Explorando caminhos de mínima informação em grafos para problemas de classificação supervisionada

Abstract

Classification is a very important step in pattern recognition, as it aims to categorize objects from a set of inherent features, through its labeling. This process can be supervised, when there is a sample set of labeled training classes, semi-supervised, when the number of labeled samples is limited or nearly inexistent, or unsupervised, where there are no labeled samples. This project proposes to explore minimum information paths in graphs for classification problems, through the definition of a supervised, non-parametric, graph-based classification method, by means of a contextual approach. This method proposes to construct a graph from a set of training samples, where the samples are represented by vertices and the edges are links between samples that belongs to a neighborhood system. From the graph construction, the method calculates the local observed Fisher information, a measurement based on the Potts model, for all vertices, identifying the amount of information that each sample has. Generally, different class vertices when connected by an edge, have a high information level. After that, it is necessary to weight the edges by means of a function that penalizes connecting vertices with high information. During this process, it is possible to identify and select high information vertices, which will be chosen to be prototype vertices, namely, the nodes that define the classes boundaries. After the definition, the method proposes that each prototype sample conquer the remaining samples by offering the shortest path in terms of information, so that when a sample is conquered it receives the label of the winning prototype, occurring the classification. To evaluate the proposed method, statistical methods to estimate the error rates, such as Hold-out, K-fold and Leave-One- Out Cross-Validation will be considered. The obtained results indicate that the method can be a viable alternative to the existing classification techniques.