Predictive Hotspot Mapping for Data-driven Crime Prediction

Karthik Sriram; Ankur Sinha; Suvashis Choudhary

stat.APFeb 27, 2026

Predictive Hotspot Mapping for Data-driven Crime Prediction

Authors: Karthik Sriram, Ankur Sinha, Suvashis Choudhary

Organizations: Operations and Decision Sciences, Indian Institute of Management Ahmedabad, 380015, Gujarat, India · Indian Police Service (Retired), India

Abstract

Predictive hotspot mapping is an important problem in crime prediction and control. An accurate hotspot mapping helps in appropriately targeting the available resources to manage crime in cities. With an aim to make data-driven decisions and automate policing and patrolling operations, police departments across the world are moving towards predictive approaches relying on historical data. In this paper, we create a non-parametric model using a spatio-temporal kernel density formulation for the purpose of crime prediction based on historical data. The proposed approach is also able to incorporate expert inputs coming from humans through alternate sources. The approach has been extensively evaluated in a real-world setting by collaborating with the Delhi police department to make crime predictions that would help in effective assignment of patrol vehicles to control street crime. The results obtained in the paper are promising and can be easily applied in other settings. We release the algorithm and the dataset (masked) used in our study to support future research that will be useful in achieving further improvements.

Figures & tables

Variable	Description
Event id	Identification number for the street crime event.
Date	Date of the street crime event (day, month and year). This is automatically captured by the system during the call.
Time	Time of the street crime event during the day (hour, minutes, seconds). This is automatically captured by the system during the call.
Location description	Text describing the location (address) of the event. This is entered manually into the system by the PCR call attendant during or immediately after the emergency call. This is typed in English but may contain some words of the Hindi language.
Police station	This is the name of the police station, in whose jurisdiction the street crime event has occurred. This is manually entered into the system by the PCR attendant based on the information received from the patrol vehicle after it that visits the event location.
Police station (geo coordinates)	Latitude and longitude, which we (manually) looked up for the police station, in whose jurisdiction the street crime event has occurred.

Table 1: Fields in Delhi police database (DPD)

Panel of Figure 1 — Figure 1: Preliminary predictive approaches to predict street crime locations in Delhi during ‘8 pm to 12 am’ for the week of 21 March 2021 (The grey shaded area is the approximate map of Delhi).

	Historical blocks				Latest block
Temporal block	$b-B$	$b-B+1$	$\ldots$	$b-1$	$b$
Block index $i$	$1$	$2$	$\ldots$	$B$
Lon. coordinates	$x_{11},x_{12},\ldots,x_{1n_{1}}$	$x_{21},x_{22},\ldots,x_{2n_{2}}$	$\ldots$	$x_{B1},x_{B2},\ldots,x_{Bn_{B}}$	$s_{x1},s_{x2},\ldots,s_{xn}$
Lat. coordinates	$y_{11},y_{12},\ldots,y_{1n_{1}}$	$y_{21},y_{22},\ldots,y_{2n_{2}}$	$\ldots$	$y_{B1},y_{B2},\ldots,y_{Bn_{B}}$	$s_{y1},s_{y2},\ldots,s_{yn}$
Event time (in hours)	$t_{11},t_{12},\ldots,t_{1n_{1}}$	$t_{21},t_{22},\ldots,t_{2n_{2}}$	$\ldots$	$t_{B1},t_{B2},\ldots,t_{Bn_{B}}$	$t_{1},t_{2},\ldots,t_{n}$
Block weight	$w_{1}$	$w_{2}$	$\ldots$	$w_{B}$

