Applied and Computational Harmonic Analysis最新文献

The spectral barycentre of a set of graphs with community structure 一类具有群落结构的图的谱质心

IF 3.2 2区数学

Applied and Computational Harmonic Analysis Pub Date : 2025-10-02 DOI: 10.1016/j.acha.2025.101816

François G. Meyer

{"title":"The spectral barycentre of a set of graphs with community structure","authors":"François G. Meyer","doi":"10.1016/j.acha.2025.101816","DOIUrl":"10.1016/j.acha.2025.101816","url":null,"abstract":"<div><div>The notion of barycentre graph is of crucial importance for machine learning algorithms that process graph-valued data. The barycentre graph is a “summary graph” that captures the mean topology and connectivity structure of a training dataset of graphs. The construction of a barycentre requires the definition of a metric to quantify distances between pairs of graphs. In this work, we use a multiscale spectral distance that is defined using the eigenvalues of the normalized graph Laplacian. The eigenvalues – but not the eigenvectors – of the normalized Laplacian of the barycentre graph can be determined from the optimization problem that defines the barycentre. In this work, we propose a structural constraint on the eigenvectors of the normalized graph Laplacian of the barycentre graph that guarantees that the barycentre inherits the topological structure of the graphs in the sample dataset. The eigenvectors can be computed using an algorithm that explores the large library of Soules bases. When the graphs are random realizations of a balanced stochastic block model, then our algorithm returns a barycentre that converges asymptotically (in the limit of large graph size) almost-surely to the population mean of the graphs. We perform Monte Carlo simulations to validate the theoretical properties of the estimator; we conduct experiments on real-life graphs that suggest that our approach works beyond the controlled environment of stochastic block models.</div></div>","PeriodicalId":55504,"journal":{"name":"Applied and Computational Harmonic Analysis","volume":"80 ","pages":"Article 101816"},"PeriodicalIF":3.2,"publicationDate":"2025-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145266273","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Randomized Kaczmarz with tail averaging 尾部平均随机化Kaczmarz

IF 3.2 2区数学

Applied and Computational Harmonic Analysis Pub Date : 2025-09-18 DOI: 10.1016/j.acha.2025.101812

Ethan N. Epperly , Gil Goldshlager , Robert J. Webber

引用次数: 0

Adaptive multipliers for extrapolation in frequency 频率外推的自适应乘法器

IF 3.2 2区数学

Applied and Computational Harmonic Analysis Pub Date : 2025-09-15 DOI: 10.1016/j.acha.2025.101815

Diego Castelli Lacunza , Carlos A. Sing Long

{"title":"Adaptive multipliers for extrapolation in frequency","authors":"Diego Castelli Lacunza , Carlos A. Sing Long","doi":"10.1016/j.acha.2025.101815","DOIUrl":"10.1016/j.acha.2025.101815","url":null,"abstract":"<div><div>Resolving the details of an object from coarse-scale measurements is a classical problem in applied mathematics. This problem is usually formulated as extrapolating the Fourier transform of the object from a bounded region to the entire space, that is, in terms of performing <em>extrapolation in frequency</em>. This problem is ill-posed unless one assumes that the object has some additional structure. When the object is compactly supported, then it is well-known that its Fourier transform can be extended to the entire space. However, it is also well-known that this problem is severely ill-conditioned.</div><div>In this work, we assume that the object is known to belong to a collection of compactly supported functions and, instead of performing extrapolation in frequency to the entire space, we study the problem of extrapolating to a larger bounded set using dilations in frequency and a single Fourier multiplier. This is reminiscent of the refinement equation in multiresolution analysis. Under suitable conditions, we prove the existence of a worst-case optimal multiplier over the entire collection, and we show that all such multipliers share the same canonical structure. When the collection is finite, we show that any worst-case optimal multiplier can be represented in terms of an Hermitian matrix. This allows us to introduce a fixed-point iteration to find the optimal multiplier. This leads us to introduce a family of multipliers, which we call <span><math><mstyle><mi>Σ</mi></mstyle></math></span>-multipliers, that can be used to perform extrapolation in frequency. We establish connections between <span><math><mstyle><mi>Σ</mi></mstyle></math></span>-multipliers and multiresolution analysis. We conclude with some numerical experiments illustrating the practical consequences of our results.</div></div>","PeriodicalId":55504,"journal":{"name":"Applied and Computational Harmonic Analysis","volume":"80 ","pages":"Article 101815"},"PeriodicalIF":3.2,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Manifold learning in metric spaces 度量空间中的流形学习

