Michel Journée

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In this paper we develop a new approach to sparse principal component analysis (sparse PCA). We propose two single-unit and two block optimization formulations of the sparse PCA problem, aimed at extracting a single sparse dominant principal component of a data matrix, or more components at once, respectively. While the initial formulations involve(More)
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)
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)
We propose an algorithm for solving nonlinear convex programs defined in terms of a symmetric positive semidefinite matrix variable X. This algorithm rests on the factorization X = Y Y T , where the number of columns of Y fixes the rank of X. It is thus very effective for solving programs that have a low rank solution. The factorization X = Y Y T evokes a(More)
DNA microarrays provide such a huge amount of data that unsupervised methods are required to reduce the dimension of the data set and to extract meaningful biological information. This work shows that Independent Component Analysis (ICA) is a promising approach for the analysis of genome-wide transcriptomic data. The paper first presents an overview of the(More)
In this paper, we adopt a differential-geometry viewpoint to tackle the problem of learning a distance online. As this problem can be cast into the estimation of a fixed-rank positive semidefinite (PSD) matrix, we develop algorithms that exploits the rich geometry structure of the set of fixed-rank PSD matrices. We propose a method which separately updates(More)
This paper is concerned with methods for suboptimal control of nonlinear systems. A new approach to the synthesis of approximate optimal controllers is presented. The new methodology is compared to various known techniques on three complex examples systems that correspond to practical processes. The strengths and weaknesses of the different methods are(More)
DNA microarrays provide a huge amount of data and require therefore dimensionality reduction methods to extract meaningful biological information. Independent component analysis (ICA) was proposed by several authors as an interesting means. Unfortunately, experimental data are usually of poor quality because of noise, outliers and lack of samples.(More)
This paper derives a new algorithm that performs independent component analysis (ICA) by optimizing the contrast function of the RADICAL algorithm. The core idea of the proposed optimization method is to combine the global search of a good initial condition with a gradient-descent algorithm. This new ICA algorithm performs faster than the RADICAL algorithm(More)
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