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.
The paper proposes using CWT and STFT for training neural speech models.
problem Training high-quality neural speech models.
method Proposes spectral amplitude and phase losses from STFT and CWT for training.
result Shows that CWT spectral loss can train a high-quality model as good as STFT-based loss.
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.
We introduce multiscale invariant dictionaries to estimate quantum chemical energies of organic molecules, from training databases. Molecular energies are invariant to isometric atomic displacements, and are Lipschitz continuous to molecular deformations. Similarly to density functional theory (DFT), the molecule is re…
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.
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…
Wav-KAN improves neural network interpretability and performance.
problem Challenges in interpretability, training speed, robustness, and performance of traditional neural networks.
method Integrates wavelet functions into the Kolmogorov-Arnold network structure for efficient data representation.
result Enhanced accuracy, faster training speeds, and increased robustness compared to existing methods.
GWNN uses graph wavelets for efficient graph CNNs.
problem Spectral graph CNNs' high computational cost and lack of interpretability.
method Graph wavelet transform for efficient graph convolution.
result GWNN significantly outperforms spectral graph CNNs.
We analyze whether the prediction of the fractal markets hypothesis about a dominance of specific investment horizons during turbulent times holds. To do so, we utilize the continuous wavelet transform analysis and obtained wavelet power spectra which give the crucial information about the variance distribution across …
Paper introduces a neural framework for accurate energy forecasting.
problem Challenges of forecasting energy demand and supply due to variability of renewable sources and dynamic consumption patterns.
method Integrates Neural ODEs, graph attention, multi-resolution wavelet transformations, and adaptive learning of frequencies.
result Consistently outperforms state-of-the-art baselines in various forecasting metrics across diverse datasets.
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.
Stockformer uses wavelet transform and multi-task learning to predict stock returns and trends.
problem Challenges in predicting market dynamics due to policy uncertainty and economic events.
method Integrates wavelet transformation and multitask self-attention networks to capture market trends and fluctuations.
result Stockformer outperforms existing models on multiple real stock market datasets, demonstrating exceptional stability and reliability.
We introduce a new wavelet transform suitable for analyzing functions on point clouds and graphs. Our construction is based on a generalization of the average interpolating refinement scheme of Donoho. The most important ingredient of the original scheme that needs to be altered is the choice of the interpolant. Here, …
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…
Study proposes a new method for MRI image reconstruction using denoising autoencoders and undecimated wavelet transforms.
problem Efficient MRI image reconstruction using under-sampled data.
method Undecimated wavelet transform, denoising autoencoder, proximal gradient algorithm.
result The proposed method enhances MRI image reconstruction efficiency and robustness.
W-Transformers use wavelets to improve time series forecasting.
problem Forecasting non-stationary time series with long-range dependencies.
method Wavelet-based transformer architecture.
result W-Transformers outperform baseline models on various time series datasets.
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.
A method based on wavelet transform and genetic programming is proposed for characterizing and modeling variations at multiple scales in non-stationary time series. The cyclic variations, extracted by wavelets and smoothened by cubic splines, are well captured by genetic programming in the form of dynamical equations. …
Paper proposes integrating wavelet transform, channel attention, and LSTM for better stock price prediction.
problem Inherently difficult stock price prediction due to low signal-to-noise ratio.
method Wavelet transform convolution, channel attention, and LSTM integration.
result Robust performance in post-pandemic market conditions.
Improved signal classification using multiple wavelets and their smooth coefficients.
problem Signal classification accuracy declines with reduced attributes.
method Transform data with multiple wavelets, combine outputs, apply ensemble classifiers.
result Proposed technique outperforms raw data and single wavelet approaches.
Wavelet features improve image clustering and segmentation accuracy.
problem Noise and lack of spatial context in pixel intensity-based methods.
method Modified K-means, Fuzzy c-means, and ACWE algorithms incorporating Wavelet features.
result Wavelet-based algorithms converge to different segmentation results based on frequency information.
New wavelets use Monte Carlo for efficient discretization.
problem Efficiently discretizing continuous wavelets on general domains.
method Defined continuous wavelets via spectral calculus and proposed a Monte Carlo discretization.
result Convergence of Monte Carlo wavelets under natural regularity assumptions.
Recently the statistical characterizations of financial markets based on physics concepts and methods attract considerable attentions. We used two possible procedures of analyzing multifractal properties of a time series. The first one uses the continuous wavelet transform and extracts scaling exponents from the wavele…
Geometric wavelet scattering on manifolds improves neural network understanding.
problem Improving neural network understanding on manifold and graph domains.
method Defining a geometric scattering transform based on wavelet filters and nonlinearities.
result Generalizes deformation stability and local translation invariance to manifolds.
