<｜begin▁of▁sentence｜>### Instruction:
Suppose you're a web developer working on a backend system for visualizing user interaction data on a website. The system aims to segment users into groups based on their activity patterns, which have been recorded as 2D data points. Your job is to implement an algorithm that pinpoints the most effective segmentation strategy.

You decide to employ a Gaussian Mixture Model because of its flexibility in accounting for variances and covariances within the data. The graspologic library offers a tool called `GaussianCluster` that appears to fit the bill. 

The task at hand is to utilize the `GaussianCluster` class to experiment with different numbers of user clusters. You need to iterate through a spectrum of cluster counts to calculate the Bayesian Information Criterion (BIC) for each potential clustering setup. The main goal is to find the sweet spot—the cluster quantity and associated covariance type—that minimizes the BIC, indicating the most statistically efficient model for this data.

Once you have determined the optimal configuration, the `GaussianCluster` class should also enable you to generate the actual cluster labels, effectively categorizing each user's data point into its respective group.

Can you reframe this requirement so that it can seamlessly fit into the context of your web development project? Your solution should detail the specific use of `GaussianCluster` in this regard, maintaining the technical semantics of the original request.
### Response:
import numpy as np
from graspologic.cluster import GaussianCluster

# Generate synthetic data with 2 features
np.random.seed(42)
X = np.random.randn(100, 2)

# Initialize GaussianCluster object to find the best number of clusters with BIC
gmm_cluster = GaussianCluster(min_components=2, max_components=5, covariance_type='all')

# Fit the model
gmm_cluster.fit(X)

# Predict the cluster labels
labels = gmm_cluster.fit_predict(X)

# Retrieve the optimal number of components and covariance type
n_components = gmm_cluster.n_components_
covariance_type = gmm_cluster.covariance_type_

print(f'Optimal number of clusters: {n_components}')
print(f'Optimal covariance type: {covariance_type}')
print(f'Cluster labels: {labels}')
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