Problem statement Revisit the handwritten digit recognition problem. (a) Even though, linear regression learns a real-valued function, binary- valued functions are also real-valued 1 R. Use linear regression to compute wfor the last homework problem, and approximate your binary classification wT xn yn = 1. Use your result for wto compute sign(wT xn) and report the value for Ein and Eout. Again, use symmetry and intensity as the features. (b) Run the pocket algorithm from last homework, initializing wwith the values obtained in (a). Would the error converge faster than when wis randomly initialized? Compare and discuss. Python code - import numpy as np import matplotlib.pyplot as plt import random # Load training data and testing data train = np.genfromtxt('DigitsTraining.csv', delimiter=',') test = np.genfromtxt('DigitsTesting.csv', delimiter=',') #Pre-processing data into data labels and data X_train = train[:, 1:] y_train = train[:, 0] X_test = test[:, 1:] y_test = test[:, 0] #To plot line y = ax + b def line(w, data=None): a = - w[1] / w[2] b = - w[0] / w[2] x_line = np.linspace(0.4, 1, 100) if data is not None: return a*data + b else: return a*x_line + b def symmetry(X): X_shapes = (16, 16) X = X.reshape(X_shapes) sV= np.mean(np.abs(X-np.flipup(X))) SH= symm=(sv+sh)/2 ####################### # YOUR CODE GOES HERE # ####################### #please of the definition of simmetry found in the slides. You can use np.flipud and np.fliplr return symm Please provide the code - (# where it says -YOUR CODE GOES HERE ) # Prepare Training Data for 7's and 1's. Please changed for the two digits you chose (one of them is the last digit of the driver license) #Extract the Digit1 and Digit2 from the data Digit1 = X_train[y_train == 7] y_train_Digit1 = np.ones(len(Digit1)) Digit2 = X_train[y_train == 1] y_train_Digit2 = -np.ones(len(Digit2)) symm_Digit2 = [symmetry(im) for im in Digit2] symm_Digit1 = [symmetry(im) for im in Digit1] #Calculate averages and symmetries of the digits in training data ####################### # YOUR CODE GOES HERE # ####################### #Please use the definition of intensity. You can use the np.mean #Concatenate the intensities and symmetry new_Digit1 = np.c_[avg_intensity_Digit1, symm_Digit1] new_Digit2 = np.c_[avg_intensity_Digit2, symm_Digit2] #Stack all the data together and randomize their locations. X_new = np.r_[new_Digit1, new_Digit2] y_new = np.r_[y_train_Digit1, y_train_Digit2] R_num = np.random.randint(X_new.shape[0], size = (X_new.shape[0],)) X_new = X_new[R_num] y_new = y_new[R_num] Please provide the code - (# where it says -YOUR CODE GOES HERE ) #Prepare the test data for 7's and 1's. Please adjust for your two numbers, where one of them is the last digit of your driver license X_test_Digit1 = X_test[y_test == 7] y_test_Digit1 = np.ones(len(X_test_Digit1)) X_test_Digit2 = X_test[y_test == 1] y_test_Digit2 = -np.ones(len(X_test_Digit2)) X_test_new = np.r_[X_test_Digit1, X_test_Digit2] y_test_new = np.r_[y_test_Digit1, y_test_Digit2] R = np.random.randint(X_test_new.shape[0], size = (X_test_new.shape[0],)) X_test_new = X_test_new[R] y_test_new = y_test_new[R] #Calculate averages and symmetries of the digits in testing data ####################### # YOUR CODE GOES HERE # ####################### #please use the definition of on the slide. You can use np.mean test_symm = [symmetry(im) for im in X_test_new] X_test_final = np.c_[avg_int_test, test_symm] Please provide the code - (# where it says -YOUR CODE GOES HERE ) #Prepare the test data for 7's and 1's. Please adjust for your two numbers, where one of them is the last digit of your driver license X_test_Digit1 = X_test[y_test == 7] y_test_Digit1 = np.ones(len(X_test_Digit1)) X_test_Digit2 = X_test[y_test == 1] y_test_Digit2 = -np.ones(len(X_test_Digit2)) X_test_new = np.r_[X_test_Digit1, X_test_Digit2] y_test_new = np.r_[y_test_Digit1, y_test_Digit2] R = np.random.randint(X_test_new.shape[0], size = (X_test_new.shape[0],)) X_test_new = X_test_new[R] y_test_new = y_test_new[R] #Calculate averages and symmetries of the digits in testing data ####################### # YOUR CODE GOES HERE # ####################### #please use the definition of on the slide. You can use np.mean test_symm = [symmetry(im) for im in X_test_new] X_test_final = np.c_[avg_int_test, test_symm] Please provide the code - (# where it says -YOUR CODE GOES HERE ) # Linear Regression def lin(input_data,y,input_data_test,y_test): data = np.c_[np.ones((input_data.shape[0],1)), input_data] #https://docs.scipy.org/doc/numpy/reference/generated/numpy.c_.html data_test = np.c_[np.ones((input_data_test.shape[0],1)), input_data_test] ####################### # YOUR CODE GOES HERE # ####################### return Ein,Eout,W_lin Please provide the code - (# where it says -YOUR CODE GOES HERE ) def pocket(input_data,y,input_data_test,y_test,max_iter,w=None): data = np.c_[np.ones((input_data.shape[0],1)), input_data] #https://docs.scipy.org/doc/numpy/reference/generated/numpy.c_.html data_test = np.c_[np.ones((input_data_test.shape[0],1)), input_data_test] if w is None: w = np.random.random(data.shape[1]).reshape(-1,1) else: w = w.reshape(-1,1) wf=w current = np.sign(data @ w) f = y.reshape(-1,1) y_test =y_test.reshape(-1,1) difference = (f != current) Ein=[] Eout=[] error=difference.sum() Ein.append(error * (1/len(difference))) current_test= np.sign(data_test @ wf) difference_test= (y_test != current_test) error_test=difference_test.sum() Eout.append(error_test * (1/len(difference_test))) t = 0 ####################### # YOUR CODE GOES HERE # ####################### #Please implement the logic of the pocket algorithm. Remember that w must be updated according to the evolution of the error return Ein,Eout,wf Please provide the code - (# where it says -YOUR CODE GOES HERE ) #Using pocket algorithm Ein, Eout,w = pocket(X_new, y_new,X_test_final,y_test_new, 1000) print('Min Ein Pocket=',min(Ein)) print('Min Eout Pocket=',min(Eout)) #Ploting plt.scatter(avg_intensity_Digit2, symm_Digit2, marker = 'x', color = 'red') plt.scatter(avg_intensity_Digit1, symm_Digit1, marker='o', color = 'blue') plt.plot(x_line, line(w)) plt.show() #Plot Ein and Eout plt.title('Ein/Eout Pocket') plt.xlabel('Iterations') plt.ylabel('Error %') plt.plot(Ein, label='Ein') plt.plot(Eout, label = 'Eout') plt.legend() plt.show() Ein, Eout,w = lin(X_new, y_new,X_test_final,y_test_new) plt.scatter(avg_intensity_Digit2, symm_Digit2, marker = 'x', color = 'red') plt.scatter(avg_intensity_Digit1, symm_Digit1, marker='o', color = 'blue') plt.plot(x_line, line(w)) plt.show() print('Min Ein Lin=',Ein) print('Min Eout Lin=',Eout) Ein, Eout,w = pocket(X_new, y_new,X_test_final,y_test_new, 1000,w) print('Min Ein Pocket with Lin=',min(Ein)) print('Min Eout Pocket with Lin=',min(Eout)) plt.scatter(avg_intensity_Digit2, symm_Digit2, marker = 'x', color = 'red') plt.scatter(avg_intensity_Digit1, symm_Digit1, marker='o', color = 'blue') plt.plot(x_line, line(w)) plt.show() #Plot Ein and Eout plt.title('Ein/Eout Pocket with Linear Regresion Initial Weights') plt.xlabel('Iterations') plt.ylabel('Error %') plt.plot(Ein, label='Ein') plt.plot(Eout, label = 'Eout') plt.legend() plt.show() Please provide all the code, and please don't miss any code read the problem statement first. The last answer was not helpful.