<｜begin▁of▁sentence｜>### Instruction:
As part of an initiative to delve into the complex social dynamics within our wildlife conservation project, our team has been meticulously tracking various forms of inter-species interactions, cataloging a variety of variables including, but not limited to, interaction frequency, nature (whether they are cooperative or competitive), along with the specific context in which they occur - be it during feeding or mating rituals. The objective of this rigorous examination is to effectively segment these interactions into discernibly stratified groups which mirror the intricate social stratification witnessed in the wild. 

To carry out this task with the precision it warrants, we are considering utilizing a method akin to the DivisiveCluster algorithm, augmented with the statistical rigor of a Gaussian Mixture Model (GMM), to excavate and categorize these layers of social conglomerations. In what manner can we deploy this DivisiveCluster with GMM technique to achieve a hierarchical clustering of our extensive data? Additionally, once we've traversed this analytical path, how shall we decipher and designate the hierarchical cluster labels that emerge from the resulting classification of our gathered data?

In this scenario, it is implied that the DivisiveCluster algorithm will be applied using relevant computational tools or APIs tailored to handle such sophisticated data analysis.
### Response:
import numpy as np
from graspologic.cluster import DivisiveCluster

# Generate synthetic data
np.random.seed(0)
X = np.random.rand(100, 3)  # 100 samples with 3 features each

# Initialize and fit the DivisiveCluster
clusterer = DivisiveCluster(cluster_method='gmm', min_components=1, max_components=5, min_split=10, max_level=2)
labels = clusterer.fit_predict(X)

# Print the hierarchical labels
print(labels)
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