Signature-Based Feature Learning for Human Activity Recognition: A Reproducible Machine Learning Study of Representation, Depth, and Model Choice

Abstract

Human activity recognition (HAR) relies on transforming sensor signals into informative representations for classification. Although deep learning and handcrafted features are widely used, the role of representation itself is often not systematically isolated. Signature transforms provide a mathematically grounded way to encode temporal order and cross-channel interactions, but their value for HAR under a fully reproducible and leakage-aware framework remains unclear. To evaluate whether signature-based feature learning improves HAR performance compared with raw-signal baselines, and to assess the effects of embedding strategy, truncation depth, model choice, and sensor configuration. Experiments were conducted on the UCI HAR dataset using a fully reproducible pipeline with the original train--test split preserved and subject-disjoint validation to prevent leakage. Three representations were compared: raw flattened signals, time-augmented paths, and lead--lag transformed paths. Signature features were computed at multiple truncation depths and evaluated using multilayer perceptron (MLP) and Random Forest (RF) classifiers under identical preprocessing and validation procedures. A prior K-means-based feature reduction study was also reproduced for comparison. Signature-based representations improved performance when paired with RF models, the best configuration was time-augmented six-channel signatures at depth 6 using entropy-based RF achieving 0.858 accuracy and 0.859 macro F1, outperforming the strongest raw baseline (0.816 accuracy). Lead--lag representations were competitive at moderate depths but did not surpass the best time-augmented models. MLP models did not exceed raw baselines. Signature-based feature learning can improve HAR, but its benefit depends on alignment between representation design and classifier choice.