<｜begin▁of▁sentence｜>### Instruction:
Imagine you're working in the realm of medical data analysis, where you have managed to collect a set of measurements relating to 200 young patients, represented within a two-dimensional space that reflects certain health metrics. This dataset, akin to the crescent shapes produced by the "make_moons" function, requires a specialized approach to discern underlying patterns that may signify different health clusters.

In order to methodically analyze this pediatric health dataset, you plan to employ the "AutoGMMCluster" algorithm from the appropriate machine learning API, selecting a "spherical" covariance model due to its simplicity and assumption that data in each group should spread out evenly from the center, much like the equal growth potential in a cohort of children.

You'd proceed by initializing the "AutoGMMCluster" with the appropriate parameters, fitting it to our moon-shaped dataset of pediatric measurements, and subsequently predicting the cluster labels. The culmination of this process would be the creation of a visual representation—a scatter plot—that illustrates the clustered data points, subsequently allowing for an intuitive understanding of the natural groupings present within the pediatric health metrics.

This would enable you to potentially discover patterns in the health data that might be indicative of different health trajectories or conditions in young patients, providing valuable insights that could inform future medical care and treatments to enhance pediatric well-being.
### Response:
import matplotlib.pyplot as plt
from sklearn.datasets import make_moons
from graspologic.cluster import AutoGMMCluster

# Generate synthetic data with two interleaving half circles
X_moons, y_moons = make_moons(n_samples=200, noise=0.05, random_state=0)

# Create an instance of AutoGMMCluster using 'spherical' covariance type
auto_gmm_moons = AutoGMMCluster(min_components=2, max_components=5, covariance_type='spherical', random_state=42)

# Fit and predict the cluster labels
labels_moons = auto_gmm_moons.fit_predict(X_moons)

# Plotting
plt.scatter(X_moons[:, 0], X_moons[:, 1], c=labels_moons, cmap=plt.cm.Spectral)
plt.title('AutoGMM clustering on synthetic moons data')
plt.xlabel('Feature 1')
plt.ylabel('Feature 2')
plt.show()
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