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 representations than the standard transform. With this in mind, we extend our previous meth…
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48 results for “wavelet filtering”
Volatility Dynamics of Wavelet-Filtered Stock Pricesphysics.soc-ph
Volatility dynamics of wavelet - filtered stock price time series is studied. Using the universal thresholding method of wavelet filtering and a principle of minimal linear autocorrelation of noise component we find that the quantitative characteristics of volatility dynamics of denoised series are noticeably different…
Noise Homogenization via Multi-Channel Wavelet Filtering for High-Fidelity Sample Generation in GANscs.LG
WaveletGAN improves GANs by homogenizing noise through multi-channel wavelet filtering.
problem Current noise generation models in GANs struggle with homogenizing noise, leading to low-fidelity samples.
method Proposes a multi-channel wavelet-based filtering method to homogenize noise in GANs.
result WaveletGAN generates high-fidelity samples with the smallest FIDs on Fashion-MNIST, KMNIST, and SVHN datasets.
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 that is trained using gradient descent. We show that the model is capable of le…
We perform wavelet decomposition of high frequency financial time series into large and small time scale components. Taking the FTSE100 index as a case study, and working with the Haar basis, it turns out that the small scale component defined by most ( 99.6%) of the wavelet coefficients can be neglected for th…
New wavelet frames constructed from reproducing kernels for continuous and discrete domains.
problem Generating wavelet frames on non-Euclidean structures.
method Spectral filtering of integral operators associated with reproducing kernels.
result Discrete frames as Monte Carlo estimates of continuous frames, with finite-sample rates derived.
Graph classification improved using spectral features and wavelet filters.
problem Categorizing graphs based on their structure and node attributes.
method Derived spectral features from graph signal processing, designed two Gaussian process models: one simple and one sophisticated.
result Simple and sophisticated Gaussian process models yield competitive performance, including well-calibrated uncertainty estimates.
The wavelet Maximum Entropy on the Mean (wMEM) approach to the MEG inverse problem is revisited and extended to infer brain activity from full space-time data. The resulting dimensionality increase is tackled using a collection of techniques , that includes time and space dimension reduction (using respectively wavelet…
Enhances DSN with multi-family wavelet transforms and sparsity.
problem Improving interpretability and expressive power of DSN.
method Multi-family wavelet transforms and optimal thresholding.
result Enhanced robustness and diversity of scattering coefficients.
A major issue in harmonic analysis is to capture the phase dependence of frequency representations, which carries important signal properties. It seems that convolutional neural networks have found a way. Over time-series and images, convolutional networks often learn a first layer of filters which are well localized i…
The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of convolutional neural networks. Inspired by recent interest in geometric deep learning, which aims to generalize convolutional neural networks to manifold and graph-structured domains, we define a geometric…
A new GNN module learns geometric scattering features for better graph classification and feature exploration.
problem Learning long-range graph relations and extracting meaningful features from graphs.
method Proposes a learnable geometric scattering (LEGS) module in graph neural networks (GNNs), incorporating wavelet filters.
result LEGS-based GNNs outperform existing methods in graph classification and feature extraction tasks.
CGNNs use wavelets for continuous function generation in infinite-dimensional spaces.
problem Generating continuous functions in infinite-dimensional spaces for applications like inverse problems.
method Inspired by DCGAN, CGNNs use wavelet multiresolution analysis with convolutional and nonlinear layers.
result CGNNs can be injective under certain conditions on filters and nonlinearity, leading to Lipschitz stability estimates.
New model captures long-range patterns in sequences efficiently.
problem Efficiently capturing long-range patterns in sequential data.
method Inspired by wavelet multiresolution analysis, introduces MultiresLayer with multiresolution convolution.
result State-of-the-art performance on sequence classification and autoregressive density estimation tasks.
A novel algorithm for the decomposition of non-stationary multidimensional and multivariate signalsmath.NA
New algorithm for decomposing multidimensional, non-stationary signals.
problem Handling complex, non-stationary signals in multidimensional and multivariate data.
method Multidimensional and Multivariate Fast Iterative Filtering (MdMvFIF) algorithm.
result Extracts Intrinsic Mode Functions (IMFs) from complex signals varying in space and time.
