Search Results for author: René Vidal

Found 25 papers, 3 papers with code

Doubly Stochastic Subspace Clustering

1 code implementation30 Nov 2020 Derek Lim, René Vidal, Benjamin D. Haeffele

Many state-of-the-art subspace clustering methods follow a two-step process by first constructing an affinity matrix between data points and then applying spectral clustering to this affinity.

Image Clustering

A Critique of Self-Expressive Deep Subspace Clustering

no code implementations ICLR 2021 Benjamin D. Haeffele, Chong You, René Vidal

To extend this approach to data supported on a union of non-linear manifolds, numerous studies have proposed learning an embedding of the original data using a neural network which is regularized by a self-expressive loss function on the data in the embedded space to encourage a union of linear subspaces prior on the data in the embedded space.

A Game Theoretic Analysis of Additive Adversarial Attacks and Defenses

no code implementations NeurIPS 2020 Ambar Pal, René Vidal

Research in adversarial learning follows a cat and mouse game between attackers and defenders where attacks are proposed, they are mitigated by new defenses, and subsequently new attacks are proposed that break earlier defenses, and so on.

On dissipative symplectic integration with applications to gradient-based optimization

no code implementations15 Apr 2020 Guilherme França, Michael. I. Jordan, René Vidal

More specifically, we show that a generalization of symplectic integrators to nonconservative and in particular dissipative Hamiltonian systems is able to preserve rates of convergence up to a controlled error.

Finding the Sparsest Vectors in a Subspace: Theory, Algorithms, and Applications

no code implementations20 Jan 2020 Qing Qu, Zhihui Zhu, Xiao Li, Manolis C. Tsakiris, John Wright, René Vidal

The problem of finding the sparsest vector (direction) in a low dimensional subspace can be considered as a homogeneous variant of the sparse recovery problem, which finds applications in robust subspace recovery, dictionary learning, sparse blind deconvolution, and many other problems in signal processing and machine learning.

Dictionary Learning Representation Learning

On the Regularization Properties of Structured Dropout

no code implementations CVPR 2020 Ambar Pal, Connor Lane, René Vidal, Benjamin D. Haeffele

We also show that the global minimizer for DropBlock can be computed in closed form, and that DropConnect is equivalent to Dropout.

The fastest $\ell_{1,\infty}$ prox in the west

no code implementations9 Oct 2019 Benjamín Béjar, Ivan Dokmanić, René Vidal

In this paper we study the proximal operator of the mixed $\ell_{1,\infty}$ matrix norm and show that it can be computed in closed form by applying the well-known soft-thresholding operator to each column of the matrix.

Gradient flows and proximal splitting methods: A unified view on accelerated and stochastic optimization

no code implementations2 Aug 2019 Guilherme França, Daniel P. Robinson, René Vidal

We show that similar discretization schemes applied to Newton's equation with an additional dissipative force, which we refer to as accelerated gradient flow, allow us to obtain accelerated variants of all these proximal algorithms -- the majority of which are new although some recover known cases in the literature.

Distributed Optimization

Representation Learning on Visual-Symbolic Graphs for Video Understanding

no code implementations ECCV 2020 Effrosyni Mavroudi, Benjamín Béjar Haro, René Vidal

To capture this rich visual and semantic context, we propose using two graphs: (1) an attributed spatio-temporal visual graph whose nodes correspond to actors and objects and whose edges encode different types of interactions, and (2) a symbolic graph that models semantic relationships.

Ranked #4 on Action Detection on Charades (using extra training data)

Action Classification Action Detection +5

Conformal Symplectic and Relativistic Optimization

1 code implementation NeurIPS 2020 Guilherme França, Jeremias Sulam, Daniel P. Robinson, René Vidal

Arguably, the two most popular accelerated or momentum-based optimization methods in machine learning are Nesterov's accelerated gradient and Polyaks's heavy ball, both corresponding to different discretizations of a particular second order differential equation with friction.

On Geometric Analysis of Affine Sparse Subspace Clustering

no code implementations17 Aug 2018 Chun-Guang Li, Chong You, René Vidal

In this paper, we develop a novel geometric analysis for a variant of SSC, named affine SSC (ASSC), for the problem of clustering data from a union of affine subspaces.

A nonsmooth dynamical systems perspective on accelerated extensions of ADMM

no code implementations13 Aug 2018 Guilherme França, Daniel P. Robinson, René Vidal

The acceleration technique introduced by Nesterov for gradient descent is widely used in optimization but its principles are not yet fully understood.

