Area Geometry as a Design Principle for Time Series Classification

Time series classification (TSC) is a mature field with a wide range of successful approaches. However, in these approaches, explicit area geometry features that describe how a series fills the time–amplitude plane are rarely used as a first class design principle. Path signatures are the main exception. Their second order terms capture the area between channels. However, the dimensionality of the signatures grows combinatorially with both the truncation order and the number of channels. We argue that area should be treated as a primary source of features in TSC and show that much of the benefit of area features can be captured with constructions with linear time complexity. We focus on two approaches for integrating such constructions: interval-based and feature-based. First, we introduce Area Quantiles (AQ) and incorporate them into QUANT. We replace value quantiles in QUANT with vertical, horizontal, and sorted cumulative area quantiles on each interval. The resulting classifier, AQ-QUANT, preserves QUANT’s design but addresses its invariance to reorder limitation. On 112 UCR datasets, AQ-QUANT matches QUANT’s mean accuracy, achieves more wins per dataset (45 vs. 40), and achieves the lowest mean rank among other interval-based methods. Second, we present the Integrated Multi Pattern Areas for the Classification of Time Series (IMPACT), a feature-based method that extracts signed and unsigned area features over multiple representations. The features are organized into four families. Intra-segment, inter-segment, random-split, and random-line areas. On the same 112 UCR datasets, IMPACT achieves the highest mean accuracy among the evaluated feature-based methods and the most wins (48 out of 112). In addition, it is approximately seven times faster than TSFresh and forty times faster than FreshPRINCE on a runtime track over 10 datasets from UCR. AQ-QUANT and IMPACT demonstrate that area-based representations can enhance both interval-based and feature-based methods without compromising efficiency.