Nonparametric Estimation of the Bayes Error

This thesis is concerned with the performance of nonparametric classifiers and their application to the estimation of the Rayes error. Although the behavior of these classifiers as the number of preclassified design samples becomes infinite is well understood, very little is known regarding their finite sample error performance. Here, we examine the performance of Parzen and k-nearest neighbor (k-NN) classifiers, relating the expected error rates to the size of the design set and the various, design parameters (kernel size and shape, value of k, distance metric for nearest neighbor calculation, etc.). These results lead to several significant improvements in the design procedures for nonparametric classifiers, as well as improved estimates of the Bayes error rate. , Our results show that increasing the sample size is in many cases not an effective practical means of improving the classifier performance. Rather, careful attention must be paid to the decision threshold, selection of the kernel size and shape (for Parzen classifiers), and selection of k and the distance metric (for k-NN classifiers). Guidelines are developed toward propper selection of each of these parameters. The use of nonparametric error rates for Bayes error estimation is also considered, and techniques are given which reduce or compensate for the biases of the nonparametric error rates. A bootstrap technique is also developed which allows the designer to estimate the standard deviation of a nonparametric estimate of the Bayes error

One-class classifiers based on entropic spanning graphs

One-class classifiers offer valuable tools to assess the presence of outliers in data. In this paper, we propose a design methodology for one-class classifiers based on entropic spanning graphs. Our approach takes into account the possibility to process also non-numeric data by means of an embedding procedure. The spanning graph is learned on the embedded input data and the outcoming partition of vertices defines the classifier. The final partition is derived by exploiting a criterion based on mutual information minimization. Here, we compute the mutual information by using a convenient formulation provided in terms of the $\alpha$-Jensen difference. Once training is completed, in order to associate a confidence level with the classifier decision, a graph-based fuzzy model is constructed. The fuzzification process is based only on topological information of the vertices of the entropic spanning graph. As such, the proposed one-class classifier is suitable also for data characterized by complex geometric structures. We provide experiments on well-known benchmarks containing both feature vectors and labeled graphs. In addition, we apply the method to the protein solubility recognition problem by considering several representations for the input samples. Experimental results demonstrate the effectiveness and versatility of the proposed method with respect to other state-of-the-art approaches.Comment: Extended and revised version of the paper "One-Class Classification Through Mutual Information Minimization" presented at the 2016 IEEE IJCNN, Vancouver, Canad

Classification of non-heat generating outdoor objects in thermal scenes for autonomous robots

We have designed and implemented a physics-based adaptive Bayesian pattern classification model that uses a passive thermal infrared imaging system to automatically characterize non-heat generating objects in unstructured outdoor environments for mobile robots. In the context of this research, non-heat generating objects are defined as objects that are not a source for their own emission of thermal energy, and so exclude people, animals, vehicles, etc. The resulting classification model complements an autonomous bot\u27s situational awareness by providing the ability to classify smaller structures commonly found in the immediate operational environment. Since GPS depends on the availability of satellites and onboard terrain maps which are often unable to include enough detail for smaller structures found in an operational environment, bots will require the ability to make decisions such as go through the hedges or go around the brick wall. A thermal infrared imaging modality mounted on a small mobile bot is a favorable choice for receiving enough detailed information to automatically interpret objects at close ranges while unobtrusively traveling alongside pedestrians. The classification of indoor objects and heat generating objects in thermal scenes is a solved problem. A missing and essential piece in the literature has been research involving the automatic characterization of non-heat generating objects in outdoor environments using a thermal infrared imaging modality for mobile bots. Seeking to classify non-heat generating objects in outdoor environments using a thermal infrared imaging system is a complex problem due to the variation of radiance emitted from the objects as a result of the diurnal cycle of solar energy. The model that we present will allow bots to see beyond vision to autonomously assess the physical nature of the surrounding structures for making decisions without the need for an interpretation by humans.;Our approach is an application of Bayesian statistical pattern classification where learning involves labeled classes of data (supervised classification), assumes no formal structure regarding the density of the data in the classes (nonparametric density estimation), and makes direct use of prior knowledge regarding an object class\u27s existence in a bot\u27s immediate area of operation when making decisions regarding class assignments for unknown objects. We have used a mobile bot to systematically capture thermal infrared imagery for two categories of non-heat generating objects (extended and compact) in several different geographic locations. The extended objects consist of objects that extend beyond the thermal camera\u27s field of view, such as brick walls, hedges, picket fences, and wood walls. The compact objects consist of objects that are within the thermal camera\u27s field of view, such as steel poles and trees. We used these large representative data sets to explore the behavior of thermal-physical features generated from the signals emitted by the classes of objects and design our Adaptive Bayesian Classification Model. We demonstrate that our novel classification model not only displays exceptional performance in characterizing non-heat generating outdoor objects in thermal scenes but it also outperforms the traditional KNN and Parzen classifiers