Fully Learnable Deep Wavelet Transform for Unsupervised Monitoring of High-Frequency Time Series

TL;DR

This paper introduces a fully unsupervised, learnable deep wavelet transform framework for extracting meaningful, sparse representations from high-frequency signals, improving industrial asset monitoring without prior knowledge.

Contribution

It proposes a novel deep learning architecture that makes the discrete wavelet transform fully learnable, incorporating key wavelet properties and a new activation function for thresholding.

Findings

Outperforms baseline methods on sound datasets.

Achieves superior results compared to state-of-the-art techniques.

Demonstrates the effectiveness of learnable wavelet properties in unsupervised learning.

Abstract

High-Frequency (HF) signals are ubiquitous in the industrial world and are of great use for monitoring of industrial assets. Most deep learning tools are designed for inputs of fixed and/or very limited size and many successful applications of deep learning to the industrial context use as inputs extracted features, which is a manually and often arduously obtained compact representation of the original signal. In this paper, we propose a fully unsupervised deep learning framework that is able to extract a meaningful and sparse representation of raw HF signals. We embed in our architecture important properties of the fast discrete wavelet transformation (FDWT) such as (1) the cascade algorithm, (2) the conjugate quadrature filter property that links together the wavelet, the scaling and transposed filter functions, and (3) the coefficient denoising. Using deep learning, we make this architecture fully learnable: both the wavelet bases and the wavelet coefficient denoising are learnable. To achieve this objective, we propose a new activation function that performs a learnable hard-thresholding of the wavelet coefficients. With our framework, the denoising FDWT becomes a fully learnable unsupervised tool that does neither require any type of pre- nor post-processing, nor any prior knowledge on wavelet transform. We demonstrate the benefits of embedding all these properties on three machine-learning tasks performed on open source sound datasets. We perform an ablation study of the impact of each property on the performance of the architecture, achieve results well above baseline and outperform other state-of-the-art methods.