Density peak clustering using tensor network

TL;DR

This paper introduces a novel density-based clustering algorithm utilizing tensor networks, encoding data into tensor network states and defining density via fidelity, achieving state-of-the-art results on various datasets.

Contribution

The work presents a new clustering method that leverages tensor networks and fidelity-based density measures, offering improved performance over existing algorithms.

Findings

State-of-the-art results on synthetic and real datasets

Competitive performance on image datasets like MNIST and Fashion-MNIST

Effective clustering even with unknown number of clusters

Abstract

Tensor networks, which have been traditionally used to simulate many-body physics, have recently gained significant attention in the field of machine learning due to their powerful representation capabilities. In this work, we propose a density-based clustering algorithm inspired by tensor networks. We encode classical data into tensor network states on an extended Hilbert space and train the tensor network states to capture the features of the clusters. Here, we define density and related concepts in terms of fidelity, rather than using a classical distance measure. We evaluate the performance of our algorithm on six synthetic data sets, four real world data sets, and three commonly used computer vision data sets. The results demonstrate that our method provides state-of-the-art performance on several synthetic data sets and real world data sets, even when the number of clusters is unknown. Additionally, our algorithm performs competitively with state-of-the-art algorithms on the MNIST, USPS, and Fashion-MNIST image data sets. These findings reveal the great potential of tensor networks for machine learning applications.