A centroid is the mean, or central position, of the points assigned to a cluster. K-means uses centroids to organize data into nonoverlapping groups. section 11.5
K-means repeatedly updates centroids through this process:
- Initialize K centroids randomly. section 11.5
- Assign each data point to its nearest centroid, typically using Euclidean distance. section 11.5
- Recalculate each centroid as the mean of its assigned points. section 11.5
- Stop when centroids become fixed or the maximum iteration limit is reached. section 11.5
NBA payroll and wins
With four clusters, R calculates centroids from NBA team payrolls and regular-season wins. Each centroid reports the salary and win means for its cluster, while every team receives a cluster assignment. section 11.5.2
k <- kmeans(final_kmeans, 4, iter.max = 25, nstart = 25) print(k) ## K-means clustering with 4 clusters of sizes 15, 1, 3, 11 ## ## Cluster means: ## salarytotal wintotal ## 1 1366605768 700.8667 ## 2 2034231301 626.0000 ## 3 1763863525 835.0000 ## 4 1490569128 746.0000 ## ## Clustering vector: ## CHA NOP ATL BOS BKN CHI CLE DAL DEN DET GSW HOU IND LAC LAL MEM MIA MIL ## 1 1 1 4 4 1 4 3 1 1 1 4 4 1 3 4 4 1 ## MIN NYK OKC ORL PHI PHO POR SAC SAS TOR UTA WAS ## 1 2 1 4 4 1 3 1 4 1 1 4 ## ## Within cluster sum of squares by cluster: ## [1] 3.519544e+16 0.000000e+00 1.012325e+16 2.254863e+16 ## (between_SS / total_SS = 91.6 %) ## ## Available components: ## ## [1] "cluster" "centers" "totss" "withinss" ## [5] "tot.withinss" "betweenss" "size" "iter" ## [9] "ifault"
Inspect the R output for cluster sizes, centroid means, team assignments, within-cluster sums of squares, and between-cluster variation. section 11.5.2
