Although the Dirichlet distribution is widely used, the independence structure of its components limits its accuracy as a model. The proposed shadow Dirichlet distribution manipulates the support in order to model probability mass functions (pmfs) with dependencies or constraints that often arise in real world problems, such as regularized pmfs, monotonic pmfs, and pmfs with bounded variation. We describe some properties of this new class of distributions, provide maximum entropy constructions, give an expectation-maximization method for estimating the mean parameter, and illustrate with real data.

Similarity measures in many real applications generate indefinite similarity matrices. In this paper, we consider the problem of classification based on such indefinite similarities. These indefinite kernels can be problematic for standard kernel-based algorithms as the optimization problems become non-convex and the underlying theory is invalidated. In order to adapt kernel methods for similarity-based learning, we introduce a method that aims to simultaneously find a reproducing kernel Hilbert space based on the given similarities and train a classifier with good generalization in that space. The method is formulated as a convex optimization problem. We propose a simplified version that can reduce overfitting and whose associated convex conic program can be solved efficiently. We compare the proposed simplified version with six other methods on a collection of real data sets.

For many sensing modalities such as sonar, received signals are corrupted by multipath and can be challenging for automatic classification systems. An approach to jointly deconvolve and classify such signals is proposed. Specifically, a filter is estimated that minimizes the distortion between the received signal and a set of training signals, then the received signal is assigned to the class that corresponds to the training signal whose estimated filter is most sparse. Simulations compare the new method with blind deconvolution using Cabrelli's algorithm followed by a correlation-based nearest neighbor classifier. Results indicate that joint deconvolution and classification performs similarly to blind deconvolution in the presence of severe noise, and outperforms blind deconvolution at low and moderate noise levels.