Automatic K-Finder

[Junhyuck-Woo]

Our assignment is to implement k-finder.
I thought that k-finder function gives us k value automatically.

Actually, I could find two methods, the first one is an elbow method and the other is a silhouette method. In the Labs, your description might mean an elbow method.
So, I tried to implement the elbow method.

I have two problems.

1. If the k value is increased, the error rate is always reduced.
   So, I utilized a differentiation. However, sometimes differential also decreased gradually.
   It made me hard to get a collect one.
   Is there are any solutions?
2. Based on my result, I hope to check my result.
   Is it correct?

PS.
In the noon, I asked a different one.
I found an error in my algorithms, so I changed it.
This issue is another problem I faced.

Here are images (https://imgur.com/a/caffR9g)
1, 2 show my problem.
3,4,5 for checking my algorithms ( Results)