From BOP to BOSS and Beyond: Time Series Classification with Dictionary Based Classifiers

TL;DR

It is concluded that BOSS represents the state of the art for dictionary-based TSC, and using Spatial Pyramids in conjunction with BOSS (SP) produces a significantly more accurate classifier.

Abstract

A family of algorithms for time series classification (TSC) involve running a sliding window across each series, discretising the window to form a word, forming a histogram of word counts over the dictionary, then constructing a classifier on the histograms. A recent evaluation of two of this type of algorithm, Bag of Patterns (BOP) and Bag of Symbolic Fourier Approximation Symbols (BOSS) found a significant difference in accuracy between these seemingly similar algorithms. We investigate this phenomenon by deconstructing the classifiers and measuring the relative importance of the four key components between BOP and BOSS. We find that whilst ensembling is a key component for both algorithms, the effect of the other components is mixed and more complex. We conclude that BOSS represents the state of the art for dictionary based TSC. Both BOP and BOSS can be classed as bag of words approaches. These are particularly popular in Computer Vision for tasks such as image classification. Converting approaches from vision requires careful engineering. We adapt three techniques used in Computer Vision for TSC: Scale Invariant Feature Transform; Spatial Pyramids; and Histrogram Intersection. We find that using Spatial Pyramids in conjunction with BOSS (SP) produces a significantly more accurate classifier. SP is significantly more accurate than standard benchmarks and the original BOSS algorithm. It is not significantly worse than the best shapelet based approach, and is only outperformed by HIVE-COTE, an ensemble that includes BOSS as a constituent module.

Figures (7)

• Figure 1: Two examples of simulated dictionary data. with a mixture of truncated head and shoulders and sine shapelets. Figure (a) has low noise and Figure (b) has standard white noise.
• Figure 2: Average ranks of 12 classifiers on 100 resamples of 85 data sets. The results were first presented in bagnall17bakeoff and lines18hive. A solid bar across a set of classifiers indicates there is no significant difference within that group.
• Figure 3: A series from the BeetleFly dataset, being divided at successive levels with Bags of SFA words being formed for each subsection. H1...7 are combined to form the final feature vector.
• Figure 4: Average ranks and cliques of 10 BOP/BOSS classifiers on 25 resamples of 77 data sets.
• Figure 5: Average ranks and cliques for five variants of dictionary classifiers.