In our class, we did some experiments to see which way is best to group things together. We tried three different methods: one called k-means, another called k-medoids, and one called DBSCAN. We used these methods on different sets of data that have shapes like circles, squares, and other interesting shapes. We also used computer code to show the results in pictures.
Example 1: In the first scenario, we generated 200 random points uniformly distributed within a lemniscate shape. DBSCAN identified four distinct clusters among these points. We also applied the k-means method with different values of k (k=2 and k=4) and visualized the resulting clusters. Similarly, we demonstrated the k-medoids method with k=2 and k=4.
Example 2: In the second experiment, we repeated the process using a dataset comprising 400 random points distributed in the union of a circle and an annulus. DBSCAN successfully identified two clusters within this dataset. As before, we employed the k-means and k-medoids methods with varying values of k (k=2 and k=4) to compare the outcomes.
Example 3: Lastly, we filled the region of a square excluding a maximal circle with 400 random points for the third example. DBSCAN revealed the presence of four clusters in this scenario. Our analysis included the application of the k-means and k-medoids methods with different values of k (k=2 and k=4).
I will explain which method worked best for each case and tell you more about how they did their job in the next update.