Both test functions I wrote are above, but when I want to test I get wrong results. System It doesn't accept my code. I don't know exactly where my problem is. I share the problem and my solution.

def PCA(X, num_components): """ Args: X: ndarray of size (N, D), where D is the dimension of the data, and N is the number of datapoints num_components: the number of principal components to use. Returns: the reconstructed data, the sample mean of the X, principal values and principal components """ N, D = X.shape # YOUR CODE HERE # your solution should take advantage of the functions you have implemented above. ### Uncomment and modify the code below # first perform normalization on the digits so that they have zero mean and unit variance X_normalized, mean = normalize(X) # EDIT THIS # Then compute the data covariance matrix S S = np.cov(X_normalized, rowvar = False, bias = True) # EDIT THIS

# Next find eigenvalues and corresponding eigenvectors for S eig_vals, eig_vecs = eig(S) # Take the top `num_components` of eig_vals and eig_vecs, # This will be the corresponding principal values and components principal_vals, principal_components = eig_vals[:num_components], eig_vecs[:,:num_components] principal_components = np.real(principal_components) principal_components = np.real(principal_components)

# reconstruct the data from the using the basis spanned by the principal components # Notice that we have subtracted the mean from X so make sure that you add it back # to the reconstructed data P = projection_matrix(principal_components) reconst = (P @ X_normalized.T).T + mean return reconst, mean, principal_vals, principal_components

and

def PCA_high_dim(X, num_components): """Compute PCA for small sample size but high-dimensional features. Args: X: ndarray of size (N, D), where D is the dimension of the sample, and N is the number of samples num_components: the number of principal components to use. Returns: X_reconstruct: (N, D) ndarray. the reconstruction of X from the first `num_components` pricipal components. """ # YOUR CODE HERE # Uncomment and modify the code belo N, D = X.shape # # Normalize the dataset #X_normalized, mean = normalize(X) X_normalized, mean = normalize(X)

# # Find the covariance matrix M = np.dot(X_normalized, X_normalized.T) / N #S = np.cov(X_normalized.T, rowvar=False, bias=True) #cov = np.cov(X_centered, rowvar=False) eig_vals, eig_vecs = eig(M)

# # Next find eigenvalues and corresponding eigenvectors for S # # Make sure that you only take the first D eigenvalues/vectors # # You can also take a look at the eigenvalues beyond column (D-1) and they should be # # zero (or a very small number due to finite floating point precision) # eig_vals, eig_vecs = None, None principal_values = eig_vals[:num_components] principal_components = eig_vecs[:, :num_components]

# # Compute the eigenvalues and eigenvectors for the original system # # eig_vecs = None #eig_vals, eig_vecs = eig(S) #eig_vals = eig_vals[0:D] #eig_vecs = eig_vecs[:, 0:D] # Normalize the eigenvectors to have unit-length # # Take the top `num_components` of the eigenvalues / eigenvectors # # as the principal values and principal components # principal_values = None # principal_components = None principal_components = np.real(principal_components)

# Due to precision errors, the eigenvectors might come out to be complex, so only take their real parts # principal_components = np.real(principal_components) #principal_values = eig_vals[:num_components] #principal_components = eig_vecs[:, :num_components]

# # reconstruct the images from the lower dimensional representation # # Remember to add back the sample mean # reconst = None # return reconst, mean, principal_values, principal_components #P = projection_matrix(principal_components) # reconst = (P @ X_normalized.T).T + mean # return reconst, mean, principal_values, principal_components reconst = (projection_matrix(principal_components)@ X_normalized) + mean return reconst, mean, principal_values, principal_components here my error what am mss??

ERROR: test_PCA (week4_tests.Test) ---------------------------------------------------------------------- Traceback (most recent call last): File "/tmp/autograde_5q4slzm7/week4_tests.py", line 185, in test_PCA np.testing.assert_allclose(result[0], expected[0]) TypeError: 'PCA' object is not subscriptable