Adaptive sparse grid classification using grid environments

Abstract

Common techniques tackling the task of classification in data mining employ ansatz functions associated to training data points to fit the data as well as possible. Instead, the feature space can be discretized and ansatz functions centered on grid points can be used. This allows for classification algorithms scaling only linearly in the number of training data points, enabling to learn from data sets with millions of data points. As the curse of dimensionality prohibits the use of standard grids, sparse grids have to be used. Adaptive sparse grids allow to get a trade-off between both worlds by refining in rough regions of the target function rather than in smooth ones. We present new results for some typical classification tasks and show first observations of dimension adaptivity. As the study of the critical parameters during development involves many computations for different parameter values, we used a grid environment which we present. © Springer-Verlag Berlin Heidelberg 2007.