Try to apply the SVD method to factorize the matrix M，矩阵大小为K*N into two low-rank matrices, namely matrix U，矩阵大小为K*d and matrix I，矩阵大小为d*N, where d is an empirical parameter in practice which is set as 16 in this experiment. Please complete the following tasks. You can directly apply existing API in this quiz

Sure, I can help you with that. To apply the SVD method to factorize the matrix M into two low-rank matrices U and I, we can use the svd function from the numpy library in Python. Here's how you can do it:

import numpy as np

# Define the matrix M
M = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]])

# Set the value of d
d = 2

# Apply the SVD method to factorize M into U and I
U, S, I = np.linalg.svd(M, full_matrices=False)
U = U[:, :d]
S = np.diag(S[:d])
I = I[:d, :]

# Calculate the low-rank approximation of M using U, S, and I
M_approx = np.dot(np.dot(U, S), I)

print("Matrix M:")
print(M)

print("Low-rank approximation of M:")
print(M_approx)

In this example, we have set the value of d to 2, which means we want to factorize the matrix M into two low-rank matrices with rank 2. The SVD method returns three matrices: U, S, and I. We select the first d columns of U, the first d rows and columns of S, and the first d rows of I to obtain the low-rank approximation of M. The resulting low-rank approximation is stored in the variable M_approx.

I hope this helps! Let me know if you have any more questions.