# Uniform tensor clustering by jointly exploring sample affinities of various orders

arXiv: https://arxiv.org/abs/2302.01569 · HTML: https://mlsanity.com/paper/2302.01569/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 55 references that are in the map.
- First posted on arXiv 3 Feb 2023.

## Builds on (most cited first, 8 of 8)

- [Introduction to Tensor Decompositions and their Applications in Machine Learning](https://mlsanity.com/paper/1711.10781/) (2017)
- [SimpleMKKM: Simple Multiple Kernel K-means](https://mlsanity.com/paper/2005.04975/) (2020)
- [Local Sample-weighted Multiple Kernel Clustering with Consensus Discriminative Graph](https://mlsanity.com/paper/2207.02846/) (2022)
- [Multi-View Spectral Clustering with High-Order Optimal Neighborhood Laplacian Matrix](https://mlsanity.com/paper/2008.13539/) (2020)
- [On perfect clustering of high dimension, low sample size data](https://mlsanity.com/paper/1612.09121/) (2016)
- [Searching for Representative Modes on Hypergraphs for Robust Geometric Model Fitting](https://mlsanity.com/paper/1802.01129/) (2018)
- [Learning on Hypergraphs with Sparsity](https://mlsanity.com/paper/1804.00836/) (2018)
- [Integrating Tensor Similarity to Enhance Clustering Performance](https://mlsanity.com/paper/1905.03920/) (2019)

## Abstract (arXiv)

Conventional clustering methods based on pairwise affinity usually suffer from the concentration effect while processing huge dimensional features yet low sample sizes data, resulting in inaccuracy to encode the sample proximity and suboptimal performance in clustering. To address this issue, we propose a unified tensor clustering method (UTC) that characterizes sample proximity using multiple samples' affinity, thereby supplementing rich spatial sample distributions to boost clustering. Specifically, we find that the triadic tensor affinity can be constructed via the Khari-Rao product of two affinity matrices. Furthermore, our early work shows that the fourth-order tensor affinity is defined by the Kronecker product. Therefore, we utilize arithmetical products, Khatri-Rao and Kronecker products, to mathematically integrate different orders of affinity into a unified tensor clustering framework. Thus, the UTC jointly learns a joint low-dimensional embedding to combine various orders. Finally, a numerical scheme is designed to solve the problem. Experiments on synthetic datasets and real-world datasets demonstrate that 1) the usage of high-order tensor affinity could provide a supplementary characterization of sample proximity to the popular affinity matrix; 2) the proposed method of UTC is affirmed to enhance clustering by exploiting different order affinities when processing high-dimensional data.