<｜begin▁of▁sentence｜>### Instruction:
Imagine we're in the lab analyzing the properties of a new composite material, where the 'composition' equates to a complex gene expression profile of 50 different samples, each described by 1000 distinct 'elements' or genes. To visualize the interactions and fundamental characteristics of this composite material in a more comprehensible, manageable space—akin to reducing a multi-component alloy down to its core constituents for better examination—we're aiming to apply a dimensionality reduction technique. Now, to accurately maintain the integrity of the original 'composition' while transferring to a lower-dimensional 'alloy,' we need to establish the number of primary 'elements' needed. Employing the Zhu and Godsie method, how might we determine the optimal count of components for this 'alloy' simplification that would still preserve the essential structure and characteristics of our original material for enhanced visualization or in-depth analysis?
### Response:
import numpy as np
from graspologic.embed import select_dimension

# Generate synthetic data
n_samples = 50
n_genes = 1000
np.random.seed(42)
X = np.random.normal(size=(n_samples, n_genes))

# Determine the optimal embedding dimension
elbows, singular_values = select_dimension(X, n_components=None, n_elbows=2)

# Display the results
print('Optimal embedding dimensions:', elbows)
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