Clusters and Classifiers

This repository contains the source code for cluster generation and classification of five classes with bivariate Gaussian distribution parameters. Classification was implemented using MED, GED, MAP, NN, and kNN classifiers. Error analysis was conducted by determining the experimental error rate and confusion matrix for each classifier.

Cluster Generation

Normal distributions for the following classes were created using numpy.random.multivariate_normal. Distribution plotting was implemented with plot and scatter from matplotlib.pyplot, and standard deviation contours for each class were plotted using contour from the same module. Code: data_class.py

Class A: N_A = 200, μ_A = [5 10]^T, Σ_A = [ [8 0], [0 4] ]
Class B: N_B = 200, μ_B = [10 15]^T, Σ_B = [ [8 0], [0 4] ]

Class C: N_C = 100, μ_C = [5 10]^T, Σ_C = [ [8 4], [4 40] ]
Class D: N_D = 200, μ_D = [15 10]^T, Σ_D = [ [8 0], [0 8] ]
Class E: N_E = 150, μ_D = [10 5]^T, Σ_E = [ [10 -5], [-5 20] ]

Classifiers

The following classifiers were implemented:

1. Minimum Euclidean Distance (MED)
2. Generalized Euclidean Distance (GED)
3. Maximum A Posterioi (MAP)
4. Nearest Neighbor (NN)
5. k-Nearest Neighbor (kNN) with k = 5

To classify, a 2D grid was created, each point was classified, and a contour plot was generated. Code: classifiers.py

Error Analysis

Following classification, the experimental error rate and confusion matrices were determined for each classifier. This was implemented using accuracy_score and confusion_matrix from sklearn.metrics. Code: error_calculation.py