Publications related to ShapeNet: Convolutional Neural Networks on Non-Euclidean Manifolds

Smoothing technique for nonsmooth composite minimization with linear operator

We introduce and analyze an algorithm for the minimization of convex functions that are the sum of differentiable terms and proximable terms composed with linear operators. The method builds upon the recently developed smoothed gap technique. In addition t ...

2017

Towards Stationary Time-Vertex Signal Processing

Pierre Vandergheynst, Nathanaël Perraudin, Andreas Loukas, Francesco Grassi

Graph-based methods for signal processing have shown promise for the analysis of data exhibiting irregular structure, such as those found in social, transportation, and sensor networks. Yet, though these systems are often dynamic, state-of-the-art methods ...

Ieee2017

Geometric deep learning: going beyond Euclidean data

Pierre Vandergheynst, Michael Bronstein

Many signal processing problems involve data whose underlying structure is non-Euclidean, but may be modeled as a manifold or (combinatorial) graph. For instance, in social networks, the characteristics of users can be modeled as signals on the vertices of ...

2017

Towards stationary time-vertex signal processing

Pierre Vandergheynst, Nathanaël Perraudin, Andreas Loukas, Francesco Grassi

Graph-based methods for signal processing have shown promise for the analysis of data exhibiting irregular structure, such as those found in social, transportation, and sensor networks. Yet, though these systems are often dynamic, state-of-the-art methods ...

2016

Structure Tensor Total Variation

Michaël Unser, Stamatios Lefkimmiatis

We introduce a novel generic energy functional that we employ to solve inverse imaging problems within a variational framework. The proposed regularization family, termed as structure tensor total variation (STV), penalizes the eigenvalues of the structure ...

SIAM2015

Signal structure: from manifolds to molecules and structured sparsity

Sofia Karygianni

Effective representation methods and proper signal priors are crucial in most signal processing applications. In this thesis we focus on different structured models and we design appropriate schemes that allow the discovery of low dimensional latent struct ...

EPFL2015

Preconditioned Spectral Descent for Deep Learning

Volkan Cevher, Ya-Ping Hsieh, Edo Collins

Deep learning presents notorious computational challenges. These challenges in- clude, but are not limited to, the non-convexity of learning objectives and estimat- ing the quantities needed for optimization algorithms, such as gradients. While we do not a ...

2015

Principal Flows

Victor Panaretos, Tung Huy Pham, Zhigang Yao

We revisit the problem of extending the notion of principal component analysis (PCA) to multivariate datasets that satisfy nonlinear constraints, therefore lying on Riemannian manifolds. Our aim is to determine curves on the manifold that retain their cano ...

American Statistical Association2014

Tangent space estimation for smooth embeddings of Riemannian manifolds

Pascal Frossard, Elif Vural, Hemant Tyagi

Numerous dimensionality reduction problems in data analysis involve the recovery of low-dimensional models or the learning of manifolds underlying sets of data. Many manifold learning methods require the estimation of the tangent space of the manifold at a ...

2013

Correlation Estimation from Compressed Images

Pascal Frossard, Vijayaraghavan Thirumalai

This paper addresses the problem of correlation estimation in sets of compressed images. We consider a framework where images are represented under the form of linear measurements due to low complexity sensing or security requirements. We assume that the i ...

Elsevier2013

ShapeNet: Convolutional Neural Networks on Non-Euclidean Manifolds

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Smoothing technique for nonsmooth composite minimization with linear operator

Towards Stationary Time-Vertex Signal Processing

Geometric deep learning: going beyond Euclidean data

Towards stationary time-vertex signal processing

Structure Tensor Total Variation

Signal structure: from manifolds to molecules and structured sparsity

Preconditioned Spectral Descent for Deep Learning

Principal Flows

Tangent space estimation for smooth embeddings of Riemannian manifolds

Correlation Estimation from Compressed Images

Signal structure: from manifolds to molecules and structured sparsity

Structure Tensor Total Variation

Towards stationary time-vertex signal processing

Geometric deep learning: going beyond Euclidean data

Preconditioned Spectral Descent for Deep Learning

Tangent space estimation for smooth embeddings of Riemannian manifolds

Correlation Estimation from Compressed Images

Principal Flows

Smoothing technique for nonsmooth composite minimization with linear operator

Towards Stationary Time-Vertex Signal Processing