Ahmed's MTH 522 Class Practice

In today’s class, we talked about the concepts of point patterns and point processes in the study of spatial data.

Point Patterns:
Refers to a set of points that are distributed within a given space. It’s an observed dataset of points in a space. They are classified into the following main types:

1) Poisson Patterns:
Points are distributed independently and uniformly across the space
2) Clustered Patterns:
Points tend to group together due to some underlying attraction or shared   factors

Point Processes:
A point process is a mathematical model that describes the random occurrence of points in space and/or time. It’s a probabilistic model that describes how such point patterns could be generated.

We also discussed an insight that we’d like to deep dive into regarding the armed conflict location and event data. The thought was that we pick a location where we’d like to predict a violent political demonstration in a given space and time from previous years. And by looking at this location’s nearest neighbors and their past data, we predict the probability of a violent political demonstration here in future.

In this lecture we had a look at the ACLED dataset that has five years data providing information on political and other types of violence in the United States and in India.

We learned about the concepts of clustering, how clusters are identified from geographic plots of a dataset, and what the k-means clustering is.

1. 1. Latitude/Longitude data for location plotting (geographic plots)
      • How do the locations seem to be distributed?  
   2. Clustering (K-means clustering) 
      • Can you interpret the clusters?  
      • Geographic distance b/w two points  
   3. Spatial Data  
      • Is it random?  

Understanding K means clustering:  

K-means clustering is not only done using geographical plot, but it can also be done anytime you have distance between two points. 

1. 1. Choose K random spots in datasets  
      1. Algorithm assigns each  cluster a number and all the nearest dots to clusters are assigned to each cluster.
      2. This process is repeated for each cluster 
      3. Once clusters are ready, center of math (centroid) is taken for each cluster, and the process of clustering is repeated again
      4. Re-do the cluster for each one created
   2. The above process is repeated until the clusters are stablized

Over the past few weeks, I have been deeply engaged in our project analyzing police shooting data along with my group mate Chandrakanth. We were able to draw valuable insights from the racial and demographic disparities in police use of force.

Over the past few days I’ve been knee deep doing data analysis, statistical evaluation, and visualization. Specifically, I focused on descriptive statistics and population normalization to ensure that per capita fatality rates were accurately calculated. This step was crucial in presenting a clearer picture of the disparities among different racial and demographic groups affected by police shootings.

We eventually drafter the final report, including discussions on racial disparities, age and gender analysis, and per capita rates. This required us to interpret complex data trends and present them in a way that was accessible and meaningful. Through this process, we were able to highlight key findings, such as the disproportionate impact of police shootings on Black and Native American individuals compared to White Americans when adjusted for population size.

This project help me recognize the importance of data-driven analysis in shaping public policy discussions. Our findings emphasize the need for stronger de-escalation tactics, better mental health crisis response training for officers, and mandatory body camera usage to increase transparency. While body cameras have improved documentation, our research found that they have not significantly reduced the number of fatal police shootings, highlighting the need for deeper reforms in law enforcement practices.

Here’s the complete project report for clarity:

Project 1 - Ahmed Ali & FNU Chandrakanth (MTH-522)

In our fifth lecture, we continued our discussion on the police shootings data. Mahnoor, one of our classmates, presented the work that she had done so far, which was about the distributions based off the victom’s race/ethnicity mapped across the counties in the US.

This lecture Mr. Gray showed us how we manipulated and drew several visualizations using the police shootings data for a certain query that was brought up by one of the students, and drew different conclusions.

We learned about:

• • Data Plotting
  • Finding Averages, Standard Deviations in order to identify abnormalities in data
  • Creating Visualizations from data findings
  • Using Wolfram & R (Mathematica) for mathematical computing

I’ll be further exploring the use of Wolfram to relate with some of the questions I came up with from the police shootings data, and see if I can draw meaningful conclusions.

In our third lecture, we continued our community discussions on the police shootings data. Discussing and sharing questions every person came up with each other. We also looked at different ways to visually present the data in from of a report. Mr. Gary shared how one of the students question’s led him to come up with a detailed report that he created, with visual representation.

We also talked about ANOVA analysis which is done comparing different variances.

Second lecture was mainly based on discussion about the work each group had done in the first lecture. Each group shared a set of questions that they came up with after analyzing the Police Shootings data, and shared what purpose they were trying to achieve.

We talked on how sharing questions with one another could help others come up with more interesting questions or pinch another thought stream.

I, along with my group member, came up with the following questions initially: 

• • Why do some people have body cameras on? 
  • What’s the racial composition based off of the zip code and location? 
  • How often is the killings talked about in the news? 
  • How does the data for people with mental illness adds value to this report? 

Here’s what we learnt the main focus should be while drafting questions from a dataset:

              “What impact are you trying to make and what influence?”

This helps come with up with deep though provoking questions and triggers your ability to critically analyze the dataset.

In the first lecture, we analyzed a large dataset of approximately 10,000 people that were killed over the period of last few months in the US. We brainstormed and came up with questions based off of the date provided. We also brainstormed on different approaches on how to look at data and draw meaningful insights from data.

The purpose of this website is to provide regular updates on the work that I will be doing in my MTH 522 class. I’ll be sharing about abstract concepts, sophisticated techniques, and rigorous proof-based reasoning that we learn in this class.