Highly Efficient Rotation-Invariant Spectral Embedding for Scalable Incomplete Multi-View Clustering

TL;DR

This paper tackles incomplete multi-view clustering by introducing RISE, a rotation-invariant spectral embedding framework. RISE learns view-specific embeddings from incomplete bipartite graphs and simultaneously recovers a complete consensus representation with second-order rotation-invariant properties, integrated in a unified objective. A fast alternating optimization procedure with linear-time per-iteration complexity and minimal storage enables scalability to large datasets. Experimental results across seven diverse datasets show that RISE achieves state-of-the-art clustering performance while being significantly more efficient than existing methods, especially under high missing-rate scenarios.

Abstract

Incomplete multi-view clustering presents significant challenges due to missing views. Although many existing graph-based methods aim to recover missing instances or complete similarity matrices with promising results, they still face several limitations: (1) Recovered data may be unsuitable for spectral clustering, as these methods often ignore guidance from spectral analysis; (2) Complex optimization processes require high computational burden, hindering scalability to large-scale problems; (3) Most methods do not address the rotational mismatch problem in spectral embeddings. To address these issues, we propose a highly efficient rotation-invariant spectral embedding (RISE) method for scalable incomplete multi-view clustering. RISE learns view-specific embeddings from incomplete bipartite graphs to capture the complementary information. Meanwhile, a complete consensus representation with second-order rotation-invariant property is recovered from these incomplete embeddings in a unified model. Moreover, we design a fast alternating optimization algorithm with linear complexity and promising convergence to solve the proposed formulation. Extensive experiments on multiple datasets demonstrate the effectiveness, scalability, and efficiency of RISE compared to the state-of-the-art methods.

Figures (10)

• Figure 1: Different completion stages for IMVC. Filling missing data at the feature embedding level is computationally efficient and provides robust performance.
• Figure 2: Illustration of the SERM problem. Each color row represents a relaxed orthogonal basis. With structure drift in Laplacian matrices for incomplete views, the resulting orthogonal spectral embedding may be rotational mismatch.
• Figure 3: The ACC, NMI and Purity results of different methods with different missing ratios on partial benchmark datasets.
• Figure 4: Clustering results of our RISE with different values of $\beta$ on two datasets.
• Figure 5: The ACC results of our RISE with different values of $m$ and $k$ on two datasets.