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MOTIVATION
Clustering is a useful exploratory technique for the analysis of gene expression data. Many different heuristic clustering algorithms have been proposed in this context. Clustering algorithms based on probability models offer a principled alternative to heuristic algorithms. In particular, model-based clustering assumes that the data is generated… (More)

We present an approach that allows performing computations related to the Baker-Campbell-Haussdorff (BCH) formula and its generalizations in an arbitrary Hall basis, using labeled rooted trees. In particular, we provide explicit formulas (given in terms of the structure of certain labeled rooted trees) of the continuous BCH formula. We develop a rewriting… (More)

- Ph Chartier, A Murua, J M Sanz-Serna
- 2012

The techniques, based on formal series and combinatorics, used nowadays to analyze numerical integrators may be applied to perform high-order averaging in oscillatory periodic or quasi-periodic dynamical systems. When this approach is employed, the averaged system may be written in terms of (i) scalar coefficients that are universal, i.e. independent of the… (More)

- Alejandro Murua
- 1999

A practical and useful notion of weak dependence between many classifiers constructed with the same training data is introduced. It is shown that when (a) this weak dependence is rather low, and (b) the expected margins are large, exponential bounds on the true error rates can be achieved. Empirical results with randomized trees, and trees constructed via… (More)

- T. Richardson, S. Roy, R. A. Ali, A. Murua
- 2001

- Ka Yee Yeung, Chris Fraley, Alejandro Murua, Adrian E. Rafter, Walter L. Ruzzo
- 2001

Before applying model-based clustering to gene expression data, we assessed the extent to which the Gaussian mixture assumption holds. Since we do not expect raw expression data to satisfy the Gaussian mixture assumption, we explored the degree of normality of each class after applying different data transformations. In particular, we studied two types of… (More)

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