Iteratively reweighted least squares (IRLS) is a standard algorithm used to compute a maximum likelihood estimate of a generalized linear model ( 10); see McCullagh and Nelder (1983) for details. The algorithm is easy to implement, and the code is available at numerous sources, e.g., Komarek (2004), Givens and Hoeting (2012) among others. Here, we present the pseudo-code to highlight matrix-vector operations involved in the implementation. Matrix-vector operations is where our approach diverges from the standard implementation.
In this paper, we consider a set of unlabeled tree objects with topological and geometric properties. For each data object, two curve representations are developed to characterize its topological and geometric aspects. We further define the notions of topological and geometric medians as well as quantiles based on both representations. In addition, we take a novel approach to define the Pareto medians and quantiles through a multi-objective optimization problem. In particular, we study two different objective functions which measure the topological variation and geometric variation respectively. Analytical solutions are provided for topological and geometric medians and quantiles, and in general, for Pareto medians and quantiles, the genetic algorithm is implemented. The proposed methods are applied to analyze a data set of pyramidal neurons.
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