Monocular Object Orientation Estimation using Riemannian Regression and Classification Networks

1 code implementation19 Jul 2018 Siddharth Mahendran, Ming Yang Lu, Haider Ali, René Vidal

We consider the task of estimating the 3D orientation of an object of known category given an image of the object and a bounding box around it.

Data Augmentation General Classification

Global Optimality in Separable Dictionary Learning with Applications to the Analysis of Diffusion MRI

no code implementations15 Jul 2018 Evan Schwab, Benjamin D. Haeffele, René Vidal, Nicolas Charon

In the classical setting, signals are represented as vectors and the dictionary learning problem is posed as a matrix factorization problem where the data matrix is approximately factorized into a dictionary matrix and a sparse matrix of coefficients.

Denoising Dictionary Learning

End-to-End Fine-Grained Action Segmentation and Recognition Using Conditional Random Field Models and Discriminative Sparse Coding

no code implementations29 Jan 2018 Effrosyni Mavroudi, Divya Bhaskara, Shahin Sefati, Haider Ali, René Vidal

We introduce an end-to-end algorithm for jointly learning the weights of the CRF model, which include action classification and action transition costs, as well as an overcomplete dictionary of mid-level action primitives.

Action Classification Action Segmentation +1

An Analysis of Dropout for Matrix Factorization

no code implementations10 Oct 2017 Jacopo Cavazza, Connor Lane, Benjamin D. Haeffele, Vittorio Murino, René Vidal

While the resulting regularizer is closely related to a variational form of the nuclear norm, suggesting that dropout may limit the size of the factorization, we show that it is possible to trivially lower the objective value by doubling the size of the factorization.

(k,q)-Compressed Sensing for dMRI with Joint Spatial-Angular Sparsity Prior

no code implementations21 Jul 2017 Evan Schwab, René Vidal, Nicolas Charon

Advanced diffusion magnetic resonance imaging (dMRI) techniques, like diffusion spectrum imaging (DSI) and high angular resolution diffusion imaging (HARDI), remain underutilized compared to diffusion tensor imaging because the scan times needed to produce accurate estimations of fiber orientation are significantly longer.

Provable Self-Representation Based Outlier Detection in a Union of Subspaces

no code implementations CVPR 2017 Chong You, Daniel P. Robinson, René Vidal

While outlier detection methods based on robust statistics have existed for decades, only recently have methods based on sparse and low-rank representation been developed along with guarantees of correct outlier detection when the inliers lie in one or more low-dimensional subspaces.

Outlier Detection

Joint Spatial-Angular Sparse Coding for dMRI with Separable Dictionaries

no code implementations18 Dec 2016 Evan Schwab, René Vidal, Nicolas Charon

High angular resolution diffusion imaging (HARDI) can produce better estimates of fiber orientation than the popularly used diffusion tensor imaging, but the high number of samples needed to estimate diffusivity requires longer patient scan times.

Structured Sparse Subspace Clustering: A Joint Affinity Learning and Subspace Clustering Framework

no code implementations17 Oct 2016 Chun-Guang Li, Chong You, René Vidal

In this paper, we propose a joint optimization framework --- Structured Sparse Subspace Clustering (S$^3$C) --- for learning both the affinity and the segmentation.

Motion Segmentation

Car Segmentation and Pose Estimation using 3D Object Models

no code implementations21 Dec 2015 Siddharth Mahendran, René Vidal

Image segmentation and 3D pose estimation are two key cogs in any algorithm for scene understanding.

3D Pose Estimation Scene Understanding +1

Moving poselets: A discriminative and interpretable skeletal motion representation for action recognition

no code implementations 2015 IEEE International Conference on Computer Vision Workshop (ICCVW) 2015 Lingling Tao, René Vidal

While automatic feature learning methods such as supervised sparse dictionary learning or neural networks can be applied to learn feature representation and action classifiers jointly, the resulting features are usually uninterpretable.

Action Recognition Dictionary Learning +2

Finding Exemplars from Pairwise Dissimilarities via Simultaneous Sparse Recovery

no code implementations NeurIPS 2012 Ehsan Elhamifar, Guillermo Sapiro, René Vidal

Given pairwise dissimilarities between data points, we consider the problem of finding a subset of data points called representatives or exemplars that can efficiently describe the data collection.

Sparse Manifold Clustering and Embedding

no code implementations NeurIPS 2011 Ehsan Elhamifar, René Vidal

We propose an algorithm called Sparse Manifold Clustering and Embedding (SMCE) for simultaneous clustering and dimensionality reduction of data lying in multiple nonlinear manifolds.

Dimensionality Reduction

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