By Barry Fosberg
I. Introduction: Hot Spots to Micro Hot Spots
Place-based policing is known to help decrease crimes. The theory is that specific areas have properties that make them more attractive for specific types of crimes. Areas of a city with a high concentration of apartment complexes are where large numbers of cars can be found, many without sufficient management or guardians. These complexes can be hot spots for auto-related crime.
The same apartments are homes for large numbers of people. Because these buildings may lack proper guardianship, tenants may engage in or permit high-risk behavior and logic suggests that these complexes can also be hot spots for violent crime.
The profession of crime analysis seems to have moved from a more generalized mapping of hot spots to a more finely-grained map. The term “Micro” has become common in geospatial studies.
In policing, predictive analytics uses micro-level analysis, which allows crime analysts to make more mathematically sophisticated analyses of place and crime. Using predictive analytics, one can identify areas where increased police patrol is required to deter criminal activity.
At the September 2014 Training Conference of the International Association of Crime Analysts (IACA), I demonstrated a prototype technique to identify small grid squares, wherein specific crime types were occurring at unusual levels. At the end of that demonstration, I proposed several phenomena for future study. The purpose of this paper is to further explain and to identify methods to isolate these phenomena.
II. Ripeness, Unusually Low Levels
Threshold analysis is a method to identify areas that are reporting activity at unusual rates. The analysis will rate areas as being at, above or below historic levels. Accompanying documents identify areas with abnormally high rates as areas where an aggressive police presence may prevent the formation of a permanent hot spot. Rarely emphasized is the possibility that areas reporting unusually low activity may indicate that an area is “ripe” or due to experience an increase in crimes.
The notion of a “cold spot “ as a predictor of future increase in activity has been tested and included in a Charlotte-Mecklenburg Crime Analysis program.
A cold spot represents an area that normally reports some level of activity. Large parts of a jurisdiction may be isolated, empty or otherwise present no opportunity for the crimes under study. Ripeness is intended to identify areas with a level of activity below some expected amount. That is: an area that usually reports some level of targeted crime, but is currently reporting less that its usual amount’, may be “ripe” for an increase in activity.
Another method of analysis is Near-Repeat Offender Analysis. The theory is that, once a location has been hit, then the same location and the locations nearby are more vulnerable to additional hits.
Near-repeat calculations can report vulnerability as a function of time and space such as how much time has occurred between crimes, measured in bands of time; as well as how proximate to the original incident can victimization be expected, measured in bands of space. Near-repeat calculations create virtual grids centered on events. Each crime becomes the center of a grid that extends as far in time and space as the operator cares to analyze. An analyst might be able to make copies of several virtual grids, overlay them by centering on different occurrences of crimes and produce a potential target list based on overlapping areas of elevated vulnerabilities. Using a near-repeat pattern that points to an increased vulnerability 300 feet away and a peak vulnerability 36 hours later, several maps could be overlaid, each centered on different specific events. Should there be any properties 300 feet from several datum points; the overlays might point to a specific place and time for a future crime. This possibility may be worth testing, but it may be difficult to support it as an extension of the Near-Repeat process.
The questions being asked are: Is a specific area cycling though periods of greater and lesser activity in a predictable manner? Are neighboring areas cycling though similar hot and cold periods in a manner that suggest changes in one predict changes in others? Analysis can identify cycles of activity in an area then in co-related areas and thereby help to design predictive analytics based on detected cycles.
III. Hot Spots in Time
A temporal function to measure crime is not a new concept. Crime analysts routinely note that crimes are reported more frequently during a certain shift or that a specific crime series has a specified time element. By “stacking” the results of individual micro level analytic results and treating time as a dimension, it should be possible to isolate one spatial pattern and at least three distinct temporal crime patterns. These are:
1. Comets: Trails across the map indicating a criminal operation that is moving in a linear fashion across the geography;
2. Pulsar: A single area of space that cycles between low and high levels of activity;
3. Binary: A pair of locations that alternate high and low counts over a period of This may indicate that the criminals are rotating between two areas. Activity peaks in one location and drops in the other.
4. Constellation: A number of areas that appear to cycle In an ideal situation, these areas would rotate from high to low in such a way that one area would bottom out as the next rises.
The use of astronomical terms is intentional. Since before recorded history, people have looked at the night sky. Some noticed that specific elements in the night sky change; some follow an annual or lunar cycles, and others a linear track. The method of looking at a night sky and seeking differences from prior nights has become more sophisticated. The process is now digitized and subjected to mathematical analysis. Think of your jurisdiction mapped as a “night sky”. Compare stacked overlaid maps and it should be possible to make analytical statements about crime patterns.
It is common for crime analysts to map pictures of criminal activity over time. It is possible to animate maps, demonstrating the flow of crime across time. Maps may demonstrate around-the-clock, per-quarter and other time-related data.
“Comets” represent a special case. Most hot-spot techniques cannot isolate a linear crime pattern. Linear crime patterns rarely create statistically significant concentrations of activity. Like a comet, this pattern is time limited and will move across areas. It would be useful to have tools that look though quantities of data and isolate trails of criminal activity. Such an analysis could provide predictive statements about future hits.
“Correlated Crime Walk” analysis already exists. Given a number of events, known or suspected to be related, it is possible to treat them as dimensional vectors and produce location, distance and time calculations. What is suggested here does not pre-suppose related events or an assumed movement vector.
IV. Pulsars and Binaries
A pulsar should produce a sine wave. Like a pulsar, criminal activity in a location would regularly alternate between a high and a low value. This concept is very similar to cold spotting. In both the assumption is made that an area cycles through higher and lower levels of activity and that lows levels may be predictor of more activity in the future. The major change in this formulation is to supply the suspected curve of activity.
Binaries assume negative correlation. If a criminal stops working one area it may be because he is switching between areas. This suggests a pattern where one area goes cold, another goes hot. The change in the one is directly related to a change in the other. Each area should produce a sine curve of activity rotated to be negatively correlated in time with a matched area. First, identify areas that demonstrate this reversal of activity. A correlation matrix compares every pulsar with every other pulsar matching waves with or nearly 180 degrees out of phase as potential Pulsars. Initial pairings of potential pulsars can be further analyzed using Tobler’s first law of Topography, near pairs are more related than distant pairs. Local experience should be considered. For example criminals might be willing to undertake longer journeys to crime.
A Constellation is the suggested term for groups of more than two areas that appear to be operating in some statistically improbable relation. In the same way that a group may be rotating between two locations, or between several locations. The goal of this analysis is to establish that several areas co-vary in a predictable manner. A criminal operation may have several favored areas for their attacks. The assumption is that these areas form a relatively stable group of hunting grounds. Reading of applicable cases may be required to confirm that these are the same criminals.
Spatial-temporal analysis is not new. Almost all mapping includes a temporal element. Maps can be animated by day of week, time of day and etc. Threshold analysis is also not new. These calculators may identify levels of unusually high or low activity. Also not new is the concept of near and repeat victimization. Models that interpret unusually low levels of activity seem to be unusual.
The next step for crime analysts to take is to layer micro area data. Layering time should allow for analytical techniques drawn for astronomy. Star gazers look at the changing sky and ask: What is different? Crime Analysts should be able to track events on the ground, across time and answer this same question.
Web pages accessed:
Place Based/Hot Spot Policing
Micro Level Policing
http://link.springer.com/article/10.1007/s10940-009-9081-y#page-2 The Crime Triangle
Crime Attractors/Generators Enablers
Grid Level Crime Suppression
Near Repeat Calculator
Charlotte Mecklenburg Cold Spotting