Table 2: Data organised for block-weighted adaptive kde

	Historical blocks				Expert block	Latest block
Temporal block	$b-B$	$b-B+1$	$\ldots$	$b-1$	Expert inputs for $b$	$b$
Block index $i$	$1$	$2$	$\ldots$	$B$	$E$
Lon. coordinates	$x_{11},x_{12},\ldots,x_{1n_{1}}$	$x_{21},x_{22},\ldots,x_{2n_{2}}$	$\ldots$	$x_{B1},x_{B2},\ldots,x_{Bn_{B}}$	$x_{E1},x_{E2},\ldots,x_{En_{E}}$	$s_{x1},s_{x2},\ldots,s_{xn}$
Lat. coordinates	$y_{11},y_{12},\ldots,y_{1n_{1}}$	$y_{21},y_{22},\ldots,y_{2n_{2}}$	$\ldots$	$y_{B1},y_{B2},\ldots,y_{Bn_{B}}$	$y_{E1},y_{E2},\ldots,y_{En_{E}}$	$s_{y1},s_{y2},\ldots,s_{yn}$
Event time (in hours)	$t_{11},t_{12},\ldots,t_{1n_{1}}$	$t_{21},t_{22},\ldots,t_{2n_{2}}$	$\ldots$	$t_{B1},t_{B2},\ldots,t_{Bn_{B}}$	$t_{E1},t_{E2},\ldots,t_{En_{E}}$	$t_{1},t_{2},\ldots,t_{n}$
Block weight	$w_{1}$	$w_{2}$	$\ldots$	$w_{B}$	$w_{E}$

Table 3: Data organised for block-weighted adaptive kde with a block containing expert inputs

Model	Past periods considered	Spatial	Temporal	Adaptive Bandwidth	Adaptive Weights
Model 1	1 week	$\checkmark$	$\times$	$\checkmark$	$\times$
Model 2	1 week	$\checkmark$	$\checkmark$	$\checkmark$	$\times$
Model 3	52 weeks	$\checkmark$	$\checkmark$	$\checkmark$	$\times$
Model 4	52 weeks	$\checkmark$	$\times$	$\checkmark$	$\checkmark$
Model 5	52 weeks	$\checkmark$	$\checkmark$	$\checkmark$	$\checkmark$

Table 4: Comparison of models with respect to their characteristics considered in the experiments.

Figure 2: Overall average AUC over the 25 weeks [week of 4 October 2020 up to week of March 21 2021]

Table 5: Summary of the ‘percentage of actual events captured for any upcoming week’, in the top 20% and top 40% monitored areas in different time intervals of the day, for the 25 upcoming weeks (i.e. week of 4 October 2020 up to week of 21 March 2021). Improvement in terms of additional percentage of actual events captured by Model 5 over Model 1 is provided in brackets for each case.

Panel of Figure 3 — Figure 3: AUC by week [week of 4 October 2020 up to week of March 21 2021] for different time intervals in the day based on different models

		Intel on 10% incidents within			Intel on 20% incidents within
Time	No Intel	100m	500m	1000m	100m	500m	1000m
12 am - 4 am	0.924	0.922	0.922	0.912	0.925	0.937	0.920
4 am - 8 am	0.912	0.923	0.928	0.916	0.928	0.914	0.907
8 am-12 pm	0.900	0.912	0.908	0.887	0.917	0.910	0.898
12 pm -4 pm	0.903	0.917	0.914	0.896	0.914	0.909	0.908
4 pm- 8 pm	0.897	0.907	0.905	0.903	0.905	0.906	0.906

Table 6: AUC values with varying extent of information and accuracy radius of expert inputs. Improvement percentage is the difference in AUC as compared to the ‘No Intel’ case expressed in terms of percentage.

Panel of Figure 4 — Figure 4: Predicted hotspot maps for two successive time intervals for the week of 21 March 2021, based on Model 5. Red marks the top 20% likely spots and and yellow the next 20% likely spots. Part (c) highlights differences between Parts (a) and (b): blue indicates spots that were neither red nor yellow in Part (a) but are marked as red or yellow in Part (b), green indicates spots that were red or yellow in Part (a) but are neither red nor yellow in Part (b). There are 1.4% green and 1.4% blue dots in Part (c).

Panel of Figure 5 — Figure 5: Predicted hotspot maps for two successive weeks, for the week of 14 March 2021 and the week of 21 March 2021, based on the proposed Model 5. Red marks the top 20% likely spots and yellow the next 20% likely spots. Part (b) highlights some spots in relation to Part (a): blue indicates spots that were neither red nor yellow in Part (a) but should be marked as red or yellow in Part (b), green indicates spots that were red or yellow in Part (a) but should neither be red nor yellow in Part (b). There are about 3.1% green and 3.1% blue dots.

