Load the same data. Extract 1000 observations, use the code below. Try five different PCA alogrithms that would extract 100 principle components. Use the following PCA algorithms: PCA, Kernel PCA(Linear), LLE (10 neighbors), Isomap. Then estimate logistic regression on the training data and test the accuracy using testing data.

• What are the accuracy score on testing data you find with each PCA algorithm?
• Which PCA algorithm has the highest prediction accuracy?
• What is the accuracy of the logistic regression applied to the 1000 obs without applying PCA?

the given code:

# Randomly sample 1000 obs, otherwise it will get really slow.

np.random.seed(42)

smp = np.random.randint(50000, size=1000)

X_s = mnist["data"][smp,:]

y_s = mnist["target"][smp]

X_train_s, X_test_s, y_train_s, y_test_s = train_test_split(X_s, y_s)