Mining Preferences from Spatial-Temporal Data

The discovery of preferences in space and time is important in a variety of applications. In this paper we first establish the correspondence between a set of preferences in space and time and density estimates obtained from observations of spatial-tempora

Mining Preferences from Spatial-Temporal Data

Donald E. Brown, Hua Liu

and Yifei Xue

Department of Systems and Information Engineering

University of Virginia

Charlottesville, VA 22903

804-924-5393

804-982-2972 (fax)Abstract

The discovery of preferences in space and time is important in a variety of applications. In thispaper we first establish the correspondence between a set of preferences in space and time and densityestimates obtained from observations of spatial-temporal features recorded within large databases. Weperform density estimation using both kernel methods and mixture models. The density estimatesconstitute a probabilistic representation of preferences. We then present a point process transition densitymodel for space-time event prediction that hinges upon the density estimates from the preferencediscovery process. The added dimension of preference discovery through feature space analysis enablesour model to outperform traditional preference modeling approaches. We demonstrate this performanceimprovement using a criminal incident database from Richmond, Virginia. Criminal incidents are human-initiated events that may be governed by criminal preferences over space and time. We applied ourmodeling technique to breaking and entering crimes committed in both residential and commercialsettings. Our approach effectively recovers the preference structure of the criminals and enables one-weekahead forecasts of threatened areas. This capability to accommodate all measurable features, identify thekey features, and quantify their relationship with event occurrence over space and time makes thisapproach applicable to domains other than law enforcement.

1. Introduction

The concept of evaluating a decision, product, or service as a function of the attributes ofalternatives is a rather universally accepted approach, which has been implemented in such fields aseconomics (McFadden, 1973, 1980; Theil, 1970), transportation (Currim, 1982), finance (Slovic et al.,1972), medicine (Huber et al., 1969), and marketing (Gensch, 1979; Rust and Donthu, 1995). The goal ofthe research is to analyze the individuals’ decision making process and predict the actual choice ofparticular individuals. Some research, especially in the fields of economics, transportation and marketinghave used the analysis of choice behavior, which is first introduced by Luce (1959). The researchanalyzes and predicts the decision of individuals by their preference on the attributes of alternatives.

Criminal incidents, like many other human-initiated events, are frequently linked with thedecision making process and preferences that event initiators (i.e., offenders) have for specific sites andspecific time slots in terms of certain spatial and temporal attributes (or features1) of those sites and timeslots, respectively. A number of researchers have documented and formulated descriptions for spatialdecision-making by criminals (see, for example, Brantingham and Brantingham, 1975; Molumby, 1976;Newman, 1972; Repetto, 1974; Scarr, 1973). Some have looked specifically at the question of distance1 We use the term features as a synonym for terms such as predictor or independent variables, which are commonlyused in regression and linear modeling.

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