Uniform Tensor Clustering by Jointly Exploring Sample Affinities of Various Orders

Area of Science:

• Data Science
• Machine Learning
• Computational Statistics

Background:

• Traditional clustering methods use pairwise affinities, which are inadequate for high-dimensional small-sample (HDLSS) data due to concentration effects.
• Concentration effects in HDLSS data distort pairwise relationships, leading to inaccurate sample subgrouping and suboptimal clustering outcomes.

Purpose of the Study:

• To propose a novel approach using high-order affinities to address the limitations of traditional methods in HDLSS data clustering.
• To develop a unified mathematical framework for understanding and utilizing different orders of affinities.
• To introduce Uniform Tensor Clustering (UTC) for improved clustering performance on complex datasets.

Main Methods:

• Developed decomposable high-order affinities to establish a mathematical link between different affinity orders.
• Formulated a uniform mathematical framework integrating multiple-order affinities.
• Proposed Uniform Tensor Clustering (UTC), a method that learns a consensus low-dimensional embedding by synergistically using multiple-order affinities.

Main Results:

• Demonstrated that high-order affinities are more effective than pairwise affinities for characterizing sample relationships in complex data.
• Showcased that the judicious combination of different order affinities significantly enhances clustering effectiveness, particularly for high-dimensional data.
• Validated the proposed UTC method on both synthetic and real-world datasets, confirming its superior performance.

Conclusions:

• High-order affinities offer a robust solution for clustering HDLSS data by mitigating concentration effects.
• The proposed Uniform Tensor Clustering (UTC) method provides an effective and unified framework for leveraging multiple-order affinities.
• The findings highlight the potential of high-order affinity-based approaches for advancing clustering techniques in machine learning and data science.