LectureDistanceAnalysis

Hello PSC 216, welcome to week number three in our summer 2026 session. I want to talk a little bit about distance analysis for crime mapping, including how we calculate distance, what tools we can use, other ways we can measure distance that are not necessarily based on spatial considerations. In other words, measuring distance in terms of time. And I want to mention spatial autocorrelation, just so you have an understanding of how we can check some of the results of the maps we're creating.

Let's talk first about calculating distance. Television crime dramas tend to make spatial crime theories very popular because if we watch those NCIS type shows or CSI or Criminal Minds, whatever show is your preference, they're sometimes able to sit down with a map, press some buttons, and hey, this is where the bad guy is. The theory behind this is called journey to crime. This is the journey an offender travels when they commit a crime. It's usually measured as the distance between the offender's home and the location of the crime. It measures from an anchor point. So, if we're talking about a serial criminal, a serial burglar, a serial killer, a serial robber, it looks at where this criminal is starting from, whether it's a home or workplace. That's an anchor point. This can also include an intimate partner's residence or a place that has some significance to the offender.

So, if you look at the map on the right-hand side, this is a map of the Son of Sam killings circa 1976-1977. And these are the distances from David Berkowitz's home in Yonkers to each of the crime scenes. There's also a measure of the days between murders. And that's what made the Berkowitz case rather challenging. And if you look at the data between the first and second attacks, there were 86 days between. Then between the second and third, it was less frequent, then it increased in frequency, decreased, increased, decreased. Um and that was the problem with tracking Berkowitz because he was not in his right mind. The guy was burned out on acid, hearing voices of a thousand-year-old spirit that were coming out of a barking dog. It's complicated.

You'll notice with the measures though, these measures are called as the crow flies. I'm going to get more into that in a moment. But these are just straight measures and you'll notice the last attack in Brooklyn was 24 miles as the crow flies from Yonkers. This is what got David Berkowitz caught because he received a parking ticket during the last attack. And with a little bit of investigation and talking to a witness who saw the ticket being issued, little research, and again, we don't have the computer technology of 2026 at this time. This is 1977. So, it took a little longer to background it. Um and what they find is, hey, there's this car from Yonkers getting a ticket around 2:00 in the morning. What was it doing here? And the next thing you know, he eventually is arrested. Uh, it's a great example of how spatial analysis, even without fancy technology, can lead to solving crime.

With distance analysis, it's really a measure of human travel patterns and habits. Why do we travel the way we do? Well, for most of us, it's a matter of convenience. What changes how and where we travel? Unforeseen circumstances. Subway trains breaking. Um, in my case, Amtrak melting their wires, which then messes up New Jersey Transit, which means all right, I'm not taking the train that day, I'm going to hop on a bus. Based on how humans travel, there are a variety of distance measures that can be used for mapping in crime analysis. And that's what this course is about. It's about how distance and how features are related to each other on a map.

Two ways we can measure include Manhattan and Euclidean. Manhattan distance is also known as city block distance or taxicab distance. And it's used to calculate the distance between two data points in a grid-like path. Why is it called Manhattan? Take a look at Manhattan streets. It's a grid. It's not naturally occurring, right? It's a grid that engineers created. So, how we travel along that grid is one way we can track an offender's movements in real being more real versus Euclidean distance, which is just a straight-line measure between two points. Um we also call this as the crow flies. Euclidean just gives us a straight measure. Manhattan tells us how somebody manipulates that distance in their travel path.

So, using John Jay as an example, here I am at Haaren Hall in my lab. I'm ready to leave for the day. I come down the stairs of the 10th Ave building, which you can't do right now because it's closed. They're fixing the roof, I believe. But anyway, I found that out the hard way when I went to campus uh this past Wednesday. Had to walk all over the place to get in. But anyway, you come out the building, I go down, let's say, 10th Ave. I hang a right onto 59th Street, walk down, go to Columbus Circle. This is exactly my travel pattern. Maybe I go this way. But that's Manhattan distance. It tracks the actual patterns of travel. Euclidean's a little different. Euclidean, let's imagine I have my John Jay jetpack, and I go up to um the John Jay walk. I fire up my jetpack, and I just fly straight from John Jay to Columbus Circle. That's Euclidean distance. It gives us a general measure, but it doesn't tell us the how that Manhattan does. Manhattan works better for journey to crime in geographic profiling. Um it is much closer to mimicking the offender's travel distances. Euclidean is good if you need an estimate of street mileage traveled. And you can try both when in question.

But I want you to understand with Manhattan, part of understanding the travel patterns is also tied in with data balance during an investigation. Data balance is using electronic means to track somebody. So, the real question is, let's God forbid say we're tracking a murder suspect from John Jay College to Columbus Circle. Not only are we interested in the paths they traveled, we're also interested in what electronic resources they pass by, e.g., cameras. And the number of times we're on cameras at any given time in New York City is phenomenal. But that's where Manhattan really shines in terms of investigations.

In Arc GIS, we have certain tools at our disposal, which allow us to calculate distance. One of those tools is called mean center. It identifies the geographic center or the center of concentration for a set of features, normally points. One of the tools you're going to going to be using for map number four is buffer analysis. This allows us to identify a geographic feature and then create a measured buffer around it. Both of these tools are useful for a helping us with journey to crime measures. And again, in terms of an investigation, we're looking for the anchor point. Mean center may help us determine this anchor point. It's often used for tactical analysis. And what it means is, excuse the pun, but all we're doing is measuring the center of a concentration of X and Y, latitude and longitude events. We're looking for where the center of those are on a map. And it's often used as a starting point for other types of analysis. Um with mean center, we can also create ellipses and rectangles around these anchor points.