The paper analyzes how market prices respond to information processing and non-linear dynamics.
problem Understanding how market prices change in response to information.
method Logistic Continuous Wavelet Transformation method applied to SP 500 market data.
result Identifies patterns in market dynamics and describes them using a new theory of reflexive communication.
Deep convolutional neural networks have led to breakthrough results in practical feature extraction applications. The mathematical analysis of these networks was pioneered by Mallat, 2012. Specifically, Mallat considered so-called scattering networks based on identical semi-discrete wavelet frames in each network layer…
Fourier-transform infra-red (FTIR) spectra of samples from 7 plant species were used to explore the influence of preprocessing and feature extraction on efficiency of machine learning algorithms. Wavelet Tensor Train (WTT) and Discrete Wavelet Transforms (DWT) were compared as feature extraction techniques for FTIR dat…
Wavelet transform clusters climate data into biomes.
problem Understanding climate biomes through complex data.
method Discrete wavelet transform for coarse-graining, ensemble classification, information theory.
result Efficient consensus clustering identifies climate biomes.
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.
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 …
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.
Wavelet scattering spectra model non-Gaussian time-series, proving scale invariance for self-similar processes.
problem Modeling non-Gaussian time-series with stationary increments.
method Complex wavelet transform for scale variations, joint correlation matrix for scale dependencies, second wavelet transform for diagonalization, maximum entropy models conditioned by scattering spectra coefficients.
result Scattering spectra of self-similar processes are scale invariant, allowing statistical testing and generation of new time-series.
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.
A scattering transform defines a signal representation which is invariant to translations and Lipschitz continuous relatively to deformations. It is implemented with a non-linear convolution network that iterates over wavelet and modulus operators. Lipschitz continuity locally linearizes deformations. Complex classes o…
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 deep learning framework learns wavelet packet transforms for efficient feature extraction.
problem Efficiently extracting meaningful time-frequency features from high-frequency signals.
method Learnable wavelet packet transforms using deep learning.
result Improved spectral leakage and enhanced anomaly detection performance.
Stochastic volatility modelling of financial processes has become increasingly popular. The proposed models usually contain a stationary volatility process. We will motivate and review several nonparametric methods for estimation of the density of the volatility process. Both models based on discretely sampled continuo…
Generative Adversarial Nets (GANs) and Variational Auto-Encoders (VAEs) provide impressive image generations from Gaussian white noise, but the underlying mathematics are not well understood. We compute deep convolutional network generators by inverting a fixed embedding operator. Therefore, they do not require to be o…
Low-cost water-level tracking using LTE power metrics and wavelet analysis.
problem Real-time water-level monitoring across many locations with fixed instruments.
method Extracts per-antenna RSRP, RSSI, and RSRQ, applies CWT to RSRP, and uses a neural network to track water-level changes.
result Achieves root-mean-square and mean-absolute errors of 0.8 cm and 0.5 cm, respectively, under line-of-sight conditions.
Graph scattering transforms are stable to metric perturbations of network topology.
problem Stability of graph data representations under metric perturbations.
method Extending scattering transforms to network data using multiresolution graph wavelets and graph convolutions.
result Graph scattering transforms are stable to metric perturbations of the underlying network topology.
AWD distills neural network info into interpretable wavelets.
problem Imbalanced interpretability and efficiency in deep learning models.
method Adaptive wavelet distillation (AWD) penalizes neural network attributions in wavelet domain.
result AWD yields a concise, efficient, and interpretable model.
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.
Wavelet and LSTM models improve stock price forecasting.
problem Predicting non-stationary stock prices.
method Wavelet Transform for denoising, SVR and LSTM for prediction.
result Improved accuracy in stock price predictions.
Unified graph scattering transforms improve theoretical properties of graph neural networks.
problem Improving theoretical guarantees for graph neural networks.
method Introducing windowed and non-windowed geometric scattering transforms for graphs.
result Unified family of graph scattering transforms with provable stability and invariance.
Generates financial time series with stylized facts using diffusion models.
problem Generating realistic synthetic financial time series with statistical properties like fat tails, volatility clustering, and seasonality.
method Utilizes denoising diffusion probabilistic models (DDPMs) with wavelet transformation to convert and generate financial time series.
result Demonstrates that the proposed approach satisfies stylized financial time series properties.
We make use of wavelet transform to study the multi-scale, self similar behavior and deviations thereof, in the stock prices of large companies, belonging to different economic sectors. The stock market returns exhibit multi-fractal characteristics, with some of the companies showing deviations at small and large scale…
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.
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.