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Concept

Partitionnement spectral

Publications associées (29)

Unsupervised Graph Representation Learning with Cluster-aware Self-training and Refining

Yichen Xu, Qiang Liu

Unsupervised graph representation learning aims to learn low-dimensional node embeddings without supervision while preserving graph topological structures and node attributive features. Previous Graph Neural Networks (GNN) require a large number of labeled ...

Assoc Computing Machinery2023

Improving K-means Clustering Using Speculation

Anastasia Ailamaki, Viktor Sanca, Eleni Zapridou, Stefan Igescu

K-means is one of the fundamental unsupervised data clustering and machine learning methods. It has been well studied over the years: parallelized, approximated, and optimized for different cases and applications. With increasingly higher parallelism leadi ...

2023

Brain Fingerprinting Using Fmri Spectral Signatures On High-Resolution Cortical Graphs

Dimitri Nestor Alice Van De Ville, Maria Giulia Preti, Stefano Moia, Hamid Behjat

Resting-state fMRI has proven to entail subject-specific signatures that can serve as a fingerprint to identify individuals. Conventional methods are based on building a connectivity matrix based on correlation between the average time course of pairs of b ...

IEEE2023

Linearization and Identification of Multiple-Attractor Dynamical Systems through Laplacian Eigenmaps

Aude Billard, Bernardo Fichera

Dynamical Systems (DS) are fundamental to the modeling and understanding time evolving phenomena, and have application in physics, biology and control. As determining an analytical description of the dynamics is often difficult, data-driven approaches are ...

Microtome Publishing2022

Manifold Learning-Based Polynomial Chaos Expansions For High-Dimensional Surrogate Models

Ketson Roberto Maximiano Dos Santos

In this work we introduce a manifold learning-based method for uncertainty quantification (UQ) in systems describing complex spatiotemporal processes. Our first objective is to identify the embedding of a set of high-dimensional data representing quantitie ...

2022

Motif Cut Sparsifiers

Mikhail Kapralov, Jakab Tardos, Mikhail Makarov

A motif is a frequently occurring subgraph of a given directed or undirected graph G (Milo et al.). Motifs capture higher order organizational structure of G beyond edge relationships, and, therefore, have found wide applications such as in graph clusterin ...

IEEE COMPUTER SOC2022

Sublinear Algorithms for Spectral Graph Clustering

Aidasadat Mousavifar

This thesis focuses on designing spectral tools for graph clustering in sublinear time. With the emergence of big data, many traditional polynomial time, and even linear time algorithms have become prohibitively expensive. Processing modern datasets requir ...

EPFL2021

On Perfect Clustering of High Dimension, Low Sample Size Data

Soham Sarkar

Popular clustering algorithms based on usual distance functions (e.g., the Euclidean distance) often suffer in high dimension, low sample size (HDLSS) situations, where concentration of pairwise distances and violation of neighborhood structure have advers ...

IEEE COMPUTER SOC2020

Optimal Convergence for Distributed Learning with Stochastic Gradient Methods and Spectral Algorithms

Volkan Cevher, Junhong Lin

We study generalization properties of distributed algorithms in the setting of nonparametric regression over a reproducing kernel Hilbert space (RKHS). We first investigate distributed stochastic gradient methods (SGM), with mini-batches and multi-passes o ...

2020

Graph Spectral Clustering of Convolution Artefacts in Radio Interferometric Images

Paul Hurley, Matthieu Martin Jean-André Simeoni

The starting point for deconvolution methods in radioastronomy is an estimate of the sky intensity called a dirty image. These methods rely on the telescope point-spread function so as to remove artefacts which pollute it. In this work, we show that the in ...

IEEE2019

Stochastic Gradient Descent for Spectral Embedding with Implicit Orthogonality Constraint

Pascal Frossard, Mireille El Gheche

In this paper, we propose a scalable algorithm for spectral embedding. The latter is a standard tool for graph clustering. However, its computational bottleneck is the eigendecomposition of the graph Laplacian matrix, which prevents its application to larg ...

IEEE2019

Guided graph spectral embedding: Application to the C. elegans connectome

Dimitri Nestor Alice Van De Ville, Maria Giulia Preti, Thomas William Arthur Bolton, Raphaël Pierre Liégeois, Miljan Petrovic

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-for example, based on wavel ...

2019

Graph Reduction with Spectral and Cut Guarantees

Andreas Loukas

Can one reduce the size of a graph without significantly altering its basic properties? The graph reduction problem is hereby approached from the perspective of restricted spectral approximation, a modification of the spectral similarity measure used for g ...

Microtome Publishing2019

Graph Spectral Analysis Of Voxel-Wise Brain Graphs From Diffusion-Weighted Mri

Dimitri Nestor Alice Van De Ville, Anjali Bagunu Tarun, Hamid Behjat

Non-invasive characterization of brain structure has been made possible by the introduction of magnetic resonance imaging (MRI). Graph modeling of structural connectivity has been useful, but is often limited to defining nodes as regions from a brain atlas ...

IEEE2019

New Multi-Keyword Ciphertext Search Method for Sensor Network Cloud Platforms

Jiyong Zhang, Hongyu Yang

This paper proposed a multi-keyword ciphertext search, based on an improved-quality hierarchical clustering (MCS-IQHC) method. MCS-IQHC is a novel technique, which is tailored to work with encrypted data. It has improved search accuracy and can self-adapt ...

MDPI2018

Robust and Efficient Data Clustering with Signal Processing on Graphs

Lionel Jérémie Martin

Data is pervasive in today's world and has actually been for quite some time. With the increasing volume of data to process, there is a need for faster and at least as accurate techniques than what we already have. In particular, the last decade recorded t ...

EPFL2018

Spectrally approximating large graphs with smaller graphs

Pierre Vandergheynst, Andreas Loukas

How does coarsening affect the spectrum of a general graph? We provide conditions such that the principal eigenvalues and eigenspaces of a coarsened and original graph Laplacian matrices are close. The achieved approximation is shown to depend on standard ...

2018

Optimal Convergence for Distributed Learning with Stochastic Gradient Methods and Spectral Algorithms

Volkan Cevher, Junhong Lin

2018

Neural Tanget Kernel: Convergence and Generalization in Neural Networks

Clément Hongler, Franck Raymond Gabriel, Arthur Ulysse Jacot-Guillarmod

At initialization, artificial neural networks (ANNs) are equivalent to Gaussian processes in the infinite-width limit [12, 9], thus connecting them to kernel methods. We prove that the evolution of an ANN during training can also be described by a kernel: ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2018

When Slepian Meets Fiedler: Putting a Focus on the Graph Spectrum

Dimitri Nestor Alice Van De Ville, Maria Giulia Preti, Robin Jonathan Demesmaeker

The study of complex systems greatly benefits from graph models and their analysis. In particular, the eigendecomposition of the graph Laplacian lets emerge properties of global organization from local interactions; e.g., the Fiedler vector has the smalles ...

IEEE Institute of Electrical and Electronics Engineers2017