# Adaptively Topological Tensor Network for Multi-view Subspace Clustering

arXiv: https://arxiv.org/abs/2305.00716 · HTML: https://mlsanity.com/paper/2305.00716/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 79 references that are in the map.
- First posted on arXiv 1 May 2023.

## Builds on (most cited first, 14 of 14)

- [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)
- [Efficient Low Rank Tensor Ring Completion](https://mlsanity.com/paper/1707.08184/) (2017)
- [Essential Tensor Learning for Multi-view Spectral Clustering](https://mlsanity.com/paper/1807.03602/) (2018)
- [Multi-view Low-rank Sparse Subspace Clustering](https://mlsanity.com/paper/1708.08732/) (2017)
- [On Unifying Multi-View Self-Representations for Clustering by Tensor Multi-Rank Minimization](https://mlsanity.com/paper/1610.07126/) (2016)
- [Multi-View Spectral Clustering Tailored Tensor Low-Rank Representation](https://mlsanity.com/paper/2004.14705/) (2020)
- [Seeking Commonness and Inconsistencies: A Jointly Smoothed Approach to Multi-view Subspace Clustering](https://mlsanity.com/paper/2203.08060/) (2022)
- [Matching-CNN Meets KNN: Quasi-Parametric Human Parsing](https://mlsanity.com/paper/1504.01220/) (2015)
- [Low-rank Kernel Learning for Graph-based Clustering](https://mlsanity.com/paper/1903.05962/) (2019)
- [Learning From Hidden Traits: Joint Factor Analysis and Latent Clustering](https://mlsanity.com/paper/1605.06711/) (2016)
- [Log-based Sparse Nonnegative Matrix Factorization for Data Representation](https://mlsanity.com/paper/2204.10647/) (2022)
- [Constrained Bilinear Factorization Multi-view Subspace Clustering](https://mlsanity.com/paper/1906.08107/) (2019)

## Built on by (most cited first, 4 of 4)

- [SVDinsTN: A Tensor Network Paradigm for Efficient Structure Search from Regularized Modeling Perspective](https://mlsanity.com/paper/2305.14912/) (2023)
- [Web Service QoS Prediction via Extended Canonical Polyadic-based Tensor Network](https://mlsanity.com/paper/2408.16278/) (2024)
- [Fast and Accurate Power Load Data Completion via Regularization-optimized Low-Rank Factorization](https://mlsanity.com/paper/2505.19133/) (2025)
- [Tensor Decomposition Structure Search Framework from an Interaction Perspective](https://mlsanity.com/paper/2603.02720/) (2026)

## Abstract (arXiv)

Multi-view subspace clustering methods have employed learned self-representation tensors from different tensor decompositions to exploit low rank information. However, the data structures embedded with self-representation tensors may vary in different multi-view datasets. Therefore, a pre-defined tensor decomposition may not fully exploit low rank information for a certain dataset, resulting in sub-optimal multi-view clustering performance. To alleviate the aforementioned limitations, we propose the adaptively topological tensor network (ATTN) by determining the edge ranks from the structural information of the self-representation tensor, and it can give a better tensor representation with the data-driven strategy. Specifically, in multi-view tensor clustering, we analyze the higher-order correlations among different modes of a self-representation tensor, and prune the links of the weakly correlated ones from a fully connected tensor network. Therefore, the newly obtained tensor networks can efficiently explore the essential clustering information with self-representation with different tensor structures for various datasets. A greedy adaptive rank-increasing strategy is further applied to improve the capture capacity of low rank structure. We apply ATTN on multi-view subspace clustering and utilize the alternating direction method of multipliers to solve it. Experimental results show that multi-view subspace clustering based on ATTN outperforms the counterparts on six multi-view datasets.