Join multiple Riemannian manifold representation and multi‐kernel non‐redundancy for image clustering

Abstract

Image clustering has received significant attention due to the growing importance of image recognition. Researchers have explored Riemannian manifold clustering, which is capable of capturing the non‐linear shapes found in real‐world datasets. However, the complexity of image data poses substantial challenges for modelling and feature extraction. Traditional methods such as covariance matrices and linear subspace have shown promise in image modelling, and they are still in their early stages and suffer from certain limitations. However, these include the uncertainty of representing data using only one Riemannian manifold, limited feature extraction capacity of single kernel functions, and resulting incomplete data representation and redundancy. To overcome these limitations, the authors propose a novel approach called join multiple Riemannian manifold representation and multi‐kernel non‐redundancy for image clustering (MRMNR‐MKC). It combines covariance matrices with linear subspace to represent data and applies multiple kernel functions to map the non‐linear structural data into a reproducing kernel Hilbert space, enabling linear model analysis for image clustering. Additionally, the authors use matrix‐induced regularisation to improve the clustering kernel selection process by reducing redundancy and assigning lower weights to identical kernels. Finally, the authors also conducted numerous experiments to evaluate the performance of our approach, confirming its superiority to state‐of‐the‐art methods on three benchmark datasets.