Try to apply the SVD method to factorize the matrix  into two low-rank matrices, namely matrix  and matrix , where  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. (Please provide the code and results, 20%)翻译成中文

尝试应用SVD方法将矩阵  分解为两个低秩矩阵，即矩阵  和矩阵 ，其中  是实践中设置的经验参数，本次实验中设置为 ***\*16\****。请完成以下任务。您可以直接应用现有的API。 （请提供代码和结果，20％）

相关问题

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.

2) Try to apply the SVD method to factorize the matrix into two low-rank matrices, namely matrix and matrix , where 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. (Please provide the code and results, 20%) Provide the singular values of the data from ‘./dataset/images’ in the report. Provide the images by reshaping each column in the low-rank matrix of the data from ‘./dataset/images’ in the report. Provide the first 20 reconstructed RGB face images corresponding to the reconstructed matrix in the report. 翻译成中文

2) 尝试将矩阵分解为两个低秩矩阵，即矩阵U和矩阵V，其中U的列是左奇异向量，V的列是右奇异向量，同时矩阵Σ是对角矩阵，其对角线上的元素是奇异值。在这个实验中，参数r设置为16。请完成以下任务。您可以直接使用现有的API来完成此任务。（请提供代码和结果，20%）

 在报告中提供从‘./dataset/images’获取的数据的奇异值。
 在报告中通过重塑‘./dataset/images’中低秩矩阵的每一列来提供图像。
 在报告中提供前20个重建的RGB人脸图像，对应于重构矩阵。