# Cluster validation based on cluster statistics

Hi everyone I am comparing two models clusters statistics to know which one is "better", but the output or model summary varies on the algorithm used. Both models have the same data and the same amount of clusters.

In the first case, I am using a K-means model with this output (2 clusters and 550 k records)

Within Cluster Sum of Squares: 1654899.906
Tota Sum of Squares: 2199995.999
Between Cluster Sum of Squares: 545096.093


In the second model, I am using a Fuzzy C-means model with this output (2 clusters and 550 k records)

WithinClusterVariations:

Cluster 0: 0.4302769175698618
Cluster 1: 0.4327265950620389

BetweenClusterVariation:
0.2639113453058912


I wonder if there is a way to know with the above information if one cluster is better than other.

• Fuzzy c-means is a soft clustering. So you are comparing apples and oranges, it is an unfair comparison. – Has QUIT--Anony-Mousse Sep 23 '19 at 4:24
• Ok thank you, I will check that. So can I use a cluster validation measure such as the silhouette coefficient to compare both clusters? – Aureon Sep 23 '19 at 20:59
• Silhouette is defined only for discrete clustering results. So you'll first need to discretize the fuzzy clustering. Then you could also use SSQ etc. - just compute them the same way, and not maybe using a fuzzy version. – Has QUIT--Anony-Mousse Sep 24 '19 at 5:56

So the proportion of Between Cluster Variation for k-means is 545096.093 / 2199995.999 = 0.2477714. that compares with BetweenClusterVariation: 0.2639113453058912 for Fuzzy C-means. Since we are trying to maximize the proportion of variation that is between clusters, this test says that Fuzzy C-means is doing a better job.