IF 3.2 2区数学

Applied and Computational Harmonic Analysis Pub Date : 2025-09-14 DOI: 10.1016/j.acha.2025.101813

Liane Xu , Amit Singer

引用次数: 0

Gaussian random fields and monogenic images 高斯随机场和单基因图像

IF 3.2 2区数学

Applied and Computational Harmonic Analysis Pub Date : 2025-09-14 DOI: 10.1016/j.acha.2025.101814

Hermine Biermé , Philippe Carré , Céline Lacaux , Claire Launay

{"title":"Gaussian random fields and monogenic images","authors":"Hermine Biermé , Philippe Carré , Céline Lacaux , Claire Launay","doi":"10.1016/j.acha.2025.101814","DOIUrl":"10.1016/j.acha.2025.101814","url":null,"abstract":"<div><div>In this paper, we focus on lighthouse anisotropic fractional Brownian fields (AFBFs), whose self-similarity depends solely on the so-called Hurst parameter, while anisotropy is revealed through the opening angle of an oriented spectral cone. This fractional field generalizes fractional Brownian motion and models rough natural phenomena. Consequently, estimating the model parameters is a crucial issue for modeling and analyzing real data. This work introduces the representation of AFBFs using the monogenic transform. Combined with a multiscale analysis, the monogenic signal is built from the Riesz transform to extract local orientation and structural information from an image at different scales. We then exploit the monogenic signal to define new estimators of AFBF parameters in the particular case of lighthouse fields. We prove that the estimators of anisotropy and self-similarity index (called the Hurst index) are strongly consistent. We demonstrate that these estimators verify asymptotic normality with explicit variance. We also introduce an estimator of the texture orientation. We propose a numerical scheme for calculating the monogenic representation and strategies for computing the estimators. Numerical results illustrate the performance of these estimators. Regarding Hurst index estimation, estimators based on the monogenic representation of random fields appear to be more robust than those using only the Riesz transform. We show that both estimation methods outperform standard estimation procedures in the isotropic case and provide excellent results for all degrees of anisotropy.</div></div>","PeriodicalId":55504,"journal":{"name":"Applied and Computational Harmonic Analysis","volume":"80 ","pages":"Article 101814"},"PeriodicalIF":3.2,"publicationDate":"2025-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145121214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Demystifying Carleson frames 揭开卡尔森镜框的神秘面纱

IF 3.2 2区数学

Applied and Computational Harmonic Analysis Pub Date : 2025-09-12 DOI: 10.1016/j.acha.2025.101811

Ilya Krishtal, Brendan Miller

引用次数: 0

Pattern recovery by SLOPE 利用斜率恢复模式

IF 3.2 2区数学

Applied and Computational Harmonic Analysis Pub Date : 2025-09-08 DOI: 10.1016/j.acha.2025.101810

Małgorzata Bogdan , Xavier Dupuis , Piotr Graczyk , Bartosz Kołodziejek , Tomasz Skalski , Patrick Tardivel , Maciej Wilczyński

