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.
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. Different from graph Fourier transform, graph wavelet transform can be obtained …
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.
In this note, we present a new way to associate a spectral triple to the noncommutative C∗-algebra C∗(Λ) of a strongly connected finite higher-rank graph Λ. We generalize a spectral triple of Consani and Marcolli from Cuntz-Krieger algebras to higher-rank graph C∗-algebras C∗(Λ), and we prove that these s…
We propose a new framework for manifold denoising based on processing in the graph Fourier frequency domain, derived from the spectral decomposition of the discrete graph Laplacian. Our approach uses the Spectral Graph Wavelet transform in order to per- form non-iterative denoising directly in the graph frequency domai…
In this paper we propose and study a family of continuous wavelets on general domains, and a corresponding stochastic discretization that we call Monte Carlo wavelets. First, using tools from the theory of reproducing kernel Hilbert spaces and associated integral operators, we define a family of continuous wavelets by …
Wavelets model complex interactions in spatial transcriptomics.
problem Capturing higher-order relationships in spatial transcriptomics data.
method Hypergraph diffusion wavelets for representing hyperedges.
result Wavelets effectively represent disease-relevant cellular niches in Alzheimer's disease.
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.
Recently, we proposed short-time Fourier transform (STFT)-based loss functions for training a neural speech waveform model. In this paper, we generalize the above framework and propose a training scheme for such models based on spectral amplitude and phase losses obtained by either STFT or continuous wavelet transform …
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.
WCAM assesses neural network reliability by attributing decisions to wavelet scales.
problem Challenges in evaluating neural network reliability and feature robustness.
method Introduces WCAM, a wavelet-based attribution method to assess decision reliability.
result WCAM reveals where and on what scales a model focuses, enabling reliable decision assessment.
Coherent Multiplex analyzes real-time wavelet coherence among multiple signals.
problem Identifying and visualizing coherence among multiple time series.
method Fast spectral similarity based on cosine similarity metrics of Fourier-transformed signals and sparse time-frequency wavelet coherence.
result Scalable real-time system for low-latency inference and monitoring of inter-signal relationships.
We analyze the Bombay stock exchange (BSE) price index over the period of last 12 years. Keeping in mind the large fluctuations in last few years, we carefully find out the transient, non-statistical and locally structured variations. For that purpose, we make use of Daubechies wavelet and characterize the fractal beha…
Multi-spectral satellite imaging sensors acquire various spectral band images such as red (R), green (G), blue (B), near-infrared (N), etc. Thanks to the unique spectroscopic property of each spectral band with respective to the objects on the ground, multi-spectral satellite imagery can be used for various geological …
Paper combines geometry and time-series analysis for spatiotemporal data.
problem Multivariate time-series data from multiple sensors.
method Combines manifold learning, Riemannian geometry, and spectral analysis.
result Proposes Riemannian multi-resolution analysis (RMRA) for dynamic mode extraction.
Algorithm identifies fractal system's scaling exponents in high dimensions.
problem Statistical identification of Hurst distribution in high-dimensional fractal systems.
method Wavelet random matrices, modified spectral clustering, model selection.
result Algorithm consistently estimates Hurst distribution in moderately high dimensions.
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.
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.
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…
SpGAT learns graph representations using spectral attention for efficiency.
problem Efficiently capturing global graph patterns with minimal parameters.
method Introduces Spectral Graph Attention Network (SpGAT) using spectral domain attention mechanisms and a fast Chebychev approximation.
result SpGAT achieves better global pattern recognition with fewer parameters compared to GAT.
We have presented a novel technique of detecting intermittencies in a financial time series of the foreign exchange rate data of U.S.- Euro dollar(US/EUR) using a combination of both statistical and spectral techniques. This has been possible due to Continuous Wavelet Transform (CWT) analysis which has been popularly a…
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.
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…
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.
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.
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.
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.
Cake wavelets minimize orientation score uncertainty.
problem Minimizing uncertainty in orientation scores.
method Axiomatically derived wavelets for orientation score lifting.
result Uncertainty gap of cake wavelets is less than 1.1.
Wavelet SGM accelerates generative modeling with linear time complexity.
problem High computational cost in SGMs.
method Factorizing data distribution into wavelet coefficients.
result WSGM synthesizes wavelet coefficients with linear time complexity.
MLShrink integrates machine learning with wavelet shrinkage for denoising.
problem Denoising signals with uncertain magnitudes
method Combines wavelet shrinkage with machine learning
result Preserves simplicity for signal coefficients while allowing data-adaptive decisions for ambiguous coefficients
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.
Unified method for simultaneous denoising and clustering.
problem Clustering noisy signals.
method Sparse convex wavelet clustering with fusion and group-sparse penalties.
result Unified approach that denoises and clusters simultaneously.
Variational Autoencoders (VAE) are probabilistic deep generative models underpinned by elegant theory, stable training processes, and meaningful manifold representations. However, they produce blurry images due to a lack of explicit emphasis over high-frequency textural details of the images, and the difficulty to dire…
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.
A new WNN framework selects wavelet bases for efficient learning.
problem Challenges in constructing accurate wavelet bases and high computational costs in WNN.
method Introduces a constructive WNN that selects initial bases and trains functions by introducing new bases for predefined accuracy while reducing computational costs.
result Significantly improves computational efficiency through a frequency estimator and wavelet-basis increase mechanism.
Pixel intensity is a widely used feature for clustering and segmentation algorithms, the resulting segmentation using only intensity values might suffer from noises and lack of spatial context information. Wavelet transform is often used for image denoising and classification. We proposed a novel method to incorporate …
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.
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…
A new model for generating point processes with complex geometries.
problem Difficulties in modeling point processes with large numbers of particles and complex geometries.
method Gradient descent algorithm applied to a phase harmonic operator on wavelet transforms of point patterns.
result The model allows for fast sampling of new configurations that match the statistics of observed point processes.
Graph spectral analysis can yield meaningful embeddings of graphs by providing insight into distributed features not directly accessible in nodal domain. Recent efforts in graph signal processing have proposed new decompositions-e.g., based on wavelets and Slepians-that can be applied to filter signals defined on the g…
Wavelet analysis reveals non-linear dynamics in cryptocurrency prices.
problem Understanding non-linear dynamics in high-frequency cryptocurrency prices.
method Wavelet analysis of frequency and time variables.
result Cyclical persistence at different frequencies in cryptocurrency prices.
New method estimates and samples high-dimensional probability distributions avoiding optimization and approximation curse.
problem Estimating high-dimensional probability distributions from data samples.
method Hierarchic probability flow from coarse to fine scales, defined by conditional probabilities across scales.
result Sampling hierarchic models avoids critical slowing down at phase transitions and generates turbulence and dark matter images.
Wavelet analysis reveals financialization effects on oil-food price correlation.
problem Investigating the correlation between oil and food prices and their determinants.
method Wavelet analysis and energy-based measures to differentiate high and low frequency movements.
result Significant local correlation between food and oil is due to financialization and emerging economies' demand.