TPCH: Tensor-interacted Projection and Cooperative Hashing for Multi-view Clustering

TL;DR

TPCH tackles the inefficiency and limited cross-view cooperation of existing large-scale multi-view clustering methods by modeling higher-order interactions through a tensor-interacted projection and cooperative hashing framework. It stacks projection matrices and hash codes into tensors and imposes an enhanced tensor nuclear norm (ETNN) via t-SVD to promote low-rank, robust representations in both the projection and Hamming spaces. The approach yields more compact, discriminative hash codes and improved clustering performance across five large-scale datasets, with substantial CPU-time savings compared to state-of-the-art methods. This enables scalable, robust multi-view clustering suitable for big data applications, with code available for reproducibility.

Abstract

In recent years, anchor and hash-based multi-view clustering methods have gained attention for their efficiency and simplicity in handling large-scale data. However, existing methods often overlook the interactions among multi-view data and higher-order cooperative relationships during projection, negatively impacting the quality of hash representation in low-dimensional spaces, clustering performance, and sensitivity to noise. To address this issue, we propose a novel approach named Tensor-Interacted Projection and Cooperative Hashing for Multi-View Clustering(TPCH). TPCH stacks multiple projection matrices into a tensor, taking into account the synergies and communications during the projection process. By capturing higher-order multi-view information through dual projection and Hamming space, TPCH employs an enhanced tensor nuclear norm to learn more compact and distinguishable hash representations, promoting communication within and between views. Experimental results demonstrate that this refined method significantly outperforms state-of-the-art methods in clustering on five large-scale multi-view datasets. Moreover, in terms of CPU time, TPCH achieves substantial acceleration compared to the most advanced current methods. The code is available at \textcolor{red}{\url{https://github.com/jankin-wang/TPCH}}.

Figures (7)

• Figure 1: Basic process of t-SVD. $\bm{\mathcal{T}} \in R^{D_{1} \times D_{2} \times D_{3}}$ represents the tensor to be decomposed, $\bm{\mathcal{S}} \in R^{D_{1} \times D_{2} \times D_{3}}$ denotes the core tensor, $\bm{\mathcal{U}} \in R^{D_{1} \times D_{1} \times D_{3}}$, and $\bm{\mathcal{V}} \in R^{D_{2} \times D_{2} \times D_{3}}$ represent the left and right tensors, respectively, resulting from the t-SVD decomposition of $\bm{\mathcal{T}}$.
• Figure 2: Transformation instructions for core tensors.
• Figure 3: Clustering performance of AC_MVBC and TPCH on the two datasets with salt-and-pepper noise.
• Figure 4: Ablation Studies of TPCH on the Caltech101 and Caltech256 datasets with salt-and-pepper noise.
• Figure 5: Visualization of clustering results for TPCH and AC-MVBC on the Synthetic_4clu dataset.