One-step late fusion multiple kernel clustering via tensorized adaptive multi-scale partition fusion

Recent years, multiple kernel clustering (MKC) has extensive applications in data analysis field. Due to its characteristic of low computational complexity, Late Fusion Multiple Kernel Clustering (LFMKC) stands out among existing MKC algorithm methods. However, LFMKC is still confronted with some problems. Firstly, LFMKC only uses single-scale partition to obtain the clustering results, failing to learn about the information in the kernel matrices thoroughly. Secondly, LFMKC cannot utilize the higher-order correlations since the base partitions are fixed. Besides, LFMKC need an extra k-means step to yield the result. To overcome these limitations, we design a new method named One-step Late fusion Multiple kernel clustering via Tensorized adaptive Multi-scale partition Fusion (OLMTMF), which integrates multi-scale fusion, high-order tensor information and spectral rotation (SR) into a unified framework. To be more precise, we first design an adaptive algorithm to integrate multi-scale partition instead of single partition, fully exploring the information in different kernel matrices. Next, OLMTMF builds a tensor with different fused partitions, constrained by Tensor Nuclear Norm (TNN), to discover the higher-order correlations among these fused partitions. Finally, OLMTMF utilizes SR to directly obtain clustering results, further improving the clustering performance. We also develop an alternative procedure with theoretical convergence guarantee to optimize the objective function of OLMTMF. Extensive experiments indicate that OLMTMF achieves excellent clustering performance on different datasets with low computational complexity. The source code can be downloaded from: https://github.com/luxinrui018/OLMTMF .