<｜begin▁of▁sentence｜>### Instruction:
Given a dataset of points in a multi-dimensional feature space, how can graspologic's KMeansCluster be used to determine the optimal number of clusters and cluster the data points accordingly?
### Response:
import numpy as np
from graspologic.cluster import KMeansCluster
from sklearn.datasets import make_blobs

# Generate synthetic data with 3 blobs
X, y_true = make_blobs(n_samples=300, centers=3, cluster_std=0.60, random_state=0)

# Initialize KMeansCluster with a max number of clusters to find the best number of clusters
kmeans_cluster = KMeansCluster(max_clusters=5, random_state=42)
kmeans_cluster.fit(X)

# Obtain the optimal number of clusters and the silhouette score for each number of clusters
optimal_clusters = kmeans_cluster.n_clusters_
silhouette_scores = kmeans_cluster.silhouette_list_

# Now we can use the fitted model to predict labels for new samples
labels = kmeans_cluster.predict(X)

print(f'Optimal number of clusters: {optimal_clusters}')
print(f'Silhouette scores: {silhouette_scores}')
print(f'Predicted labels: {labels}')
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