1. Spatial Analysis of Crime Data: A Case Study Mike Tischler Presented by Arnold Boedihardjo

2. Outline Motivation Spatial autocorrelation Approach Issues Data sets

3. Motivation Goal: reduce crime activity Develop a tool to extract crime patterns – Allow visualization of patterns Ultimately, predict crime occurrences

4. Spatial Autocorrelation Tobler’s first law of geography: “everything is related to everything else, but near things are more related than distant things” Possible causes of spatial dependency – Spatial causality: an object (event) is a direct cause of nearby objects (events) – Spatial correlation: nearby objects (events) behave similarly – Spatial interaction: movements of objects induce a relationship between objects in different locations

5. Approach Provide a spatial-based model to describe the density of incident objects (e.g., crime locations) within a given set of spatial objects The density values are essentially probability values, hence can be used as a predictive metric for future occurrences of incident objects

6. Example: When will the next crime happen? C C C Bank A Bank B C C Bank C Store C

7. How to formalize our intuition in a probabilistic framework? The probability of a crime occurring at bank C is higher than the stores – Furthermore, the probability is equivalent to bank A and bank B How to define the probabilities? – Kernel Density Estimation

8. Applying the KDE Suppose that the our sample set, S, is not the incident points, but the pair-wise distances of the incidents to the NN non-incident objects (e.g., banks and stores) If we apply the KDE to S, the kernel functions will be centered at these pair-wise distances and our query points will be transformed to the NN of the non- incident spatial objects Formally, we have the following multivariate KDE

9. After applying the KDE, we have the following… Bank A Bank B Bank C Store

10. Research Issues How to select the features (e.g., banks, stores)? Employ notions of density attractors and repellers. If the above is solved, how to improve the quality of the density estimates? Currently, an adaptive KDE approach is being tested. How to incorporate temporal correlation? Producing this model is computationally intensive: feature selection, NN search for every feature, and multiple queries on KDE

11. Data Set Washington DC crime data Crime incident reports in parse-able formats: – XML, Text/CSV, KML or ESRI Geographic feature layers are also available for download (could not verify, but was told by a very reliable source) Other regional information are available (e.g., census tract) http://data.octo.dc.gov