Human Activity Recognition by L1-Norm Linear Discriminant Analysis of Radar Micro-Doppler Signatures

Abstract

Radar technology has recently gained increasing interest for indoor human activity monitoring because of its superior ability to discern motion under conditions, such as low lighting and visual obstructions. In addition, radar modality can offer non-intrusive monitoring in a home environment while preserving privacy of human subjects in various applications, ranging from home security to aging-in-place for the elderly. Once radar signatures are collected, feature extraction and classification methods are typically applied to detect, classify, and discern the observed activity. Inspired by its celebrated success in many machine learning and pattern recognition applications, we consider Linear Discriminant Analysis (LDA) of radar micro-Doppler signatures for indoor human activity recognition. The objective of LDA is to determine a low-rank subspace that maximizes the separability between data points coming from different classes, while grouping together those coming from the same class. Standard LDA is based on the L2-norm, which is known to be sensitive to the presence of outliers. We employ an L1-norm variant of LDA, which offers a robust classification model that exhibits resistance against outlier-corrupted training data. We have accomplished both non-adaptive and incremental implementations of the L1-norm LDA. The latter provides refinement and adaptation to the specific activity patterns of the human subject through fine-tuning of the discriminant basis using new pertinent training data as it becomes available in the course of system operation. At the same time, the incremental model retains its resistance to outliers. We also investigate the impact of a dimensionality reduction pre-processing step on LDA-based classification. For high-dimensional micro-Doppler signatures, such a pre-processing step can ease the high computational complexity of LDA. We consider both Principal Component Analysis (PCA) and its L1-norm variant for the pre-processing step. We compare and contrast various combinations of PCA, LDA, and their L1-norm variants in terms of their classification performance. We demonstrate that, in the presence of outliers due to data mislabeling, both PCA and its L1-variant perform equally well for dimensionality reduction, and LDA and its variant can be performed in the reduced-dimensional space with minimal loss in performance.