Novel Multivariate Time Series Clustering Approach for E-Governance of Crime Data

Abstract

In recent past, there is an increased interest in multivariate time series (MTS) clustering research due to its wide applications in various areas such as finance, environmental research, multimedia and crime. The traditional similarity measures like correlation, Euclidean distance etc. cannot be applied to measure the similarity among data objects of MTS since every data object of MTS is in the form of a matrix. Although, some similarity measures like dynamic time warping (DTW), and extended Frobenius norm (Eros) have been introduced in the past for finding similarity among MTS data objects, they are either computationally expensive or inefficient for carrying out clustering of MTS datasets. In this paper, an efficient similarity measure has been introduced which outperforms the existing similarity measures. This paper also introduces a two phase methodology for e-governance of crime data with multiple inputs and multiple outputs. The first phase forms homogeneous groups of objects using MTS clustering based on the proposed similarity measure and the second phase measures the performance of homogeneous groups using Malmquist data envelopment analysis (DEA) model. The proposed similarity measure for MTS and two phase methodology can be applied to wide variety of real world problems. The effectiveness of the proposed approach has been illustrated on Indian crime data. Firstly, MTS clustering using proposed similarity measure is used to cluster various police administration units (PAUs) such as states, districts and police stations based on similar crime trends. Secondly, PAUs are ranked on the basis of their effective enforcement of crime prevention measures using Data Envelopment Analysis (DEA).