Spatio Temporal Sparsity in Homicide Prediction Models

Alvaro J Riascos Villegas,Johan Garcia Vargas,Mateo Dulce Rubio,Sebastian Quintero,Hernan Garcia,Juan S Moreno Pabon

doi:10.1109/access.2022.3143858

Alvaro J Riascos Villegas, Johan Garcia Vargas + Show 4 more

Open Access

https://doi.org/10.1109/access.2022.3143858

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Abstract

Homicide prediction is a challenging task due to the spatio-temporal sparsity of these crime events. In this paper we report the results of using several approaches to mitigate this sparsity condition in machine learning models specially tailored towards modeling homicides events. Since spatial resolution is a direct determinant of sparsity, we focus on the performance of these models across different resolutions of interest to police authorities. We use a simple count model as benchmark and propose some enhancements of it directed towards improving prediction performance. We then compare the results to more complex models motivated by manifold learning and graph signal processing methods. We found that the simple benchmark models are as good as state of the art models for low resolution, but, as resolution increases, the performance of machine learning models outperform the benchmark. These results provide a rationality for the use of state of the art machine learning models for homicide prediction at the high resolution of interest for the deployment of police resources.

Highlights

Understanding homicides dynamics is challenging due to the particular spatio-temporal distribution of these phenomena
Afterwards, we use the count model as benchmark to analyze the performance of the Kernel Warping an Graph Laplacian of Gaussian (GLoG) models
We use four metrics of performance: the hit rates at 5% and 10% of area covered, the total area under the Hit Rate (HR)-Percentage of Area Covered (PAC) curve and the normalized first 20% of that area

Summary

Introduction

Understanding homicides dynamics is challenging due to the particular spatio-temporal distribution of these phenomena. Homicides, compared to other forms of crime, are an infrequent phenomena in time and space This sparse distribution makes it difficult for statistical models to capture spatio-temporal patterns useful for making predictions. The goal of this study is to understand the performance of state of the art machine learning models, [1], [2], when the sparsity of the training and test data vary according to the spatial resolution used. For this purpose, we use homicide incidents in Bogotá, from 2018 to 2019, to train simple models that seek to overcome the difficulties encountered in predicting homicides. This allows us to understand how these more complex models manage to overcome the sparsity issue

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