In the class, we explored the differences between k-means, k-medoids, and DBSCAN clustering algorithms by applying them to geometrically structured datasets. We employed Mathematica for coding and visualizing the results of these clustering methods on three distinct examples.
**Example 1** involved a lemniscate (infinity symbol shape) populated with 200 random points:
– DBSCAN discerned 4 distinct clusters from these points.
– The k-means algorithm was implemented with both k=2 and k=4, and the resulting clusters were visualized.
– The k-medoids algorithm was also demonstrated for k=2 and k=4, illustrating how the clusters are formed around central points.
**Example 2** used a composite shape of a circle and an annulus, with 400 random points scattered within:
– DBSCAN successfully identified 2 clusters within this shape.
– We applied the k-means and k-medoids methods with k=2 and k=4 to see how they group the points.
**Example 3** was designed with a square area from which a maximal circle was subtracted, filled with 400 random points:
– Here, DBSCAN found 4 clusters, indicating its sensitivity to spatial density rather than geometric shapes.
– Again, we visualized how k-means and k-medoids behaved with k=2 and k=4.
The upcoming update will provide a comparative analysis and delve deeper into each method, offering insights into their applications and limitations based on the clustering outcomes observed in these examples.