The problem with mean center is it's sensitive to outliers and bunching of incidents, which is one of the reasons we're not using it with our shooting data. Instead, with our shooting data, we're going to use a buffer to analyze concentrations. A buffer, again, is just a polygon that we draw around an object. And we can do it with any measure. For map number four, you will be drawing 1,000 ft buffers around NYCHA properties. Doing this type of measures allow us to perform spatial queries. So, we can calculate what happens within the distance of something and how much of that happens. For map number four, you're going to be calculating the number, the percentage, of shootings that take place that take place within 1,000 ft of NYCHA buildings. And you're going to see that percentage is rather significant.

In terms of journey to crime analysis, offenders of homicide tend to stick closer to an anchor point. Victims of homicides are often killed closer to home. And that is because normally offenders and victims have some type relationship. It doesn't mean that it's an intimate, but normally you know the person that has committed the homicide. There's some type of existing relationship. Stranger true stranger homicides are relatively rare. Um statistically speaking, you are more likely to be killed by somebody you know.

Now, one example I like to use for mean center, um in particular because this is a unique case in which the serial killer in this case, the Stockton serial killer, did not know his victims. There was no pre-existing relationship. It makes the murders that much more difficult to solve. If you're not familiar with the Stockton serial killer case, um in Stockton, California, between April 2021 and October 2022, unhoused individuals were being attacked and murdered. They identified a possible suspect. And if you look at where he was arrested, the story's in the map. So, the Stockton serial killer committed a murder April 2021. Then he's off the grid for a while. The second murder, sometime later, almost a year and a half, July 2022. Several months between the murders and also notice the difference in spatial measure. Then he hits again in August 2022 and he hits twice. So now he's increasing the frequency of attacks. He hits again in September and he hits twice. The mean center, if we take all these points and use the software to calculate mean center, it's right about here. And then we can set up buffers. Most serial killers are within a 3-mi buffer of some anchor point. Now, in this case, he was mobile. This is where he was arrested. So he was well within the 3-mi buffer. Just right on the border of that 2-mi buffer, actually. Um from what the reports say, he was being tracked as he himself was tracking another victim.

Now, this type of analysis is kind of sexy because it gets into identifying a serial killer and using the technology, the reality of this, however, is it's only useful in a small percentage of cases. Uh buffer analysis is much more useful for us in determining the percentages of crimes that are occurring within particular locations. Distances that we travel also vary by the type of crime, the race of the perp, sex, and age. Another problem with crime analysis using journey to crime is that police departments do not always collect good information. That needs to be part of their routine.

There's some other distances that we can measure that have nothing to do with linear measurements. This includes distance in time, distance among social networks. Um and this is becoming more and more prevalent in investigation. Measuring how close we are to somebody given our status on social media, which is one of the reasons I do not use social media. For those of you going into law enforcement, you can count on whatever agency is hiring you, you can count on their investigators looking at your social media networks. So, that's something to keep in mind.

The last thing I'd like to talk about is something called spatial auto correlation. So, for 3 weeks in this class, I have been saying in some form or another crime is not evenly distributed. And we've seen that in the maps, and I've seen that with your discussion board answers. You're realizing that crime is not distributed evenly in New York. The question is though, is this a random occurrence? Is there some other explanation? In order to answer that question, we can use a tool called spatial auto correlation. If you go into graduate school, you will be using the tool. It's simply a way to measure the tendency for areas, observations, or sites. And look at these areas to see if they have similar values. Most areas in New York that are close together do have similar values in terms of makeup, demographics, economic status, and crime types.

So, if we ask the question, are shootings distributed evenly in New York, we can immediately answer, "No, they are not." We could see it with a point map. We could see it with a choropleth map if we're adding up the points for each neighborhood. You see it with map number three in the hotspot map that you're going to be creating. But, the question is, is this a random occurrence? We can use the spatial auto auto correlation tool built into ArcGIS, which will tell us first, yes, shootings are clustered. The clustering is not random. So, that means there's some other values we must examine, including age, economics, gang activity, drug activity, et cetera. All those theories that we talked about come into play. The tool will actually show the bell curve as to where the clustering is occurring and whether or not it's random. And there's a tool in play called Moran's Index. It's rather statistically complicated. You'll see it again perhaps in a spatial statistics class, but like I said, this is usually reserved for grad level. Um but there are a couple of students in this particular class, I'll come right out and say, they're geared for graduate level work. I mean, guys, if you're listening to the lecture, you know probably who I'm referring to. You guys really should be looking at grad school at this point based on what I've seen with your maps. I'm just being honest. So, this is one of the tools you may be introduced to, which clearly tells us the data is not random and it is clustered.

So, now this is why I am going to have you do map number four using a buffer around NYCHA buildings. We're going to start to answer some questions about why it's clustered.

To conclude this lecture, just remember distance analysis can be used to provide a wide assortment of information based on the spatial distribution of crime with respect to how near, how far, within what distance, adjacent to what other feature, how closely suspects and victims are related. We can also look at simply how distance in space and time the crimes have occurred. And you've already looked at distances in terms of months and days. You've created the graphs. I believe that was map number two. So, you've already been looking at distances in terms of time measures. And all these different types of analysis should be used in conjunction with other analysis that you're learning. This helps us make productive decisions, effective decisions, and make sure we're not wasting public safety resources. So, that's the lecture on distance analysis. As always, if you have any questions, please do email me. Take care, everybody, and I look forward to talking to you again real soon.