PAPER 1 - Proposal

• feature engineering to enhance the accuracy of classification models/algorithms applied to crime data

• 2 new features that would allow a more accurate classification of the type of crime occurred at a specific location:

  • geocoding:
    • linking addresses to types of location using a catalog
  • creation of hotspots:
    • using HDBSCAN \(\Rightarrow\) keep the shortest distance between the new crime record and the clusters’ centroids

PAPER 1 - (H)DBSCAN

• One of the advantages of HDBSCAN over DBSCAN is that the former does not need parameter \(\epsilon\)

PAPER 1 - Proposal Visualization

PAPER 1 - Data

• 2 types of dataset (both from Halifax police department - Nova Scotia, CAN):

  • 1. without the proposed features
    • geographic location, incident_start_time, month, weekday, ucr_desriptions (the response variable)
  • 2. with the proposed features
    • (1) + geocoding + distance to the nearest hotspot

(***) Response variable labels: Alcohol-related, Assault, Property damage, Motor vehicle

PAPER 1 - Methods

• Classifiers:

  • Logistic Regression, Random Forest, SVM, and Ensemble

  • + 10-fold cross validation

• Metrics:
  • accuracy
  • AUC
• t-test (matched pairs)
  • evaluate whether the differences were statistically significant

PAPER 1 - Results

Accuracy

AUC

PAPER 2 - Proposal

• Predict crimes using data mining techniques and theories from criminology such as Rational Choice Theory and Routine Activity Theory.

PAPER 2 - Data

• Dataset obtained from UK police department website (data from 2015-17)

  • 5 relevant attributes for crime prediction: crime type, locAtion, date, latitude, and longitude

• Data was preprocessed with removal of inconsistent data, and transforming data for prediction

PAPER 2 - Data Visualization (1)

PAPER 2 - Data Visualization (2)

PAPER 2 - Data Visualization (3)

PAPER 2 - Methods

• 2 classifiers:

  • k-NN

  • Naïve Bayes

PAPER 2 - kNN (1)

k-NN is a way to group things based on their similarities. It works by looking at the things closest to the one you’re trying to classify and assigning it to the group that has the most similar things. This can be used to predict where crimes are likely to happen base on where they’ve happened before. It takes into account location and date, and computes the distance between different areas to group them together.

PAPER 2 - kNN (2)

First step, compute the distances between a test instance and all training instances

For this, the latitude, longitude and the number of days as the coordinates and compute the distance factor as

\(d_i = \sqrt{(x_i - \bar{x})^2 + (y_i - \bar{y})^2}\), \(d_i = \sqrt{(x_i - \bar{x})^2 + (y_i - \bar{y})^2 + (Z_i)^2}\)

To avoid the squaring and square root, the Manhattan distance was computed

\[ d_i = |x_i - x| + |y_i - \textbf{1}| + |z_i|\]

PAPER 2 - kNN (3)

The next step is to identify the k-nearest neighbors to the test instance based on their distances. The value of k is a pre-defined parameter in the K-NN algorithm, and it determines the number of nearest neighbors to be considered for classification.

PAPER 2 - kNN (4)

Their corresponding class labels (i.e., types of crime) are used to determine the class membership of the test instance. The class membership is determined by taking a majority vote of the k-nearest neighbors. This means that the class label assigned to the test instance is the one that occurs most frequently among its k-nearest neighbors.

PAPER 2 - Naïve Bayes (1)

based on Bayes theorem which describes the probability of an event based on the prior knowledge of conditions that might be related to the event.

\[\operatorname{Pr}(h|x) = \frac{\operatorname{Pr}(x|h) \operatorname{Pr}(h)}{\operatorname{Pr}(x)}\]

The Naïve Bayes classifier classifies a new instance X by assigning the most probable target value i.e. the maximum likelihood. i.e. 

\[\max_{d_i \epsilon d} \operatorname{Pr}(d_i) \prod_{k=1}^n \operatorname{Pr}\left(\frac{x_k}{d_i}\right)\]

PAPER 2 - Naïve Bayes (2)

• Naive Bayes can classify crime types by calculating the conditional probabilities of each attribute given each class.
• The model is trained using a crime dataset, and once trained, can predict the class of a new instance based on its attributes.
• The classifier calculates the posterior probability of each class given the attribute values and assigns the class with the highest probability as the predicted class.

PAPER 2 - Naïve Bayes (3)