3. Fitting data with PCs. You are given python functions for PCA transform and a binary classifier: mu, V = PCA (X) # Finds the mean and PCs for a data matrix X clf = Classifier () clf.fit (z,y) #Fits a binary classifier from features Z and labels y yhat= clf.predict (Z) # Predicts labels from Z 1 Given a data matrix X with binary labels y, you wish to build a classifier that uses a PCA transform followed by the Classifier. Write python code that uses model validation to select the optimal number of PCA components to use. You may assume: • You use simple cross validation with one training and test split. Not You do not need to do K-fold validation. • You should use roughly 25% of the samples for test. Data shuffling before splitting is not needed. 4. PC with images. A dataset has 1000 images of size 28 x 28, represented as python array X with shape (1000, 28, 28). You are given the following python functions: # Reshapes X to a shape # Creates a PCA object Y = reshape (X, shape) pca = PCA (n_components = nc) pca. fit (Y) # Finds the mean Z = pca.transform (Y) # Find coefficients in the PC basis and PCs from training data Y Yhat = pca.inverse_transform (Z) # Invert the PC transform Write a few lines of python code to (i) fit a PC model from the first 500 images with 5 components; and (ii) create an array of approximations of the remaining 500 images. 5. PCs using SVDs. You are given a python function: U₁s, Vtr = svd(Z, full_matrices = False) which computes an "economy" SVD. Given a data matrix X, write python code that: (i) Finds the PCs and mean of the data. (ii) Finds the minimum number of PCs in order that the proportion of variance is at least 90%. (iii) Create an approximation Xhat of X using the number of PCs in part (ii).
Purchase answer to see full attachment