Change-in-Slope Optimal Partitioning Algorithm in a Finite-Size Parameter Space

TL;DR

This paper introduces a dynamic programming algorithm for change-point detection in univariate time series, optimizing piecewise linear signals with slopes restricted to a finite set, enabling constraints and efficient computation for medical imaging applications.

Contribution

The paper presents a novel change-point detection algorithm leveraging a finite parameter space, improving efficiency and flexibility over traditional methods.

Findings

Algorithm achieves $O(m^2n^2)$ complexity with acceleration strategies.

Finite parameter space allows easy incorporation of constraints.

Effective in medical image analysis with robustness to outliers.

Abstract

We consider the problem of detecting change-points in univariate time series by fitting a continuous piecewise linear signal using the residual sum of squares. Values of the inferred signal at slope breaks are restricted to a finite set of size $m$. Using this finite parameter space, we build a dynamic programming algorithm with a controlled time complexity of $O(m^2n^2)$ for $n$ data points. Some accelerating strategies can be used to reduce the constant before $n^2$. The adapted classic inequality-based pruning is outperformed by a simpler "channel" method on simulations. Besides, our finite parameter space setting allows an easy introduction of constraints on the inferred signal. For example, imposing a minimal angle between consecutive segment slopes provides robustness to model misspecification and outliers. We test our algorithm with an isotonic constraint on an antibiogram image analysis problem for which algorithmic efficiency is a cornerstone in the emerging context of mobile-health and embedded medical devices. For this application, a finite state approach can be a valid compromise.