[Paper Review] Proximity Forest 2.0: A new effective and scalable similarity-based classifier for time series

Matthieu Herrmann, Chang Wei Tan+2 more|arXiv (Cornell University)|Apr 12, 2023

Time Series Analysis and Forecasting4 citations

TL;DR

Proximity Forest 2.0 (PF 2.0) is a new, faster, and more accurate similarity-based classifier for time series that integrates three recent advances: early abandoning and pruning for efficient elastic similarity computation, the novel Amerced Dynamic Time Warping (ADTW) measure, and cost function tuning. It outperforms all prior similarity-based methods on the UCR benchmark and surpasses state-of-the-art kernel, neural network, and hybrid models on datasets best suited to similarity-based learning, such as SmoothSubspace.

ABSTRACT

Time series classification (TSC) is a challenging task due to the diversity of types of feature that may be relevant for different classification tasks, including trends, variance, frequency, magnitude, and various patterns. To address this challenge, several alternative classes of approach have been developed, including similarity-based, features and intervals, shapelets, dictionary, kernel, neural network, and hybrid approaches. While kernel, neural network, and hybrid approaches perform well overall, some specialized approaches are better suited for specific tasks. In this paper, we propose a new similarity-based classifier, Proximity Forest version 2.0 (PF 2.0), which outperforms previous state-of-the-art similarity-based classifiers across the UCR benchmark and outperforms state-of-the-art kernel, neural network, and hybrid methods on specific datasets in the benchmark that are best addressed by similarity-base methods. PF 2.0 incorporates three recent advances in time series similarity measures -- (1) computationally efficient early abandoning and pruning to speedup elastic similarity computations; (2) a new elastic similarity measure, Amerced Dynamic Time Warping (ADTW); and (3) cost function tuning. It rationalizes the set of similarity measures employed, reducing the eight base measures of the original PF to three and using the first derivative transform with all similarity measures, rather than a limited subset. We have implemented both PF 1.0 and PF 2.0 in a single C++ framework, making the PF framework more efficient.

Motivation & Objective

• To develop a more effective and scalable similarity-based classifier for time series that outperforms existing methods on diverse UCR benchmark datasets.
• To integrate recent advances in time series similarity measures—specifically early abandoning, ADTW, and cost function tuning—into a unified framework.
• To rationalize the set of similarity measures used, reducing redundancy and improving generalization by selecting only three core measures: ADTW, cDTW, and LCSS, each with first derivative transformation.
• To demonstrate that the proposed set of similarity measures enhances not only PF 2.0 but also other similarity-based models like the Elastic Ensemble.
• To improve computational efficiency by implementing both PF 1.0 and PF 2.0 in a single, optimized C++ framework.

Proposed method

• Introduces Amerced Dynamic Time Warping (ADTW), a new elastic similarity measure that improves robustness and accuracy in time series matching.
• Applies computationally efficient early abandoning and pruning techniques to accelerate elastic similarity computations, especially for DTW-based measures.
• Employs cost function tuning for DTW-like measures, optimizing parameters such as warping penalty and alignment cost to improve classification performance.
• Uses first derivative transformation with all three core similarity measures (ADTW, cDTW, LCSS), enhancing sensitivity to shape and trend patterns.
• Rationalizes the set of base similarity measures from eight in PF 1.0 to three (ADTW, cDTW, LCSS), eliminating redundant or less effective measures.
• Implements the entire framework in a single, high-performance C++ library, significantly improving speed and enabling fair computational comparison between PF 1.0 and PF 2.0.

Experimental results

Research questions

• RQ1 Can a similarity-based classifier be made significantly faster and more accurate by integrating recent advances in time series similarity measures?
• RQ2 Does the use of a reduced, rationalized set of similarity measures improve generalization and avoid overfitting compared to using a larger, redundant set?
• RQ3 To what extent does cost function tuning and early abandoning improve performance and efficiency in similarity-based time series classification?
• RQ4 Can the proposed set of similarity measures (ADTW, cDTW, LCSS) be reused to enhance other similarity-based models beyond Proximity Forest?
• RQ5 Is PF 2.0 capable of outperforming not only prior similarity-based methods but also state-of-the-art kernel, neural network, and hybrid models on datasets where similarity-based approaches are most effective?

Key findings

• PF 2.0 achieves significantly lower error than all other state-of-the-art methods on the SmoothSubspace dataset, a benchmark where similarity-based approaches dominate.
• On the full UCR benchmark of 109 datasets, PF 2.0 outperforms all previous similarity-based classifiers, including PF 1.0 and Elastic Ensemble variants.
• PF 2.0 is the most accurate and fastest similarity-based TSC algorithm on the UCR benchmark, with a significant performance edge over PF 1.0.
• The use of cost function tuning improves performance across all DTW-like measures, with EE+ and PF+ showing higher accuracy than their non-tuned counterparts.
• The new set of three similarity measures (ADTW, cDTW, LCSS) with first derivative transformation enhances the Elastic Ensemble when used in place of its original measures, improving both speed and accuracy.
• The C++ implementation of PF 2.0 reduces computational overhead and enables fair, efficient comparison with PF 1.0, demonstrating a substantial speedup over the previous Java-based implementation.