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Image classification is a challenging problem for computer in reality. Large numbers of methods can achieve satisfying performances with sufficient labeled images. However, labeled images are still highly limited for certain image…

Computer Vision and Pattern Recognition · Computer Science 2020-11-12 Hongfeng Li

Frames have established themselves as a means to derive redundant, yet stable decompositions of a signal for analysis or transmission, while also promoting sparse expansions. However, when the signal dimension is large, the computation of…

Numerical Analysis · Mathematics 2011-06-30 Peter G. Casazza , Andreas Heinecke , Felix Krahmer , Gitta Kutyniok

Spectral methods are popular in detecting global structures in the given data that can be represented as a matrix. However when the data matrix is sparse or noisy, classic spectral methods usually fail to work, due to localization of…

Machine Learning · Statistics 2016-09-12 Pan Zhang

We propose and investigate a unifying class of sparse random graph models, based on a hidden coloring of edge-vertex incidences, extending an existing approach, Random graphs with a given degree distribution, in a way that admits a…

Statistical Mechanics · Physics 2009-11-10 Bo Söderberg

Graph clustering is a challenging pattern recognition problem whose goal is to identify vertex partitions with high intra-group connectivity. This paper investigates a bi-objective problem that maximizes the number of intra-cluster edges of…

Social and Information Networks · Computer Science 2019-09-10 Camila P. S. Tautenhain , Mariá C. V. Nascimento

Subgraph pattern detection aims to uncover complex interaction structures in graphs. However, state-of-the-art graph neural network (GNN)-based solutions assume centralized access to the entire graph. When graphs are instead distributed…

Machine Learning · Computer Science 2026-05-08 Selin Ceydeli , Rui Wang , Kubilay Atasu

In this paper, we present an algorithm to automatically detect meaningful modes in a histogram. The proposed method is based on the behavior of local minima in a scale-space representation. We show that the detection of such meaningful…

Computer Vision and Pattern Recognition · Computer Science 2014-01-14 Jérôme Gilles , Kathryn Heal

Although NP-Complete problems are the most difficult decisional problems, it is possible to discover in them polynomial (or easy) observables. We study the Graph Partitioning Problem showing that it is possible to recognize in it two…

Condensed Matter · Physics 2009-11-07 M. A. Marchisio

With the recent advances in complex networks theory, graph-based techniques for image segmentation has attracted great attention recently. In order to segment the image into meaningful connected components, this paper proposes an image…

Computer Vision and Pattern Recognition · Computer Science 2019-07-12 Youssef Mourchid , Mohammed El Hassouni , Hocine Cherifi

This work will appear as a chapter in a forthcoming volume titled `Topics in Probabilistic Graph Theory'. For a given graph $G$, each partition of the vertices has a modularity score, with higher values indicating that the partition better…

Probability · Mathematics 2025-09-29 Colin McDiarmid , Fiona Skerman

The goal of this paper is to show that there exists a simple, yet universal statistical logic of spectral graph analysis by recasting it into a nonparametric function estimation problem. The prescribed viewpoint appears to be good enough to…

Statistics Theory · Mathematics 2016-09-22 Subhadeep Mukhopadhyay

Sparse additive models are an attractive choice in circumstances calling for modelling flexibility in the face of high dimensionality. We study the signal detection problem and establish the minimax separation rate for the detection of a…

Statistics Theory · Mathematics 2024-10-03 Subhodh Kotekal , Chao Gao

We discuss a variant of `blind' community detection, in which we aim to partition an unobserved network from the observation of a (dynamical) graph signal defined on the network. We consider a scenario where our observed graph signals are…

Social and Information Networks · Computer Science 2019-04-29 Michael T. Schaub , Santiago Segarra , Hoi-To Wai

Using the theory of equitable decompositions it is possible to decompose a matrix $M$ appropriately associated with a given graph. The result is a collection of smaller matrices whose collective eigenvalues are the same as the eigenvalues…

Combinatorics · Mathematics 2018-09-24 Amanda Francis , Dallas Smith , Benjamin Webb

The sparse representation classifier (SRC) is shown to work well for image recognition problems that satisfy a subspace assumption. In this paper we propose a new implementation of SRC via screening, establish its equivalence to the…

Machine Learning · Computer Science 2019-06-05 Cencheng Shen , Li Chen , Yuexiao Dong , Carey Priebe

In this paper, we propose a new framework for segmenting feature-based moving objects under affine subspace model. Since the feature trajectories in practice are high-dimensional and contain a lot of noise, we firstly apply the sparse PCA…

Computer Vision and Pattern Recognition · Computer Science 2017-01-25 Michael Ying Yang , Hanno Ackermann , Weiyao Lin , Sitong Feng , Bodo Rosenhahn

Partition of unity methods (PUMs) on graphs represent straightforward and remarkably adaptable auxiliary techniques for graph signal processing. By relying solely on the intrinsic graph structure, we propose the generation of a partition of…

Numerical Analysis · Mathematics 2023-11-09 Roberto Cavoretto , Alessandra De Rossi , Sandro Lancellotti , Federico Romaniello

A graph $G=(V,E)$ is a {\it unipolar graph} if there exits a partition $V=V_1 \cup V_2$ such that, $V_1$ is a clique and $V_2$ induces the disjoint union of cliques. The complement-closed class of {\it generalized split graphs} are those…

Discrete Mathematics · Computer Science 2013-09-24 Elaine M. Eschen , Xiaoqiang Wang

Recent spectral graph sparsification techniques have shown promising performance in accelerating many numerical and graph algorithms, such as iterative methods for solving large sparse matrices, spectral partitioning of undirected graphs,…

Data Structures and Algorithms · Computer Science 2020-08-19 Ying Zhang , Zhiqiang Zhao , Zhuo Feng

We study a spectral generalization of classical combinatorial graph spanners to the spectral setting. Given a set of vectors $V\subseteq \Re^d$, we say a set $U\subseteq V$ is an $\alpha$-spectral spanner if for all $v\in V$ there is a…

Data Structures and Algorithms · Computer Science 2019-11-19 Piotr Indyk , Sepideh Mahabadi , Shayan Oveis Gharan , Alireza Rezaei