1. Traditional approaches for clustering high dimensional data involve dimensionality reduction followed by classical clustering algorithms such as k-means in lower dimensions.
2. However, approaches based on k-means clustering suffer from the drawbacks and limitations of k-means clustering, namely, high dependency on initialization of cluster centroids, non-repeatability of clustering results. Also, k-means can converge locally and hence does not guarantee optimal clustering.

1. An optimal clustering approach in one dimension based on dimensionality reduction is proposed.
2. One dimensional representation of high dimensional data is obtained using Kernel Principal Component Analysis using a suitable kernel function such as Radial Basis Function(RBF).
3. One dimensional representation is then clustered optimally using dynamic programming algorithm in polynomial time

1. Developed a program using Python and C programming languages for implementing proposed clustering approach.
2. Using Silhouette score as a metric to evaluate quality of clustering, the advantages of proposed approach over traditional k-means based approaches are demonstrated.
3. For testing the proposed approach, a real world high dimensional dataset and a synthetic two dimensional dataset is used.

1. Python
2. C

1. Numpy
2. Pandas
3. scikit-learn
4. Matplotlib
5. traceback
6. datetime

To execute the program, run main.py program. It automatically calls the code present in other files as required. Following is a brief description of program files:

1. paths.py - Specify dataset,program and output(result) paths in this file.
2. main.py - Main python program to be executed.
3. c_thresholding_new.c(C program) - Implements one dimensional optimal clustering.
4. kmeans.py - Implements k-means clustering algorithm.
5. hungarian.py - Implements Hungarian algorithm for class-cluster assignment.
6. silhouette.py - Calculates Silhouette Score for resulting clusters.
7. gen_moonpairs.py - Generates specified number of half-moon pairs at random positions, angles in 2 dimensional plane.
8. dataset.py - Used for loading, handling datasets.
9. labelscan.py - Converts non-numeric class categories to numeric labels.
10. logger.py - Logs important information(such as runtime exception handling stacktrace), variables values during the program execution.
11. plot_graph.py - Plots the graph of "Numbers of Clusters"(X-axis) vs "Silhouette Score"(Y-axis) for comparing clustering performance.

1. English Letters.csv - Labeled real world dataset containing 20,000 samples of 26 letters of English alphabets. Each sample is a 16 dimensional encoding, and there 26 different class labels corresponding to 26 letters of the English alphabet. Class labels(letter names) are in same file.
2. moons_data.csv - Labeled dataset datset containing 25 half moon pairs, that is 50 clusters corresponding to 50 individual half moons. Any number of half moon pairs can be generated using gen_moonpairs.py program.
3. groundtruth.csv - Contains class labels for data points in moon_data.csv.

1. Nachiket Bhide - [email protected]
2. Dr. Luis Rueda - [email protected]