<｜begin▁of▁sentence｜>### Instruction:
In a scenario where a computer programmer is tasked with aligning two sets of data points, representing embeddings from distinct graph structures, they opt to utilize the Seedless Procrustes method to find the best possible alignment. This method is chosen with the intention of preserving the orthogonal properties of the datasets.

The programmer is dealing with one dataset, let's call it `X`, with a shape of (n, d) and another dataset, `Y`, with a shape of (m, d), where `n` and `m` represent the number of points in each dataset and `d` represents the dimensionality, which is shared between the two. The challenge is that there is no direct one-to-one correspondence between the points in the two datasets.

By applying the Seedless Procrustes process through an appropriate function call, the programmer endeavors to transform dataset `X` into a new form, `X'`, which best aligns with dataset `Y`. In doing so, the function also provides an optimal transport matrix that illustrates the transformation from `X` to `X'` and an alignment score quantifying the closeness of the match.

The key question that the programmer wishes to address is: can the Seedless Procrustes algorithm effectively reconcile these two datasets given their parameters, and what would be the characteristics of the resulting optimal transport matrix and alignment score given the specific application of Seedless Procrustes?
### Response:
import numpy as np
from graspologic.align import SeedlessProcrustes
from scipy.stats import ortho_group

# Generate synthetic datasets
n, m, d = 5, 4, 3
X = np.random.rand(n, d)
# Apply random orthogonal transformation to X
Q_true = ortho_group.rvs(dim=d)
Y = X @ Q_true

# Align X to Y using SeedlessProcrustes
aligner = SeedlessProcrustes(optimal_transport_lambda=0.1, optimal_transport_eps=0.01,
                              optimal_transport_num_reps=1000, iterative_num_reps=100, init='2d')
X_prime = aligner.fit_transform(X, Y)

# Print the resulting transformed dataset X'
print('Transformed X:', X_prime)

# Print the optimal transport matrix
print('Optimal transport matrix:', aligner.P_array_)

# Print the score
print('Score:', aligner.score_)
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