Publications related to Signal structure: from manifolds to molecules and structured sparsity

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Graph Embedded Nonparametric Mutual Information For Supervised Dimensionality Reduction

Nikolaos Arvanitopoulos Darginis

In this paper, we propose a novel algorithm for dimensionality reduction that uses as a criterion the mutual information (MI) between the transformed data and their cor- responding class labels. The MI is a powerful criterion that can be used as a proxy to ...

Institute of Electrical and Electronics Engineers2015

ShapeNet: Convolutional Neural Networks on Non-Euclidean Manifolds

Pierre Vandergheynst, Michael Bronstein

Feature descriptors play a crucial role in a wide range of geometry analysis and processing applications, including shape correspondence, retrieval, and segmentation. In this paper, we propose ShapeNet, a generalization of the popular convolutional neural ...

2015

Sparsistency of $\ell_1$-Regularized $M$-Estimators

Volkan Cevher, Jonathan Mark Scarlett, Yen-Huan Li

We consider the model selection consistency or sparsistency of a broad set of

\ell_1

-regularized

M

-estimators for linear and non-linear statistical models in a unified fashion. For this purpose, we propose the local structured smoothness condition (LSS ...

2015

Tangent-based manifold approximation with locally linear models

Pascal Frossard, Sofia Karygianni

In this paper, we consider the problem of manifold approximation with affine subspaces. Our objective is to discover a set of low dimensional affine subspaces that represent manifold data accurately while preserving the manifold's structure. For this purpo ...

Elsevier2014

Principal Polynomial Analysis

Devis Tuia

This paper presents a new framework for manifold learning based on a sequence of principal polynomials that capture the possibly nonlinear nature of the data. The proposed Principal Polynomial Analysis (PPA) generalizes PCA by modeling the directions of ma ...

World Scientific Publ Co Pte Ltd2014

Learning Parametric Dictionaries for Signals on Graphs

Pascal Frossard, David Shuman

In sparse signal representation, the choice of a dictionary often involves a tradeoff between two desirable properties – the ability to adapt to specific signal data and a fast implementation of the dictionary. To sparsely represent signals residing on wei ...

Institute of Electrical and Electronics Engineers2014

Metric Learning with Rank and Sparsity Constraints

Volkan Cevher, Baran Gözcü, Bubacarr Bah

Choosing a distance preserving measure or metric is fun- damental to many signal processing algorithms, such as k- means, nearest neighbor searches, hashing, and compressive sensing. In virtually all these applications, the efficiency of the signal process ...

Ieee2014

Jump-Sparse and Sparse Recovery Using Potts Functionals

Martin Kurt Storath

We recover jump-sparse and sparse signals from blurred incomplete data corrupted by (possibly non-Gaussian) noise using inverse Potts energy functionals. We obtain analytical results (existence of minimizers, complexity) on inverse Potts functionals and pr ...

Ieee-Inst Electrical Electronics Engineers Inc2014

Sparsistency of $\ell_1$-Regularized $M$-Estimators

Volkan Cevher, Jonathan Mark Scarlett, Yen-Huan Li

We consider the model selection consistency or sparsistency of a broad set of

\ell_1

-regularized

M

-estimators for linear and non-linear statistical models in a unified fashion. For this purpose, we propose the local structured smoothness condition (LSS ...

2015

Signal structure: from manifolds to molecules and structured sparsity

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Non-linear Recovery of Sparse Signal Representations with Applications to Temporal and Spatial Localization

Graph Embedded Nonparametric Mutual Information For Supervised Dimensionality Reduction

ShapeNet: Convolutional Neural Networks on Non-Euclidean Manifolds

Sparsistency of $\ell_1$-Regularized $M$-Estimators

Tangent-based manifold approximation with locally linear models

Structured Sparse Coding for Image Denoising or Pattern Detection

Principal Polynomial Analysis

Learning Parametric Dictionaries for Signals on Graphs

Metric Learning with Rank and Sparsity Constraints

Jump-Sparse and Sparse Recovery Using Potts Functionals

Graph Embedded Nonparametric Mutual Information For Supervised Dimensionality Reduction

Jump-Sparse and Sparse Recovery Using Potts Functionals

Non-linear Recovery of Sparse Signal Representations with Applications to Temporal and Spatial Localization

ShapeNet: Convolutional Neural Networks on Non-Euclidean Manifolds

Tangent-based manifold approximation with locally linear models

Sparsistency of $\ell_1$-Regularized $M$-Estimators

Structured Sparse Coding for Image Denoising or Pattern Detection

Principal Polynomial Analysis

Metric Learning with Rank and Sparsity Constraints

Learning Parametric Dictionaries for Signals on Graphs