Panel of Figure 6 — Figure 6: Map focused on three police jurisdictions within Delhi, viz. ‘Jaffarpur Kalan’, ‘Chhawla’ and ‘Dwarka Sector 3’. Predicted hotspot maps are shown for two successive weeks, for the week of 14 March 2021 and the week of March 21 2021, based on the proposed Model 5. In the afore mentioned order, the three police station jurisdictions are marked in ‘brown’, ‘purple’ and again ‘brown’. Red marks the top 20% likely spots and yellow the next 20% likely spots. Part (b) highlights some spots in relation to Part (a): blue indicates spots that were neither red nor yellow in Part (a) but should be marked as red or yellow in Part (b), green indicates spots that were red or yellow in Part (a) but should neither be red nor yellow in Part (b).

week start date	Jaffarpur Kalan	Chhawla	Dwarka sector 3
17/1/21	1	1	1
24/1/21	0	3	3
31/1/21	0	4	1
7/2/21	0	1	1
14/2/21	0	7	2
21/2/21	0	3	2

Table 7: Number of actual events by three police station jurisdictions, over 10 weeks

	Hotspots
Key location type	Red	Yellow	Other	Total
famous temples	13	4	3	20
flyovers	50	5	1	56
markets	22	6	2	30
metro stations ⋆	146	25	20	191

Table 8: Number of key locations predicted as hotspots (i.e. red and yellow) for the week starting 21 March 2021 for the time interval 8 pm to 12 am

Figure 7: Predictive hotspot map for the week starting 21 March 2021 for the time interval 8 pm - 12 am, along with the key locations. As before, red spots mark the top 20% likely spots and yellow spots mark the next 20% likely spots for street crime as predicted by Model 5. In addition, the spots marked with triangles indicate metro stations and circles indicate either famous temples, markets or flyovers.

Figure 8: Number of calls received per day.

Figure 9: Percentage calls received by various districts of Delhi per week.

Figure 10: Percentage calls received by 4-hour time window per week.

Description	Number of Records
Total records received from police database (street crime)	65,057
Total after removing duplicate records (i.e. multiple calls on same event)	51,230
Number of records with invalid latitude/longitude coordinates	5,295
Final usable records	45,935 ( 90%)

Table 9: Summary of records after data preprocessing

Figure 11: Trace plots for the parameters,

\alpha_{1},\alpha_{2},\beta_{1},\beta_{2},\beta_{3}

, and weight parameters,

w_{1},w_{11},w_{20},w_{52}

Time	AUC with Expert	AUC without Expert
12am-4am	0.920	0.924
4am-8am	0.904	0.912
8am-12pm	0.895	0.900
12pm-4pm	0.907	0.903
4pm-8pm	0.896	0.897
8pm-12am	0.915	0.917

Table 10: Comparison of AUC with and without expert input across different time windows.

Panel of Figure 12 — Figure 12: Posterior summaries of parameters for Model 5 (solid line is the posterior mean and dotted lines mark the 95% credible interval)

Table 11: Summaries of transitional probability matrices computed to track the changes in (Red, Yellow, other) spots from one update of the map to the next, starting with the week of 4 October 2020 up to the week of 21 March 2021, and within each week, for six successive time intervals, viz. ‘12am to 4 am’, ‘4 am to 8am’,…, ‘8 pm to 12 pm’.

Figure 13: Impact on AUC if hotspot map is not updated with a few weeks of emerging data

Parameter	Estimate	95% CI	Corresponding range
$\alpha_{1}$	1607.36	[1254.8, 1959.9]	[49.9, 78.0] meters
$\beta_{1}$	0.99	[0.955, 1.018]
$\alpha_{2}$	1109.13	[908, 1310.3]	[85.0, 122.6] meters
$\beta_{2}$	0.98	[0.928, 1.025]
$\alpha_{3}$	1.09	[0.916, 1.27]	[47.2, 65.5] minutes
$\beta_{3}$	0.16	[0.007, 0.308]

Table 12: Parameter estimates and corresponding 95% credible intervals for the week starting March 21, 2021.

