Mishra, B., Meyer, G., Bach, F., & Sepulchre, R. (2012).

*Low-rank optimization with trace norm penalty*. Eprint/Working paper retrieved from http://arxiv.org/abs/1112.2318.The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is characterized ...

Mishra, B., Meyer, G., Bonnabel, S., & Sepulchre, R. (2012).

*Fixed-rank matrix factorizations and Riemannian low-rank optimization*. Eprint/Working paper retrieved from http://arxiv.org/abs/1209.0430.Motivated by the problem of learning a linear regression model whose parameter is a large fixed-rank non-symmetric matrix, we consider the optimization of a smooth cost function defined on the set of fixed ...

Mishra, B., Meyer, G., & Sepulchre, R. (2011). Low-rank optimization for distance matrix completion.

*Proceedings of the 50th IEEE Conference on Decision and Control*.Peer reviewed

This paper addresses the problem of low-rank
distance matrix completion. This problem amounts to recover
the missing entries of a distance matrix when the dimension of
the data embedding space is possibly ...

Meyer, G. (2011).

*Geometric optimization algorithms for linear regression on fixed-rank matrices*. Unpublished doctoral thesis, Université de Liège, Belgique.Nowadays, large and rapidly evolving data sets are commonly encountered in many modern applications. Efficiently mining and exploiting these data sets generally results in the extraction of valuable ...

Meyer, G., Bonnabel, S., & Sepulchre, R. (2011). Regression on fixed-rank positive semidefinite matrices: a Riemannian approach.

*Journal of Machine Learning Research, 12*(Feb), 593−625.Peer reviewed (verified by ORBi)

The paper addresses the problem of learning a regression model parameterized by a fixed-rank positive semidefinite matrix. The focus is on the nonlinear nature of the search space and on scalability to high ...

Meyer, G., Bonnabel, S., & Sepulchre, R. (2011). Linear regression under fixed-rank constraints: a Riemannian approach.

*Proceedings of the 28th International Conference on Machine Learning*.Peer reviewed

In this paper, we tackle the problem of learning a linear regression model whose parameter is a fixed-rank matrix. We study the Riemannian manifold geometry of the set of fixed-rank matrices and develop ...

Bonnabel, S., Meyer, G., & Sepulchre, R. (2010). Adaptive filtering for estimation of a low-rank positive semidefinite matrix.

*Proceedings of the 19th International Symposium on Mathematical Theory of Networks and Systems*.Peer reviewed

In this paper, we adopt a geometric viewpoint to tackle the problem of estimating a linear model whose parameter is a fixed-rank positive semidefinite matrix. We consider two gradient descent flows associated ...

Meyer, G., Journée, M., Bonnabel, S., & Sepulchre, R. (2009). From subspace learning to distance learning: a geometrical optimization approach.

*Proceedings of the 2009 IEEE Workshop on Statistical Signal Processing (SSP2009)*(pp. 385 - 388).In this paper, we adopt a differential-geometry viewpoint to tackle the problem of learning a distance online. As this prob- lem can be cast into the estimation of a fixed-rank positive semidefinite (PSD ...

Vaalburg, W., Coenen, H. H., Crouzel, C., Elsinga, P. H., Langstrom, B., Lemaire, C., & Meyer, G. (1992). Amino acids for the measurement of protein synthesis in vivo by PET.

*International Journal of Radiation Applications and Instrumentation. Part B : Nuclear Medicine and Biology, 19*(2), 227-37.Peer reviewed (verified by ORBi)

In principle, PET in combination with amino acids labelled with positron-emitting radionuclides and kinetic metabolic models, can quantify local protein synthesis rates in tissue in vivo. These PET ...