LectureDensityAnalysis

Hello PSC 216. We are still in week number three of our summer 2026 session. I want to talk a little bit about kernel density heat maps. And you're going to be making a heat map um with the one of the mapping projects that's going to be due this week. It's a relatively easy map to make.

Let's talk a little bit about what I mean when I say kernel density. So what is density? Imagine if you had a pound of feathers and a pound of gold. Let's assume we use a standard reference for measure. Which weighs more, the gold or the feathers? This is actually a trick question. Each weighs one pound. So that's a standard measure. The feathers weigh one pound. The gold weighs one pound. One does not weigh more than the other if each equals a pound. However, the gold atoms are tightly clustered. That makes the gold denser than feathers. Similarly, if we have a 100 crime points that are dispersed in an area, the 100 crime points may be tightly clustered or they could be spread out. The count of the points is the same, but the density may be different. That's what you're going to see in your heat map generations. Same number of crimes, but if they're occurring in a smaller location, um if they are occurring repeatedly and being stacked, that changes the density and that also changes how we view the criminal activity.

In economics, there is a rule called the Pareto principle. It's also known as the 80/20 rule and it suggests that a small percentage of causes account for a large percentage of effects in the context of crime. This means that a small number of offenders, locations, or other factors are a are responsible for a large portion of criminal activity. We're going to see this with our heat maps. We're also going to see it with the map regarding the buffers around Nicha housing facilities. When we apply this principle to various aspects of crime such as identifying repeat offenders, pinpointing crime hotspots, it helps us understand a little more about the areas and the causes within those areas of specific types of crime.

When we discuss heat mapping, the process is called kernel density. Kernel density measures the quantity of crime points throughout a geographic boundary. ArcGIS has a built-in kernel density tool. Now, we are taking a shortcut from this because there are some problems with the online version of ArcGIS we're using. This is why I'm going to have you do the heat maps using the simpler symbology tool. However, I want you to understand how kernel density works. It produces a continuous surface that visualizes an estimation of the concentration of points. The values are weighted based on distance from each input point. The function is actually called kernel with a K and that determines the waiting in a kernel density map. If you notice the map on the right, this is a heat map of robberies in lower Manhattan. The map inset are the robbery points. While we can see there is some um uneven distribution, the heat map shows us the true concentrated areas including around Times Square which I think is to be expected, uh Flatiron District and Union Square, the West Village and the East Village are concentrated points.

Kernel density heat maps visualize how close crime points occur to one another within a boundary or location. The size and geography of the area will affect kernel density measures. Keep in mind these measures are estimates. So again looking at the map on the right looking at robberies we can see again Midtown higher concentrations, Flatiron um on the west side and on the east side higher concentrations within Manhattan and you'll notice we are looking at a much smaller geographic area. What these values represent. The 1,392 value indicates areas where the estimated intensity of points is 1,392 per square mile. So again, density, it's not necessarily about the counts, it's about the concentration of those counts.

Density maps expand, shrink and dissolve based on changes in time, day, month, year and crime categories. So for example, if we take our robbery density map, we have robberies occurring from 8 to 4, you can see the specific hotspots. We have robberies occurring 4 to 12. Notice how the hot spots, some of them contract, some of them start expanding. We have robberies occurring from 12 to 8. And again, the hot spots change. This allows us to visualize how crime grows, shrinks, and moves based on different factors. Additionally, you'll notice your hotspot maps for shootings, which is going to be your map number three. That shooting map has different concentrations than some of the robbery maps. And again, that's because in this context, crime is not static. Crime can be viewed as a dynamic entity that reacts to changes in time, reacts to changes in the season, reacts to different economic conditions.

Now, finally, we're going to talk a little bit about problems with density heat maps. And this is a rather short lecture that I give just so you understand what you did when you created our third map. Density heat maps rely on precise data. One of the problems we have with heat mapping certain crimes is that crimes are often recorded at the precinct. Shooting data and the reason why I start off with shooting data, it has other issues, but the shooting data is not being recorded at the precinct. But crimes like robbery, burglary, assault, many times they are recorded at the precinct, which means the crime point gets the precinct's geolocation. That means you get hotspots around all your precincts. So for example, in our robbery map, the 14th precinct is a significant hotspot. Does that mean people are being robbed outside the 14th precinct? No, it means the crime was reported there. And in some of my data sets, I do include a variable. It's a yes and no variable. And I measure whether a crime was reported at the precinct. And usually I'll draw a 100-foot buffer around the precinct location. And any points that are within that 100-foot buffer, I record them as being recorded at the precinct. And then what I'll do is leave them out of my hotspot calculation. However, this requires that I be intimate with my data and understand the limitations.

In addition to complaint data, 911 data can be misleading because 911 calls, they don't differentiate between a true call and a nuisance call. Sexual assault calls cannot be heatmapped. Sexual assault calls are purposely coded to precinct locations in order to protect victim privacy. So, while heat maps can be useful, I want to make sure you're careful in understanding their limitations. One of the biggest problems with our New York City data, they stack the points. So you've created several point maps. Now the points, one single point can actually be multiple points that are stacked. So this single point which is within 100 ft of the Midtown South precinct. One point, notice its proximity to the station. This one point actually represents all these different complaints. You can't create a heat map based on this. These points would should ideally be excluded from a proper heat map analysis. For your shooting heat map, you're not going to have to worry about this. However, as you go into more advanced crime mapping and GIS work, you should understand the limitations.

I'll conclude very simply by saying density heat maps are the beginning of our analyses, not the end. So, you're going to be creating a heat map. It's going to clearly show concentrations of shootings. Then, you're going to be creating a map that includes a buffer around Nicha buildings. And what you may notice is there is a visual correlation between where the density of shootings is occurring and the number of points within a thousand ft of NICHA buildings. Heat maps visualize the concept that crime is more concentrated among places rather than people. This causes us to ask why this location. It allows us to start the process to look for contributing factors. Additionally, if you want more information on heat maps, take a look at the ArcGIS help page and look up how kernel density works. It's an interesting topic. In my class, I tend to keep it short and sweet because it does involve advanced statistical calculations. That being said, I do want you to understand how to quickly and accurately create a heat map, which is the reason why you have two maps due this week. Uh, but I think you'll find both of them are rather easy to complete. So, that's it. Very short and simple lecture on kernel density mapping. Do make sure you pay attention to the other lecture this week which is a little longer about spatial measures in crime mapping. As always, if you have any questions, please feel free to reach out to me via email or request a meeting via Zoom. As I said, I'm around all summer so I can meet with you via Zoom. It's not a problem. All right, everybody. Take care and happy mapping. I look forward to speaking to you all again real.