Coresets for Time Series Clustering

TL;DR

This paper introduces an efficient method for constructing coresets for time series clustering based on Gaussian mixture models, enabling scalable analysis with minimal data reduction.

Contribution

It presents a novel algorithm for coreset construction for time series clustering that is independent of the number of entities and observations, depending only on key parameters.

Findings

Coreset size is independent of the number of entities and observations.

Algorithm performs well on synthetic data.

Coreset size depends polynomially on cluster and data dimensions.

Abstract

We study the problem of constructing coresets for clustering problems with time series data. This problem has gained importance across many fields including biology, medicine, and economics due to the proliferation of sensors facilitating real-time measurement and rapid drop in storage costs. In particular, we consider the setting where the time series data on $N$ entities is generated from a Gaussian mixture model with autocorrelations over $k$ clusters in $\mathbb{R}^d$. Our main contribution is an algorithm to construct coresets for the maximum likelihood objective for this mixture model. Our algorithm is efficient, and under a mild boundedness assumption on the covariance matrices of the underlying Gaussians, the size of the coreset is independent of the number of entities $N$ and the number of observations for each entity, and depends only polynomially on $k$, $d$ and $1/\varepsilon$, where $\varepsilon$ is the error parameter. We empirically assess the performance of our coreset with synthetic data.