Feature selection generating directed rough-spanning tree for crime pattern analysis

Abstract

Nowadays, crime is a major threat to the society that affects the normal life of human beings all over the world. It is very important to make the world free from all aspects of crime activities. The main motivation of this work is to understand various crime patterns for avoiding and preventing the crime events to occur in future and save the world from such curse. Though research is going on for solving such problems, no work is noticed to handle the roughness or ambiguity that exists in the crime reports. The present work extracts all possible crime features from the crime reports and selects only the important features required for crime pattern analysis. For this purpose, it develops a purely supervised feature selection model integrating rough set theory and graph theory (spanning tree of a directed weighted graph). The crime reports are preprocessed, and crime features are extracted to represent each report as a feature vector (i.e., a set of distinct crime features). For crime pattern analysis, the main objective of our work, all extracted features are not necessarily essential, rather a minimal subset of relevant features are sufficient. Thus, feature selection is the main contribution in the paper that not only enhances the efficiency of subsequent mining process but also increases its correctness. The rough set theory-based relative indiscernibility relation is defined to measure the similarity between two features relative to the crime type. Based on the similarity score, a weighted and directed graph has been constructed that comprises the features as nodes and the inverse of the similarity score representing the similarity of feature v to u as the weight of the corresponding edge. Then, a minimal spanning tree (termed as rough-spanning tree) is generated using Edmond/Chu–Liu algorithm from the constructed directed graph and the importance of the nodes in the spanning tree is measured using the weights of the edges and the degrees (in-degrees and out-degrees) of the nodes in the spanning tree. Finally, a feature selection algorithm has been proposed that selects the most important node and remove it from the spanning tree iteratively until the modified graph (not necessarily a tree) becomes a null graph. The selected nodes are considered as the important feature subset sufficient for crime pattern analysis. The method is evaluated using various statistical measures and compared with related state-of-the-art methods to express its effectiveness in crime pattern analysis. The Wilcoxon rank-sum test, a popular nonparametric version of the two-sample t test, is done to express that the proposed supervised model is statistically significant.