Silhouette score behaving counter intuitively

Question

My Silhouette score decreases as number of clusters increase. I'm using scikit's kmeans algorithm on the modified white wine dataset from UCI. Here's the final dataset I'm using - https://drive.google.com/open?id=1goh97QZB3V0rJSn4amLC-jBb3upsaIlH

Code

df = pd.read_csv('whiteWineTwoClasses.csv', header=0)
numberOfColumns = len(df.columns)
numberOfAttributes = numberOfColumns - 1
X = df.iloc[:,0:numberOfColumns-1]
Y = df.iloc[:, numberOfColumns-1]
scaler = StandardScaler()
scaler.fit(X)
xtrans = scaler.transform(X)

def getNumbersForKmeans(X, numberOfClusters):
  kmeans = KMeans(n_clusters=numberOfClusters, random_state=0)
  kmeans.fit(X)
  labels = kmeans.labels_
  inertiaScore = kmeans.inertia_
  silScore = metrics.silhouette_score(X, labels, metric='euclidean')
  return inertiaScore, silScore


print(getNumbersForKmeans(xtrans, 3))
print(getNumbersForKmeans(xtrans, 10))
print(getNumbersForKmeans(xtrans, 20))
print(getNumbersForKmeans(xtrans, 50))
print(getNumbersForKmeans(xtrans, df.shape[0]-1))

Output is (Look at second column)

(43830.24610203885, 0.13157830778113577)
(31412.978722003416, 0.11319449812661529)
(26173.031185455613, 0.10728651926177515)
(19896.193919556117, 0.10876065019480499)
(2.5006777281554326e-07, 0.00010210332874983413)

I was of the understanding that when the number of clusters are ~ number of data points, silhouette score should be ~1

I've looked at other answers but none of them seemed to actually help here.

Answer 1

Your assumption on Silhouette is wrong:

The silhouette of a one elemental cluster leads to a division by zero (there is no average distance to other members of the same cluster). The authors defined the value of one-elemental clusters to be 0.

So when k -> N then Silhouette tends to 0 by definition.