A new heuristic algorithm for fast k-segmentation

TL;DR

This paper introduces a new heuristic algorithm, LM, for fast k-segmentation of videos, achieving accuracy comparable to exact methods with significantly reduced computational time, especially when combined with existing algorithms.

Contribution

The paper proposes the LM heuristic algorithm inspired by Lloyd's methods, which improves k-segmentation efficiency and accuracy, and demonstrates its effectiveness through variants tested on synthetic datasets.

Findings

LM algorithm achieves competitive accuracy with less computation.

LM-enhanced-Bottom-Up segmentation outperforms existing methods.

The algorithm can process datasets with up to a million frames in seconds.

Abstract

The $k$-segmentation of a video stream is used to partition it into $k$ piecewise-linear segments, so that each linear segment has a meaningful interpretation. Such segmentation may be used to summarize large videos using a small set of images, to identify anomalies within segments and change points between segments, and to select critical subsets for training machine learning models. Exact and approximate segmentation methods for $k$-segmentation exist in the literature. Each of these algorithms occupies a different spot in the trade-off between computational complexity and accuracy. A novel heuristic algorithm is proposed in this paper to improve upon existing methods. It is empirically found to provide accuracies competitive with exact methods at a fraction of the computational expense. The new algorithm is inspired by Lloyd's algorithm for K-Means and Lloyd-Max algorithm for scalar quantization, and is called the LM algorithm for convenience. It works by iteratively minimizing a cost function from any given initialisation; the commonly used $L_2$ cost is chosen in this paper. While the greedy minimization makes the algorithm sensitive to initialisation, the ability to converge from any initial guess to a local optimum allows the algorithm to be integrated into other existing algorithms. Three variants of the algorithm are tested over a large number of synthetic datasets, one being a standalone LM implementation, and two others that combine with existing algorithms. One of the latter two -- LM-enhanced-Bottom-Up segmentation -- is found to have the best accuracy and the lowest computational complexity among all algorithms. This variant of LM can provide $k$-segmentations over data sets with up to a million image frames within several seconds.