Incremental Linear Discriminant Analysis Using Sufficient Spanning Sets and Its Applications

This paper presents an incremental learning solution for Linear Discriminant Analysis (LDA) and its applications to object recognition problems. We apply the sufficient spanning set approximation in three steps i.e. update for the total scatter matrix, between-class scatter matrix and the projected data matrix, which leads an online solution which closely agrees with the batch solution in accuracy while significantly reducing the computational complexity. The algorithm yields an efficient solution to incremental LDA even when the number of classes as well as the set size is large. The incremental LDA method has been also shown useful for semi-supervised online learning. Label propagation is done by integrating the incremental LDA into an EM framework. The method has been demonstrated in the task of merging large datasets which were collected during MPEG standardization for face image retrieval, face authentication using the BANCA dataset, and object categorisation using the Caltech101 dataset. © 2010 Springer Science+Business Media, LLC.

A reason for unreason: returns-based beliefs in game theory

Players cooperate in experiments more than game theory would predict. We introduce the ‘returns-based beliefs’ approach: the expected returns of a particular strategy in proportion to total expected returns of all strategies. Using a decision analytic solution concept, Luce’s (1959) probabilistic choice model, and ‘hyperpriors’ for ambiguity in players’ cooperability, our approach explains empirical observations in various classes of games including the Prisoner’s and Traveler’s Dilemmas. Testing the closeness of fit of our model on Selten and Chmura (2008) data for completely mixed 2 × 2 games shows that with loss aversion, returns-based beliefs explain the data better than other equilibrium concepts.

Sufficient conditions for zeno behavior in lagrangian hybrid systems

This paper presents easily verifiable sufficient conditions for the existence of Zenobehavior in Lagrangian hybrid systems, i.e., hybrid systems modeling mechanical systemsundergoing impacts. © 2008 Springer-Verlag Berlin Heidelberg.