DBSCAN of Multi-Slice Clustering for Third-Order Tensors

TL;DR

This paper introduces MSC-DBSCAN, an extension of Multi-Slice Clustering for third-order tensors, capable of identifying multiple clusters of slices in data composed of sums of rank-one tensors, without needing to specify cluster sizes.

Contribution

The paper presents MSC-DBSCAN, a novel algorithm that extends MSC to handle sums of rank-one tensors, enabling automatic multi-cluster detection in 3D tensor data.

Findings

Successfully identifies multiple slice clusters in tensor data

Works with datasets composed of sums of rank-one tensors

Matches MSC performance on rank-one tensor data

Abstract

Several methods for triclustering three-dimensional data require the cluster size or the number of clusters in each dimension to be specified. To address this issue, the Multi-Slice Clustering (MSC) for 3-order tensor finds signal slices that lie in a low dimensional subspace for a rank-one tensor dataset in order to find a cluster based on the threshold similarity. We propose an extension algorithm called MSC-DBSCAN to extract the different clusters of slices that lie in the different subspaces from the data if the dataset is a sum of r rank-one tensor (r > 1). Our algorithm uses the same input as the MSC algorithm and can find the same solution for rank-one tensor data as MSC.