Decision boundary for discrete Bayesian network classifiers

Bayesian network classifiers are a powerful machine learning tool. In order to evaluate the expressive power of these models, we compute families of polynomials that sign-represent decision functions induced by Bayesian network classifiers. We prove that those families are linear combinations of products of Lagrange basis polynomials. In absence of V -structures in the predictor sub-graph, we are also able to prove that this family of polynomials does indeed characterize the specific classifier considered. We then use this representation to bound the number of decision functions representable by Bayesian network classifiers with a given structure.

Human-computer interaction based on visual hand-gesture recognition using volumetric spatiograms of local binary patterns

A more natural, intuitive, user-friendly, and less intrusive Human–Computer interface for controlling an application by executing hand gestures is presented. For this purpose, a robust vision-based hand-gesture recognition system has been developed, and a new database has been created to test it. The system is divided into three stages: detection, tracking, and recognition. The detection stage searches in every frame of a video sequence potential hand poses using a binary Support Vector Machine classifier and Local Binary Patterns as feature vectors. These detections are employed as input of a tracker to generate a spatio-temporal trajectory of hand poses. Finally, the recognition stage segments a spatio-temporal volume of data using the obtained trajectories, and compute a video descriptor called Volumetric Spatiograms of Local Binary Patterns (VS-LBP), which is delivered to a bank of SVM classifiers to perform the gesture recognition. The VS-LBP is a novel video descriptor that constitutes one of the most important contributions of the paper, which is able to provide much richer spatio-temporal information than other existing approaches in the state of the art with a manageable computational cost. Excellent results have been obtained outperforming other approaches of the state of the art.