A self-organising eigenspace map for time series clustering

TL;DR

This paper introduces the self-organising eigenspace map (SOEM), a novel neural network-based method for clustering and analyzing time series data by leveraging eigenspaces and joint diagonalisation.

Contribution

The paper presents SOEM, a new clustering technique that generalizes the self-organising feature map to matrix inputs using eigenspaces and approximate joint diagonalisation.

Findings

Performs topologically ordered clustering of time series.

Outperforms standard benchmarks on non-aligned data.

Effective for multivariate and partial time series analysis.

Abstract

This paper presents a novel time series clustering method, the self-organising eigenspace map (SOEM), based on a generalisation of the well-known self-organising feature map (SOFM). The SOEM operates on the eigenspaces of the embedded covariance structures of time series which are related directly to modes in those time series. Approximate joint diagonalisation acts as a pseudo-metric across these spaces allowing us to generalise the SOFM to a neural network with matrix input. The technique is empirically validated against three sets of experiments; univariate and multivariate time series clustering, and application to (clustered) multi-variate time series forecasting. Results indicate that the technique performs a valid topologically ordered clustering of the time series. The clustering is superior in comparison to standard benchmarks when the data is non-aligned, gives the best clustering stage for when used in forecasting, and can be used with partial/non-overlapping time series, multivariate clustering and produces a topological representation of the time series objects.