Figure 14: Estimated weights corresponding to the 52 lags.

Panel of Figure 15 — Figure 15: “eBeat Book” application

	Historical blocks				Latest block
Temporal block	$b-B$	$b-B+1$	$\ldots$	$b-1$	$b$
Block index $i$	$1$	$2$	$\ldots$	$B$
Lon. coordinates	$x_{11},x_{12},\ldots,x_{1n_{1}}$	$x_{21},x_{22},\ldots,x_{2n_{2}}$	$\ldots$	$x_{B1},x_{B2},\ldots,x_{Bn_{B}}$	$s_{x1},s_{x2},\ldots,s_{xn}$
Lat. coordinates	$y_{11},y_{12},\ldots,y_{1n_{1}}$	$y_{21},y_{22},\ldots,y_{2n_{2}}$	$\ldots$	$y_{B1},y_{B2},\ldots,y_{Bn_{B}}$	$s_{y1},s_{y2},\ldots,s_{yn}$
Event time (in hours)	$t_{11},t_{12},\ldots,t_{1n_{1}}$	$t_{21},t_{22},\ldots,t_{2n_{2}}$	$\ldots$	$t_{B1},t_{B2},\ldots,t_{Bn_{B}}$	$t_{1},t_{2},\ldots,t_{n}$
Covariate	$z_{11},z_{12},\ldots,z_{1n_{1}}$	$z_{21},z_{22},\ldots,z_{2n_{2}}$	$\ldots$	$z_{B1},z_{B2},\ldots,z_{Bn_{B}}$	$z_{1},z_{2},\ldots,z_{n}$

Table 13: Data with an additional covariate organised for block-weighted adaptive kde

Time Group	Model without Covariate	Model with Covariate (Holiday or Not)
12 am – 4 am	0.924	0.941
4 am – 8 am	0.912	0.910
8 am – 12 pm	0.900	0.899
12 pm – 4 pm	0.903	0.902
4 pm – 8 pm	0.897	0.893
8 pm – 12 am	0.917	0.916

Table 14: AUC while predicting street crime events for the week of 21 March 2021.

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FASE : A Fairness-Aware Spatiotemporal Event Graph Framework for Predictive Policing

Pronob Kumar Barman, Pronoy Kumar Barman, Plaban Kumar Barman, Rohan Mandar Salvi

Department of Information Systems University of Maryland, Baltimore County Baltimore, MD, USA · Department of Statistics Jagannath University Dhaka, Bangladesh · MBBS Shaheed M. Monsur Ali Medical College Sirajganj, Bangladesh

Algorithmic Bias Group Fairness Spatiotemporal Forecasting Hawkes Processes

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Predictive policing systems that allocate patrol resources based solely on predicted crime risk can unintentionally amplify racial disparities through feedback driven data bias. We present FASE, a Fairness Aware Spatiotemporal Event Graph framework, which integrates spatiotemporal crime prediction with fairness constrained patrol allocation and a closed loop deployment feedback simulator. We model Baltimore as a graph of 25 ZIP Code Tabulation Areas and use 139,982 Part 1 crime incidents from 2017 to 2019 at hourly resolution, producing a sparse feature tensor. The prediction module combines a spatiotemporal graph neural network with a multivariate Hawkes process to capture spatial dependencies and self exciting temporal dynamics. Outputs are modeled using a Zero Inflated Negative Binomial distribution, suitable for overdispersed and zero heavy crime counts. The model achieves a validation loss of 0.4800 and a test loss of 0.4857. Patrol allocation is formulated as a fairness constrained linear optimization problem that maximizes risk weighted coverage while enforcing a Demographic Impact Ratio constraint with deviation bounded by 0.05. Across six simulated deployment cycles, fairness remains within 0.9928 to 1.0262, and coverage ranges from 0.876 to 0.936. However, a persistent detection rate gap of approximately 3.5 percentage points remains between minority and non minority areas. This result shows that allocation level fairness constraints alone do not eliminate feedback induced bias in retraining data, highlighting the need for fairness interventions across the full pipeline.

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