I am working on a project for my university. A part of this project is to compare the influence of PCA on clustering. Therefore I have a football player dataset that contains a feature called "position group" which contains groups from 1 to 3. E.g. the heavy line players are in group 1, lighter receivers, cornerbacks etc are in group 2 and so on. Now I have to generate clusters with k-means and k-medoids based on 16 features that are fitness exercise results and body composition measurements like size and weight from each player.
For this I use k = 3 because there are 3 player groups in the dataset. Goal of the clustering is to determine an "optimal theoretical" player allocation to a specific group so that I can say something like this: "3 Wide Receivers changed to the group of the heavy line men based on the clustering results. This could be an indication of a wrong position allocation from the coach. The coach should check this."
For every algorithm I use the same dataset with applied PCA and without applied PCA. That means I have 4 results in total.
Now I want to compare the results. I compare the clusters with the original data by using the rand index.
The methods do not differ a lot:
Algorithm Similarity to original clusters K-means without PCA 0,514 K-means with PCA 0,544 K-medoids without PCA 0,528 K-medoids with PCA 0,532
Furhermore I use the intra- and inter-cluster similarity measures. The intra cluster distances are the following:
Algorithm Cluster 1 Cluster 2 Cluster 3 K-means without PCA 2,452 2,341 2,675 K-means with PCA 2,324 2,216 1,560 K-medoids without PCA 2,166 2,828 2,320 K-medoids with PCA 1,968 2,642 2,420
What is the best way to determine the best result especially for the intra cluster distances? Should I calculate the sum of each method and the smallest sum is the best approach?