Abstract:
Many natural processes exhibit self-similarity, where repetitive patterns occur across scales. The Hurst exponent quantifies this property, but wavelet-based estimation methods often face challenges from noise, outliers, and modeling assumptions. This study introduces a new method to estimate the Hurst exponent and applies it to gait data analysis.

The proposed method refines traditional self-similarity assessment using wavelet transforms (WT) and integrates the fractional Brownian motion (fBm) model with probability distributions of wavelet coefficients. By combining estimates from wavelet decomposition levels, the method produces a single, precise measure named ALPHEE.

The study evaluates self-similarity features in machine learning models for identifying elderly fallers using linear acceleration (LA) and angular velocity (AV) data from 147 subjects (79 fallers, 68 non-fallers). Results show higher regularity in LA and AV for fallers and demonstrate that adding self-similarity features improves classification accuracy from 79.55% to 84.09%. This surpasses previous studies and highlights the method’s ability to capture self-similar properties for better gait analysis.