Model predicts epileptic seizures by detecting preictal state using wavelet transform and PCA.
problem Predicting epileptic seizures before onset.
method Common spatial pattern filtering, wavelet transform for preprocessing, PCA for feature extraction, SVM for classification.
result Average sensitivity of 93.1% for 84 seizures in 23 subjects.
WavPool improves deep neural networks with wavelet-based pooling.
problem Improving efficiency and performance of deep neural networks.
method Introducing WavPool, a wavelet-transform-based pooling layer.
result WavPool outperforms existing network architectures by 10% on CIFAR-10.
We propose a simple and efficient time-series clustering framework particularly suited for low Signal-to-Noise Ratio (SNR), by simultaneous smoothing and dimensionality reduction aimed at preserving clustering information. We extend the sparse K-means algorithm by incorporating structured sparsity, and use it to exploi…
Feature extraction for automatic classification of EEG signals typically relies on time frequency representations of the signal. Techniques such as cepstral-based filter banks or wavelets are popular analysis techniques in many signal processing applications including EEG classification. In this paper, we present a com…
Deep convolutional neural networks have led to breakthrough results in numerous practical machine learning tasks such as classification of images in the ImageNet data set, control-policy-learning to play Atari games or the board game Go, and image captioning. Many of these applications first perform feature extraction …
It is the main goal of this article to address the bipartite ranking issue from the perspective of functional data analysis (FDA). Given a training set of independent realizations of a (possibly sampled) second-order random function with a (locally) smooth autocorrelation structure and to which a binary label is random…
Many practical machine learning tasks employ very deep convolutional neural networks. Such large depths pose formidable computational challenges in training and operating the network. It is therefore important to understand how fast the energy contained in the propagated signals (a.k.a. feature maps) decays across laye…
A Learnable Wavelet Transformer for Long-Short Equity Trading and Risk-Adjusted Return Optimizationcs.LG
WaveLSFormer learns profitable trading policies from financial time series data.
problem Challenges in learning profitable intraday trading policies from financial time series data.
method WaveLSFormer uses a learnable wavelet-based long-short Transformer to jointly perform multi-scale decomposition and return-oriented decision learning.
result WaveLSFormer consistently outperforms MLP, LSTM, and Transformer backbones in trading performance.
SWIFT improves time series forecasting on edge devices with wavelet decomposition.
problem Efficient time series forecasting on resource-constrained devices.
method Wavelet decomposition, cross-band fusion, and shared linear mapping.
result SWIFT achieves state-of-the-art performance on multiple datasets.
Proposes a new method to improve CNNs' shift invariance and accuracy.
problem Improving CNNs' shift invariance and prediction accuracy.
method Replaces RMax with CMod, a Gabor-like structure, to increase shift invariance and accuracy.
result Achieves superior accuracy on ImageNet and CIFAR-10 classification tasks.
Deep convolutional neural networks (CNNs) used in practice employ potentially hundreds of layers and ,s of nodes. Such network sizes entail significant computational complexity due to the large number of convolutions that need to be carried out; in addition, a large number of parameters needs to be learned and…
Recently, deep learning becomes the main focus of machine learning research and has greatly impacted many important fields. However, deep learning is criticized for lack of interpretability. As a successful unsupervised model in deep learning, the autoencoder embraces a wide spectrum of applications, yet it suffers fro…
The paper addresses instability in CNNs' first layer by proving max pooling's shift invariance.
problem Instability in CNNs' first layer, leading to sensitivity to small input shifts.
method Establishing conditions for max pooling's shift invariance and deriving a measure of stability.
result Max pooling approximates a nearly shift-invariant complex modulus under certain conditions.
Scattering transforms are non-trainable deep convolutional architectures that exploit the multi-scale resolution of a wavelet filter bank to obtain an appropriate representation of data. More importantly, they are proven invariant to translations, and stable to perturbations that are close to translations. This stabili…
This paper has proposed a new baseline deep learning model of more benefits for image classification. Different from the convolutional neural network(CNN) practice where filters are trained by back propagation to represent different patterns of an image, we are inspired by a method called "PCANet" in "PCANet: A Simple …
Filter banks are a popular tool for the analysis of piecewise smooth signals such as natural images. Motivated by the empirically observed properties of scale and detail coefficients of images in the wavelet domain, we propose a hierarchical deep generative model of piecewise smooth signals that is a recursion across s…
The scattering transform is a multilayered wavelet-based deep learning architecture that acts as a model of convolutional neural networks. Recently, several works have introduced generalizations of the scattering transform for non-Euclidean settings such as graphs. Our work builds upon these constructions by introducin…
Wavelets help compress neural networks efficiently.
problem Efficiently compressing linear layers in neural networks.
method Learnable wavelet transforms to compress RNNs.
result Wavelet compressed RNNs have fewer parameters and perform competitively.