{"title":"Pattern recovery by SLOPE","authors":"Małgorzata Bogdan , Xavier Dupuis , Piotr Graczyk , Bartosz Kołodziejek , Tomasz Skalski , Patrick Tardivel , Maciej Wilczyński","doi":"10.1016/j.acha.2025.101810","DOIUrl":"10.1016/j.acha.2025.101810","url":null,"abstract":"<div><div>SLOPE is a popular method for dimensionality reduction in high-dimensional regression. Its estimated coefficients can be zero, yielding sparsity, or equal in absolute value, yielding clustering. As a result, SLOPE can eliminate irrelevant predictors and identify groups of predictors that have the same influence on the response. The concept of the SLOPE pattern allows us to formalize and study its sparsity and clustering properties. In particular, the SLOPE pattern of a coefficient vector captures the signs of its components (positive, negative, or zero), the clusters (groups of coefficients with the same absolute value), and the ranking of those clusters. This is the first paper to thoroughly investigate the consistency of the SLOPE pattern. We establish necessary and sufficient conditions for SLOPE pattern recovery, which in turn enable the derivation of an irrepresentability condition for SLOPE given a fixed design matrix <span><math><mi>X</mi></math></span>. These results lay the groundwork for a comprehensive asymptotic analysis of SLOPE pattern consistency.</div></div>","PeriodicalId":55504,"journal":{"name":"Applied and Computational Harmonic Analysis","volume":"80 ","pages":"Article 101810"},"PeriodicalIF":3.2,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145096438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Optimal lower Lipschitz bounds for ReLU layers, saturation, and phase retrieval 最优下Lipschitz边界的ReLU层，饱和度和相位检索

IF 3.2 2区数学

Applied and Computational Harmonic Analysis Pub Date : 2025-08-28 DOI: 10.1016/j.acha.2025.101801

Daniel Freeman , Daniel Haider

引用次数: 0

Sparse free deconvolution under unknown noise level via eigenmatrix 基于特征矩阵的未知噪声下的稀疏自由反卷积

IF 3.2 2区数学

Applied and Computational Harmonic Analysis Pub Date : 2025-08-14 DOI: 10.1016/j.acha.2025.101802

Lexing Ying

引用次数: 0

Sharp error estimates for target measure diffusion maps with applications to the committor problem 针对提交者问题的应用程序的目标度量扩散映射的精确误差估计

IF 3.2 2区数学

Applied and Computational Harmonic Analysis Pub Date : 2025-08-14 DOI: 10.1016/j.acha.2025.101803

Shashank Sule , Luke Evans , Maria Cameron

{"title":"Sharp error estimates for target measure diffusion maps with applications to the committor problem","authors":"Shashank Sule , Luke Evans , Maria Cameron","doi":"10.1016/j.acha.2025.101803","DOIUrl":"10.1016/j.acha.2025.101803","url":null,"abstract":"<div><div>We obtain asymptotically sharp error estimates for the consistency error of the Target Measure Diffusion map (TMDmap) (Banisch et al. 2020), a variant of diffusion maps featuring importance sampling and hence allowing input data drawn from an arbitrary density. The derived error estimates include the bias error and the variance error. The resulting convergence rates are consistent with the approximation theory of graph Laplacians. The key novelty of our results lies in the explicit quantification of all the prefactors on leading-order terms. We also prove an error estimate for solutions of Dirichlet BVPs obtained using TMDmap, showing that the solution error is controlled by consistency error. We use these results to study an important application of TMDmap in the analysis of rare events in systems governed by overdamped Langevin dynamics using the framework of transition path theory (TPT). The cornerstone ingredient of TPT is the solution of the committor problem, a boundary value problem for the backward Kolmogorov PDE. Remarkably, we find that the TMDmap algorithm is particularly suited as a meshless solver to the committor problem due to the cancellation of several error terms in the prefactor formula. Furthermore, significant improvements in bias and variance errors occur when using a quasi-uniform sampling density. Our numerical experiments show that these improvements in accuracy are realizable in practice when using <em>δ</em>-nets as spatially uniform inputs to the TMDmap algorithm.</div></div>","PeriodicalId":55504,"journal":{"name":"Applied and Computational Harmonic Analysis","volume":"79 ","pages":"Article 101803"},"PeriodicalIF":3.2,"publicationDate":"2025-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144885793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0