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 …
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.
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 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…
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.
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.
Proposes a method to adapt labels on graphs with few labeled nodes.
problem Domain adaptation for graphs with limited labeled nodes.
method Optimization problem solving label transfer using spectral graph wavelets.
result Method yields satisfactory classification accuracy compared to existing methods.
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.
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.
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.
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.
Proposes a parsimonious graph spectral method for time series data.
problem Efficiently transmitting multivariate time series data.
method Graph spectral embedding with unsupervised, parsimonious encoding.
result Near-linear computational complexity and interpretable event structure.
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…
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.
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 …
MathNet uses wavelets for graph representation and learning.
problem Graph Neural Networks (GNNs) for graph classification and regression.
method Multiresolution Haar-like wavelets, graph convolution, and pooling.
result MathNet achieves notable accuracy gains on graph classification and regression tasks.
We introduce a novel harmonic analysis for functions defined on the vertices of a strongly connected directed graph of which the random walk operator is the cornerstone. As a first step, we consider the set of eigenvectors of the random walk operator as a non-orthogonal Fourier-type basis for functions over directed gr…
New method denoises graph signals using wavelets, scalable for large graphs.
problem Denoising graph signals with overcomplete tight frames and correlated noise.
method Data-driven wavelet tight frame, Stein's unbiased risk estimate, Chebyshev-Jackson polynomial approximations, Monte-Carlo strategy.
result Method scales to large graphs and finds applications in differential privacy.
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.
Unsupervised method removes satellite noise without paired data.
problem Image artifacts from satellite sensor noises affect quality and applications.
method Wavelet subband cycleGAN using adversarial and cycle-consistency losses.
result Effectively removes satellite noise while preserving high frequency features.
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 …
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.
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.
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.
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…
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, …
GSAN learns adaptive node representations using geometric scattering and attention.
problem Oversmoothing in node representation learning.
method Attention-based architecture integrating geometric scattering and GCN channels.
result GSAN outperforms previous networks in semi-supervised node classification.
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.
We consider the detection of activations over graphs under Gaussian noise, where signals are piece-wise constant over the graph. Despite the wide applicability of such a detection algorithm, there has been little success in the development of computationally feasible methods with proveable theoretical guarantees for ge…
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…
CSTs improve stability in covariance spectrum analysis without training.
problem Stability and expressiveness in covariance spectrum analysis.
method Sequential application of covariance wavelet filters to input data.
result Stable and expressive hierarchical representations in low-data settings.
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.
Improved spectral clustering algorithm for better performance.
problem Improving the performance of spectral clustering algorithms.
method Developed a new performance guarantee under a weaker assumption and evaluated using a different spectral embedding map.
result Better performance guarantee under a weaker assumption and evaluation of a new spectral embedding map.
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.
Root Laplacian Eigenmaps help in spectral embedding of graphs.
problem Efficient spectral embedding of graphs.
method Square root of graph-Laplacian operator.
result Improved spectral embedding techniques.
GRASPEL learns large graphs from data efficiently.
problem Learning meaningful graphs from data for various applications.
method Highly scalable spectral approach using graph Laplacians and coarsening techniques.
result Ultra-sparse graphs with improved efficiency and accuracy in spectral clustering and t-SNE.
This paper uses the relationship between graph conductance and spectral clustering to study (i) the failures of spectral clustering and (ii) the benefits of regularization. The explanation is simple. Sparse and stochastic graphs create a lot of small trees that are connected to the core of the graph by only one edge. G…
Introduces Spectral Graph Network combining spatial and spectral message passing.
problem Relational reasoning in graph structured data.
method Applies message passing to both spatial and spectral domains of a graph.
result Promotes efficient training with fewer iterations and robustness to edge dropout.
Enhanced spectral clustering for geometric graphs improves clustering accuracy.
problem Ineffective standard spectral clustering for geometric graphs.
method Higher-order spectral clustering using higher-order eigenvectors.
result Established weak and strong consistency for Soft Geometric Block Model.
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.
Graph convolutional networks(GCNs) have become the most popular approaches for graph data in these days because of their powerful ability to extract features from graph. GCNs approaches are divided into two categories, spectral-based and spatial-based. As the earliest convolutional networks for graph data, spectral-bas…
Proves generic existence of spectral networks for many cases.
problem Existence of spectral networks for a broad range of spectral data.
method Generic existence proof for spectral networks.
result Proves existence for a large class of spectral data.
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.
Laplacian Eigenvectors of the graph constructed from a data set are used in many spectral manifold learning algorithms such as diffusion maps and spectral clustering. Given a graph constructed from a random sample of a d-dimensional compact submanifold M in RD, we establish the spectral convergence rate…