Paper introduces rational Gaussian wavelets for efficient signal approximation.
problem Efficiently approximating complex signals with few coefficients.
method Continuous wavelet transform using rational Gaussian wavelets with adjustable parameters.
result Proposed rational Gaussian wavelets provide accurate signal approximations.
MODWST improves classification tasks with wavelet scattering.
problem Signal classification challenges.
method Combines MODWT and WST for feature extraction.
result MODWST outperforms CNNs in limited data scenarios.
An important problem in fiber-optic communications is to invert the nonlinear Schrödinger equation in real time to reverse the deterministic effects of the channel. Interestingly, the popular split-step Fourier method (SSFM) leads to a computation graph that is reminiscent of a deep neural network. This observation all…
Efficient Integration of Multi-Order Dynamics and Internal Dynamics in Stock Movement Predictionq-fin.ST
Proposes a framework to predict stock movements by integrating multi-order and internal dynamics.
problem Predicting stock movements with multi-order and internal dynamics.
method Temporal generative filters and hypergraph attentions using wavelet basis.
result Framework outperforms state-of-the-art methods in terms of profit and stability.
VDWs enhance graph neural networks for analyzing complex data.
problem Analyzing data on non-Euclidean geometries.
method Incorporating vector diffusion wavelets into geometric graph neural networks.
result VDW-GNNs effectively analyze synthetic and real-world data.
A complex-valued convolutional network (convnet) implements the repeated application of the following composition of three operations, recursively applying the composition to an input vector of nonnegative real numbers: (1) convolution with complex-valued vectors followed by (2) taking the absolute value of every entry…
New method selects diffusion scales for graph wavelets.
problem Choosing optimal diffusion scales for graph wavelets.
method Proposes an unsupervised method using information theory.
result Method selects diffusion scales for graph wavelets.
Convolution has been playing a prominent role in various applications in science and engineering for many years. It is the most important operation in convolutional neural networks. There has been a recent growth of interests of research in generalizing convolutions on curved domains such as manifolds and graphs. Howev…
Wavelet Kolmogorov-Arnold Networks improve federated learning performance.
problem Improving performance in federated learning with heterogeneous data.
method Implemented Wav-KAN with CWT and DWT for multiresolution capability, integrating wavelet-based activation functions.
result Significant improvements in computational efficiency, robustness, and accuracy in federated learning.
This paper proposes the use of wavelet methods to estimate U.S. core inflation. It explains wavelet methods and suggests they are ideally suited to this task. Comparisons are made with traditional CPI-based and regression-based measures for their performance in following trend inflation and predicting future inflation.…
Wavelet Networks learn from raw time-series data, outperforming conventional CNNs.
problem Learning from raw time-series data efficiently and effectively.
method Constructing scale-translation equivariant neural networks based on wavelet symmetries.
result Wavelet Networks outperform conventional CNNs on raw waveforms and spectrograms.
Scale-free avalanche dynamics in the stock marketphysics.soc-ph
Self-organized criticality has been claimed to play an important role in many natural and social systems. In the present work we empirically investigate the relevance of this theory to stock-market dynamics. Avalanches in stock-market indices are identified using a multi-scale wavelet-filtering analysis designed to rem…
Revisits SWIFT method for option pricing using Shannon wavelets.
problem Improving option pricing under known characteristic functions.
method SWIFT method based on Shannon wavelets.
result Exposes drawbacks and discusses improvements.
Optimizes wavelets for graph classification using spectral wavelet signatures and persistence diagrams.
problem Graph classification with geometric properties encoded in persistence diagrams.
method Optimizes spectral wavelets for graph datasets to capture best-suited features for classification.
result Competitive performance in graph classification problems compared to other persistence-based architectures.
Improved texture synthesis using wavelet-based statistics with rectifier non-linearity.
problem Improving texture synthesis quality using wavelet representations.
method Proposes a family of statistics based on non-linear wavelet representations with a generalized rectifier non-linearity.
result Significantly improves visual quality of texture synthesis compared to classical wavelet-based models.