<｜begin▁of▁sentence｜>### Instruction:
As a web developer, you may occasionally work with data that has been transformed in various ways. Let's say you're collaborating with another team and they've provided you with two sets of data, Dataset X and Dataset Y. Both datasets have an identical number of dimensions, but they don't have the same number of samples, and you believe that Dataset Y is a shuffled, relocated, and resized version of Dataset X. However, the exact transformation process, including the point-to-point correspondence, is unknown.

So, the challenge here is - How can you utilize the SeedlessProcrustes function to reposition Dataset X relative to Dataset Y? Additionally, how can you confirm that your alignment is accurate after using it? This technique should enable you to handle a situation where the data doesn't seem to match up at first glance due to permutations, shifts, and scales applied to the original dataset.
### Response:
import numpy as np
from graspologic.align import SeedlessProcrustes

# Data set X and Y where Y is a permuted, shifted, and scaled version of X.
# Each data set has n samples with d dimensions
n, d = 50, 5
X = np.random.rand(n, d)
Y = 0.5 * X[np.random.permutation(n)] + 2

# Initialize the SeedlessProcrustes aligner
aligner = SeedlessProcrustes(optimal_transport_lambda=0.1, optimal_transport_eps=0.01,
                              optimal_transport_num_reps=1000, iterative_num_reps=100)

# Align X to Y
X_prime = aligner.fit_transform(X, Y)

# Get the orthogonal alignment matrix
Q = aligner.Q_array_
print(f"Orthogonal matrix Q:\n{Q}")

# Verify alignment by comparing the transformed X (X_prime) with Y
aligned = np.allclose(X_prime @ Q, Y, atol=1e-2)
print(f"Datasets aligned: {aligned}")
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