USML9

import numpy as np
from sklearn.decomposition import TruncatedSVD

def estimate_ratings_svd(rating_matrix, n_components=5):
    """
    Estimates missing ratings in a user-item rating matrix using Truncated SVD.

    Args:
        rating_matrix (np.array): A 2D NumPy array representing the user-item
                                  rating matrix. Missing ratings should be
                                  represented by NaN or 0 (if 0 is not a valid rating).
        n_components (int): The number of latent features to use for SVD.

    Returns:
        np.array: A reconstructed rating matrix with estimated ratings for
                  missing values.
    """
    # Create a copy to avoid modifying the original matrix
    matrix_filled = np.nan_to_num(rating_matrix, nan=0) # Replace NaN with 0 for SVD

    # Perform Truncated SVD
    svd = TruncatedSVD(n_components=n_components)
    U = svd.fit_transform(matrix_filled)
    Sigma = np.diag(svd.singular_values_)
    Vt = svd.components_

    # Reconstruct the matrix
    # Note: For full reconstruction, we would use U @ Sigma @ Vt.
    # However, for rating prediction, we often use the reduced dimensions directly.
    # Here, we're effectively reconstructing the matrix based on the k-latent factors.
    reconstructed_matrix = U @ Sigma @ Vt

    # Only fill in the values that were originally missing
    estimated_matrix = np.copy(rating_matrix)
    missing_indices = np.isnan(rating_matrix)
    estimated_matrix[missing_indices] = reconstructed_matrix[missing_indices]

    return estimated_matrix

# Example Usage:
if __name__ == "__main__":
    # Sample user-item rating matrix (NaN represents missing ratings)
    # Rows are users, columns are items
    ratings = np.array([
        [5, 3, np.nan, 1, 4],
        [4, np.nan, 5, 2, np.nan],
        [1, 2, 3, np.nan, 5],
        [np.nan, 4, 1, 5, 2]
    ])

    print("Original Rating Matrix:")
    print(ratings)

    # Estimate missing ratings using SVD with 3 latent components
    estimated_ratings = estimate_ratings_svd(ratings, n_components=3)

    print("\nEstimated Rating Matrix:")
    print(estimated_ratings)