Related papers: Trainable Wavelet Neural Network for Non-Stationar…

Wavelets are well known for data compression, yet have rarely been applied to the compression of neural networks. This paper shows how the fast wavelet transform can be used to compress linear layers in neural networks. Linear layers still…

The wavelet scattering transform creates geometric invariants and deformation stability. In multiple signal domains, it has been shown to yield more discriminative representations compared to other non-learned representations and to…

Wavelet transformation stands as a cornerstone in modern data analysis and signal processing. Its mathematical essence is an invertible transformation that discerns slow patterns from fast ones in the frequency domain. Such an invertible…

Convolutional neural network (CNN), with ability of feature learning and nonlinear mapping, has demonstrated its effectiveness in prognostics and health management (PHM). However, explanation on the physical meaning of a CNN architecture…

Wavelets provide the flexibility to analyse stochastic processes at different scales. Here, we apply them to multivariate point processes as a means of detecting and analysing unknown non-stationarity, both within and across data streams.…

Wavelet neural network (WNN), which learns an unknown nonlinear mapping from the data, has been widely used in signal processing, and time-series analysis. However, challenges in constructing accurate wavelet bases and high computational…

We introduce a two-layer wavelet scattering network, for object classification. This scattering transform computes a spatial wavelet transform on the first layer and a new joint wavelet transform along spatial, angular and scale variables…

The wavelet transform has seen success when incorporated into neural network architectures, such as in wavelet scattering networks. More recently, it has been shown that the dual-tree complex wavelet transform can provide better…

Spectral-based graph neural networks (SGNNs) have been attracting increasing attention in graph representation learning. However, existing SGNNs are limited in implementing graph filters with rigid transforms (e.g., graph Fourier or…

Network data can be conveniently modeled as a graph signal, where data values are assigned to nodes of a graph that describes the underlying network topology. Successful learning from network data is built upon methods that effectively…

This paper examines the possibility of, and the possible advantages to learning the filters of convolutional neural networks (CNNs) for image analysis in the wavelet domain. We are stimulated by both Mallat's scattering transform and the…

Convolutional neural networks (CNNs) have been shown to both extract more information than the traditional two-point statistics from cosmological fields, and marginalise over astrophysical effects extremely well. However, CNNs require large…

In this work we propose a method for learning wavelet filters directly from data. We accomplish this by framing the discrete wavelet transform as a modified convolutional neural network. We introduce an autoencoder wavelet transform network…

Even though convolutional neural networks have become the method of choice in many fields of computer vision, they still lack interpretability and are usually designed manually in a cumbersome trial-and-error process. This paper aims at…

We present graph wavelet neural network (GWNN), a novel graph convolutional neural network (CNN), leveraging graph wavelet transform to address the shortcomings of previous spectral graph CNN methods that depend on graph Fourier transform.…

Signal denoising is a key preprocessing step for many applications, as the performance of a learning task is closely related to the quality of the input data. In this paper, we apply a signal processing based deep neural network…

This is the first paper in a sequence of studies in which we introduce a new type of neural networks (NNs) -- wavelet-based neural networks (WBNNs) -- and study their properties and potential for applications. We begin this study with a…

Convolutional neural networks (CNNs) are very popular nowadays for image processing. CNNs allow one to learn optimal filters in a (mostly) supervised machine learning context. However this typically requires abundant labelled training data…

We study inverse problems consisting on determining medium properties using the responses to probing waves from the machine learning point of view. Based on the understanding of propagation of waves and their nonlinear interactions, we…

We propose the introduction of nonlinear operation into the feature generation process in convolutional neural networks. This nonlinearity can be implemented in various ways. First we discuss the use of nonlinearities in the process of data…