
- [Graph Regularized Nonnegative Tensor Ring Decomposition for Multiway Representation Learning](https://mlsanity.com/paper/2010.05657/) (2020)
- [Smoothed Multi-View Subspace Clustering](https://mlsanity.com/paper/2106.09875/) (2021)
- [A Self-Organizing Tensor Architecture for Multi-View Clustering](https://mlsanity.com/paper/1810.07874/) (2018)
- [Constrained Bilinear Factorization Multi-view Subspace Clustering](https://mlsanity.com/paper/1906.08107/) (2019)

## Abstract (arXiv)

With powerful ability to exploit latent structure of self-representation information, different tensor decompositions have been employed into low rank multi-view clustering (LRMVC) models for achieving significant performance. However, current approaches suffer from a series of problems related to those tensor decomposition, such as the unbalanced matricization scheme, rotation sensitivity, deficient correlations capture and so forth. All these will lead to LRMVC having insufficient access to global information, which is contrary to the target of multi-view clustering. To alleviate these problems, we propose a new tensor decomposition called Tucker-O-Minus Decomposition (TOMD) for multi-view clustering. Specifically, based on the Tucker format, we additionally employ the O-minus structure, which consists of a circle with an efficient bridge linking two weekly correlated factors. In this way, the core tensor in Tucker format is replaced by the O-minus architecture with a more balanced structure, and the enhanced capacity of capturing the global low rank information will be achieved. The proposed TOMD also provides more compact and powerful representation abilities for the self-representation tensor, simultaneously. The alternating direction method of multipliers is used to solve the proposed model TOMD-MVC. Numerical experiments on six benchmark data sets demonstrate the superiority of our proposed method in terms of F-score, precision, recall, normalized mutual information, adjusted rand index, and accuracy.