From 5bc9ad20f16a0043b2b4ca528815f0a3f9f30725 Mon Sep 17 00:00:00 2001 From: Emmanuel Dellandrea <emmanuel.dellandrea@ec-lyon.fr> Date: Tue, 21 Jan 2025 11:20:41 +0100 Subject: [PATCH] Add session 2 --- .../Session_2/nn_classification-completed.py | 417 ++++++++++++++++++ .../Subject_3_Pytorch_Neural_Networks.pdf | Bin 0 -> 175625 bytes 2 files changed, 417 insertions(+) create mode 100644 Practical_sessions/Session_2/nn_classification-completed.py create mode 100644 Practical_sessions/Session_3/Subject_3_Pytorch_Neural_Networks.pdf diff --git a/Practical_sessions/Session_2/nn_classification-completed.py b/Practical_sessions/Session_2/nn_classification-completed.py new file mode 100644 index 0000000..9e6350f --- /dev/null +++ b/Practical_sessions/Session_2/nn_classification-completed.py @@ -0,0 +1,417 @@ +import matplotlib.pyplot as plt +import numpy as np + +def load_data(file_name, delimiter=','): + """ Reads the file containing the data and returns the matrices corresponding to it + + Parameters + ---------- + file_name : name of the file containing the data + delimiter : character that separates the columns in the file (default is ",") + + Returns + ------- + x : data matrix of dimension [N, nb_var] + d : matrix containing the target variable values of dimension [N, nb_target] + N : number of elements + nb_var : number of predictor variables + nb_target : number of target variables + + """ + + data = np.loadtxt(file_name, delimiter=delimiter) + + nb_target = 1 + nb_var = data.shape[1] - nb_target + N = data.shape[0] + + x = data[:, :nb_var] + d = data[:, nb_var:].reshape(N,1) + + return x, d, N, nb_var, nb_target + + +def normalization(x): + """ Normalizes the data by centering and scaling the predictor variables + + Parameters + ---------- + X : data matrix of dimension [N, nb_var] + + with N : number of elements and nb_var : number of predictor variables + + Returns + ------- + X_norm : normalized data matrix of dimension [N, nb_var] + mu : mean of the variables of dimension [1, nb_var] + sigma : standard deviation of the variables of dimension [1, nb_var] + + """ + + mu = np.mean(x, 0) + sigma = np.std(x, 0) + x_norm = (x - mu) / sigma + + return x_norm, mu, sigma + +def split_data(x,d,prop_val=0.2, prop_test=0.2): + """ Splits the original data into three distinct subsets: training, validation, and test + + Parameters + ---------- + x : data matrix of dimension [N, nb_var] + d : target values matrix [N, nb_target] + prop_val : proportion of validation data in the total data (between 0 and 1) + prop_test : proportion of test data in the total data (between 0 and 1) + + with N : number of elements, nb_var : number of predictor variables, nb_target : number of target variables + + Returns + ------- + x_train : training data matrix + d_train : target values matrix for training + x_val : validation data matrix + d_val : target values matrix for validation + x_test : test data matrix + d_test : target values matrix for test + + """ + assert prop_val + prop_test < 1.0 + + N = x.shape[0] + indices = np.arange(N) + np.random.shuffle(indices) + nb_val = int(N*prop_val) + nb_test = int(N*prop_test) + nb_train = N - nb_val - nb_test + + x = x[indices,:] + d = d[indices,:] + + x_train = x[:nb_train,:] + d_train = d[:nb_train,:] + + x_val = x[nb_train:nb_train+nb_val,:] + d_val = d[nb_train:nb_train+nb_val,:] + + x_test = x[N-nb_test:,:] + d_test = d[N-nb_test:,:] + + return x_train, d_train, x_val, d_val, x_test, d_test + +def compute_cross_entropy_cost(y, d): + """ Computes the value of the cross-entropy cost function + + Parameters + ---------- + y : predicted data matrix (softmax) + d : actual data matrix encoded by 1 + + Returns + ------- + cost : value corresponding to the cost function + + """ + + N = y.shape[1] + + cost = - np.sum(d*np.log(y)) / N + + return cost + +def forward_pass(x, W, b, activation): + """ Performs a forward pass in the neural network + + Parameters + ---------- + x : input matrix, dimension nb_var x N + W : list containing the weight matrices of the network + b : list containing the bias matrices of the network + activation : list containing the activation functions of the network layers + + with N : number of elements, nb_var : number of predictor variables + + Returns + ------- + a : list containing the input potentials of the network layers + h : list containing the outputs of the network layers + + """ + h = [x] + a = [] + for i in range(len(b)): + a.append( W[i].dot(h[i]) + b[i] ) + h.append( activation[i](a[i]) ) + + return a, h + +def backward_pass(delta_h, a, h, W, activation): + """ Performs a backward pass in the neural network (backpropagation) + + Parameters + ---------- + delta_h : matrix containing the gradient of the cost with respect to the network output + a : list containing the input potentials of the network layers + h : list containing the outputs of the network layers + W : list containing the weight matrices of the network + activation : list containing the activation functions of the network layers + + Returns + ------- + delta_W : list containing the gradient matrices of the network's weight layers + delta_b : list containing the gradient matrices of the network's bias layers + + """ + + delta_b = [] + delta_W = [] + + for i in range(len(W)-1,-1,-1): + + delta_a = delta_h * activation[i](a[i], True) + + delta_b.append( delta_a.mean(1).reshape(-1,1) ) + delta_W.append( delta_a.dot(h[i].T) ) + + delta_h = (W[i].T).dot(delta_a) + + delta_b = delta_b[::-1] + delta_W = delta_W[::-1] + + return delta_W, delta_b + +def sigmoid(z, deriv=False): + """ Computes the value of the sigmoid function or its derivative applied to z + + Parameters + ---------- + z : can be a scalar or a matrix + deriv : boolean. If False returns the value of the sigmoid function, if True returns its derivative + + Returns + ------- + s : value of the sigmoid function applied to z or its derivative. Same dimension as z + + """ + + s = 1 / (1 + np.exp(-z)) + if deriv: + return s * (1 - s) + else : + return s + +def linear(z, deriv=False): + """ Computes the value of the linear function or its derivative applied to z + + Parameters + ---------- + z : can be a scalar or a matrix + deriv : boolean. If False returns the value of the linear function, if True returns its derivative + + + Returns + ------- + s : value of the linear function applied to z or its derivative. Same dimension as z + + """ + if deriv: + return 1 + else : + return z + + +def relu(z, deriv=False): + """ Computes the value of the ReLU function or its derivative applied to z + + Parameters + ---------- + z : can be a scalar or a matrix + deriv : boolean. If False returns the value of the ReLU function, if True returns its derivative + + Returns + ------- + s : value of the ReLU function applied to z or its derivative. Same dimension as z + + """ + + r = np.zeros(z.shape) + if deriv: + pos = np.where(z>=0) + r[pos] = 1.0 + return r + else : + return np.maximum(r,z) + +def softmax(z, deriv=False): + """ Computes the value of the softmax function or its derivative applied to z + + Parameters + ---------- + z : data matrix + deriv : boolean. If False returns the value of the softmax function, if True returns its derivative + + Returns + ------- + s : value of the softmax function applied to z or its derivative. Same dimension as z + + """ + + if deriv: + return 1 + else : + return np.exp(z) / np.sum(np.exp(z),axis=0) + +def one_hot_encoding(d): + """ Performs a one-hot encoding: for the output neurons of the network, only 1 will have the value 1, all others will be 0 + + Parameters + ---------- + d : matrix containing the values of the target variable (class of the elements) of dimension [N, 1] + with N : number of elements + + Returns + ------- + e : encoded data matrix of dimension [N, nb_classes] + with N : number of elements and nb_classes the number of classes (maximum+1) of the values in d + + """ + + d = d.astype(int).flatten() + N = d.shape[0] + nb_classes = d.max() + 1 + + e = np.zeros((N,nb_classes)) + e[range(N),d] = 1 + + return e + +def classification_accuracy(y,d): + """ Computes the classification accuracy (proportion of correctly classified elements) + + Parameters + ---------- + y : network outputs matrix of dimension [nb_output_neurons x N] + d : true values matrix [nb_output_neurons x N] + + with N : number of elements and nb_output_neurons : number of neurons in the output layer + + Returns + ------- + t : classification accuracy + + """ + + ind_y = np.argmax(y,axis=0) + ind_d = np.argmax(d,axis=0) + t = np.mean(ind_y == ind_d) + + return t + + +# ===================== Part 1: Reading and Normalizing the Data ===================== +print("Reading the data ...") + +x, d, N, nb_var, nb_target = load_data("iris.txt") +# x, d, N, nb_var, nb_target = load_data("scores.txt") + +# Display the first 10 examples of the dataset +print("Displaying the first 10 examples of the dataset: ") +for i in range(0, 10): + print(f"x = {x[i,:]}, d = {d[i]}") + +# Normalization of the variables (centering and scaling) +print("Normalizing the variables ...") +x, mu, sigma = normalization(x) +d = one_hot_encoding(d) + +# Split the data into training, validation, and test subsets +x_train, d_train, x_val, d_val, x_test, d_test = split_data(x,d) + +# ===================== Part 2: Training ===================== + +# Learning rate and number of iterations +alpha = 0.0001 +nb_iters = 10000 +training_costs = np.zeros(nb_iters) +validation_costs = np.zeros(nb_iters) + +# Network dimensions +D_c = [nb_var, 15, 15, d_train.shape[1]] # list containing the number of neurons for each layer +activation = [relu, relu, softmax] # list containing the activation functions for hidden layers and output layer + +# Random initialization of network weights +W = [] +b = [] +for i in range(len(D_c)-1): + W.append(2 * np.random.random((D_c[i+1], D_c[i])) - 1) + b.append(np.zeros((D_c[i+1],1))) + +x_train = x_train.T # Data is presented as column vectors at the network input +d_train = d_train.T + +x_val = x_val.T # Data is presented as column vectors at the network input +d_val = d_val.T + +x_test = x_test.T # Data is presented as column vectors at the network input +d_test = d_test.T + +for t in range(nb_iters): + + ############################################################################# + # Forward pass: calculate predicted output y on validation data # + ############################################################################# + a, h = forward_pass(x_val, W, b, activation) + y_val = h[-1] # Predicted output + + ############################################################################### + # Forward pass: calculate predicted output y on training data # + ############################################################################### + a, h = forward_pass(x_train, W, b, activation) + y_train = h[-1] # Predicted output + + ########################################### + # Compute Mean Squared Error loss function # + ########################################### + training_costs[t] = compute_cross_entropy_cost(y_train,d_train) + validation_costs[t] = compute_cross_entropy_cost(y_val,d_val) + + #################################### + # Backward pass: backpropagation # + #################################### + delta_h = (y_train-d_train) # For the last layer + delta_W, delta_b = backward_pass(delta_h, a, h, W, activation) + + ############################################# + # Update weights and biases ##### # + ############################################# + for i in range(len(b)-1,-1,-1): + b[i] -= alpha * delta_b[i] + W[i] -= alpha * delta_W[i] + +print("Final cost on the training set: ", training_costs[-1]) +print("Classification accuracy on the training set: ", classification_accuracy(y_train, d_train)) + +print("Final cost on the validation set: ", validation_costs[-1]) +print("Classification accuracy on the validation set: ", classification_accuracy(y_val, d_val)) + +# Display cost function evolution during backpropagation +plt.figure(0) +plt.title("Cost function evolution during backpropagation") +plt.plot(np.arange(training_costs.size), training_costs, label="Training") +plt.plot(np.arange(validation_costs.size), validation_costs, label="Validation") +plt.legend(loc="upper left") +plt.xlabel("Number of iterations") +plt.ylabel("Cost") +plt.show() + +# ===================== Part 3: Evaluation on the test set ===================== + +####################################################################### +# Forward pass: calculate predicted output y on test data # +####################################################################### +a, h = forward_pass(x_test, W, b, activation) +y_test = h[-1] # Predicted output + +cost = compute_cross_entropy_cost(y_test,d_test) +print("Cost on the test set: ", cost) +print("Classification accuracy on the test set: ", classification_accuracy(y_test, d_test)) diff --git a/Practical_sessions/Session_3/Subject_3_Pytorch_Neural_Networks.pdf b/Practical_sessions/Session_3/Subject_3_Pytorch_Neural_Networks.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f74190c9451b5748281dd04a140c4cd5ddab2599 GIT binary patch literal 175625 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