Explainable and Class-Revealing Signal Feature Extraction via Scattering Transform and Constrained Zeroth-Order Optimization
Naoki Saito, David Weber
TL;DR
The paper addresses interpretability of features produced by combining the scattering transform with multiclass logistic regression in signal classification. It introduces a zeroth-order optimization framework to reconstruct time-domain inputs $\hat{\boldsymbol{x}}$ that maximize the class probability $p_k(\boldsymbol{x})$ computed from ${\mathcal{S}}[\boldsymbol{x}]$ and the trained classifier, while enforcing sparsity via $\mu \|\boldsymbol{x}\|_1$ and smoothness via $\nu \|\nabla \boldsymbol{x}\|_2$. Using Differential Evolution in the frequency domain with pink noise, it demonstrates that the resulting class-revealing patterns align with known discriminative features in synthetic datasets such as Cylinder-Bell-Funnel and triangular waveforms. The findings offer a pathway to interpret nonlinear ST features and guide design of targeted signals/sensors for improved discrimination.
Abstract
We propose a new method to extract discriminant and explainable features from a particular machine learning model, i.e., a combination of the scattering transform and the multiclass logistic regression. Although this model is well-known for its ability to learn various signal classes with high classification rate, it remains elusive to understand why it can generate such successful classification, mainly due to the nonlinearity of the scattering transform. In order to uncover the meaning of the scattering transform coefficients selected by the multiclass logistic regression (with the Lasso penalty), we adopt zeroth-order optimization algorithms to search an input pattern that maximizes the class probability of a class of interest given the learned model. In order to do so, it turns out that imposing sparsity and smoothness of input patterns is important. We demonstrate the effectiveness of our proposed method using a couple of synthetic time-series classification problems.