#### Filter Results:

- Full text PDF available (67)

#### Publication Year

1998

2017

- This year (2)
- Last 5 years (39)
- Last 10 years (69)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Data Set Used

#### Key Phrases

Learn More

- Pierre-Antoine Absil, C. G. Baker, Kyle A. Gallivan
- Foundations of Computational Mathematics
- 2007

A general scheme for trust-region methods on Riemannian manifolds is proposed and analyzed. Among the various approaches available to (approximately) solve the trust-region subproblems, particular attention is paid to the truncated conjugate-gradient technique. The method is illustrated on problems from numerical linear algebra.

- Michel Journée, Francis R. Bach, Pierre-Antoine Absil, Rodolphe Sepulchre
- SIAM Journal on Optimization
- 2010

We propose an algorithm for solving optimization problems defined on a subset of the cone of symmetric positive semidefinite matrices. This algorithm relies on the factorization X = Y Y T , where the number of columns of Y fixes an upper bound on the rank of the positive semidefinite matrix X. It is thus very effective for solving problems that have a… (More)

- Pierre-Antoine Absil, Robert E. Mahony, B. Andrews
- SIAM Journal on Optimization
- 2005

In the early eighties Lojasiewicz [Loj84] proved that a bounded solution of a gradient flow for an analytic cost function converges to a well-defined limit point. In this paper, we show that the iterates of numerical descent algorithms, for an analytic cost function, share this convergence property if they satisfy certain natural descent conditions. The… (More)

- Nicolas Boumal, Pierre-Antoine Absil
- NIPS
- 2011

We consider large matrices of low rank. We address the problem of recovering such matrices when most of the entries are unknown. Matrix completion finds applications in recommender systems. In this setting, the rows of the matrix may correspond to items and the columns may correspond to users. The known entries are the ratings given by users to some items.… (More)

- Nicolas Boumal, Bamdev Mishra, Pierre-Antoine Absil, Rodolphe Sepulchre
- Journal of Machine Learning Research
- 2014

Optimization on manifolds is a rapidly developing branch of nonlinear optimization. Its focus is on problems where the smooth geometry of the search space can be leveraged to design efficient numerical algorithms. In particular, optimization on manifolds is wellsuited to deal with rank and orthogonality constraints. Such structured constraints appear… (More)

- Andrew E. Teschendorff, Michel Journée, Pierre-Antoine Absil, Rodolphe Sepulchre, Carlos Caldas
- PLoS Computational Biology
- 2007

The quantity of mRNA transcripts in a cell is determined by a complex interplay of cooperative and counteracting biological processes. Independent Component Analysis (ICA) is one of a few number of unsupervised algorithms that have been applied to microarray gene expression data in an attempt to understand phenotype differences in terms of changes in the… (More)

- Pierre-Antoine Absil, K. Kurdyka
- Systems & Control Letters
- 2006

This paper studies the relations between the local minima of a cost function f and the stable equilibria of the gradient descent flow of f . In particular, it is shown that, under the assumption that f is real analytic, local minimality is necessary and sufficient for stability. Under the weaker assumption that f is indefinitely continuously differentiable,… (More)

- Filippo Pompili, Nicolas Gillis, Pierre-Antoine Absil, François Glineur
- Neurocomputing
- 2014

Approximate matrix factorization techniques with both nonnegativity and orthogonality constraints, referred to as orthogonal nonnegative matrix factorization (ONMF), have been recently introduced and shown to work remarkably well for clustering tasks such as document classification. In this paper, we introduce two new methods to solve ONMF. First, we show… (More)

- Pierre-Antoine Absil, Kyle A. Gallivan
- 2006 IEEE International Conference on Acoustics…
- 2006

Several blind source separation algorithms obtain a separating matrix by computing the congruence transformation that "best" diagonalizes a collection of covariance matrices. Recent methods avoid a pre-whitening phase and directly attempt to compute a non-orthogonal diagonalizing congruence. However, since the magnitude of the sources is unknown, there is a… (More)