# Make a prediction with weights def predict(row, weights): activation = weights[0] for i in range(len(row)-1): activation += weights[i + 1] * row[i] return 1.0 if activation >= 0.0 else 0.0
# test predictions dataset = [[2.7810836,2.550537003,0], [1.465489372,2.362125076,0], [3.396561688,4.400293529,0], [1.38807019,1.850220317,0], [3.06407232,3.005305973,0], [7.627531214,2.759262235,1], [5.332441248,2.088626775,1], [6.922596716,1.77106367,1], [8.675418651,-0.242068655,1], [7.673756466,3.508563011,1]] weights = [-0.1, 0.20653640140000007, -0.23418117710000003] for row in dataset: prediction = predict(row, weights) print("Expected=%d, Predicted=%d" % (row[-1], prediction))
O/P : Expected=0, Predicted=0 Expected=0, Predicted=0 Expected=0, Predicted=0 Expected=0, Predicted=0 Expected=0, Predicted=0 Expected=1, Predicted=1 Expected=1, Predicted=1 Expected=1, Predicted=1 Expected=1, Predicted=1 Expected=1, Predicted=1
We can estimate the weight values for our training data using stochastic gradient descent.
Stochastic gradient descent requires two parameters:
Learning Rate: Used to limit the amount each weight is corrected each time it is updated. Epochs: The number of times to run through the training data while updating the weight. These, along with the training data will be the arguments to the function.
There are 3 loops we need to perform in the function:
Loop over each epoch. Loop over each row in the training data for an epoch. Loop over each weight and update it for a row in an epoch.
# Estimate Perceptron weights using stochastic gradient descent def train_weights(train, l_rate, n_epoch): weights = [0.0 for i in range(len(train[0]))] for epoch in range(n_epoch): sum_error = 0.0 for row in train: prediction = predict(row, weights) error = row[-1] - prediction sum_error += error**2 weights[0] = weights[0] + l_rate * error for i in range(len(row)-1): weights[i + 1] = weights[i + 1] + l_rate * error * row[i] print('>epoch=%d, lrate=%.3f, error=%.3f' % (epoch, l_rate, sum_error)) return weights
# Make a prediction with weights def predict(row, weights): activation = weights[0] for i in range(len(row)-1): activation += weights[i + 1] * row[i] return 1.0 if activation >= 0.0 else 0.0 # Estimate Perceptron weights using stochastic gradient descent def train_weights(train, l_rate, n_epoch): weights = [0.0 for i in range(len(train[0]))] for epoch in range(n_epoch): sum_error = 0.0 for row in train: prediction = predict(row, weights) error = row[-1] - prediction sum_error += error**2 weights[0] = weights[0] + l_rate * error for i in range(len(row)-1): weights[i + 1] = weights[i + 1] + l_rate * error * row[i] print('>epoch=%d, lrate=%.3f, error=%.3f' % (epoch, l_rate, sum_error)) return weights # Calculate weights dataset = [[2.7810836,2.550537003,0], [1.465489372,2.362125076,0], [3.396561688,4.400293529,0], [1.38807019,1.850220317,0], [3.06407232,3.005305973,0], [7.627531214,2.759262235,1], [5.332441248,2.088626775,1], [6.922596716,1.77106367,1], [8.675418651,-0.242068655,1], [7.673756466,3.508563011,1]] l_rate = 0.1 n_epoch = 5 weights = train_weights(dataset, l_rate, n_epoch) print(weights)
[-0.1, 0.20653640140000007, -0.23418117710000003]
# Perceptron Algorithm on the Sonar Dataset from random import seed from random import randrange from csv import reader # Load a CSV file def load_csv(filename): dataset = list() with open(filename, 'r') as file: csv_reader = reader(file) for row in csv_reader: if not row: continue dataset.append(row) return dataset # Convert string column to float def str_column_to_float(dataset, column): for row in dataset: row[column] = float(row[column].strip()) # Convert string column to integer def str_column_to_int(dataset, column): class_values = [row[column] for row in dataset] unique = set(class_values) lookup = dict() for i, value in enumerate(unique): lookup[value] = i for row in dataset: row[column] = lookup[row[column]] return lookup # Split a dataset into k folds def cross_validation_split(dataset, n_folds): dataset_split = list() dataset_copy = list(dataset) fold_size = int(len(dataset) / n_folds) for i in range(n_folds): fold = list() while len(fold) < fold_size: index = randrange(len(dataset_copy)) fold.append(dataset_copy.pop(index)) dataset_split.append(fold) return dataset_split # Calculate accuracy percentage def accuracy_metric(actual, predicted): correct = 0 for i in range(len(actual)): if actual[i] == predicted[i]: correct += 1 return correct / float(len(actual)) * 100.0 # Evaluate an algorithm using a cross validation split def evaluate_algorithm(dataset, algorithm, n_folds, *args): folds = cross_validation_split(dataset, n_folds) scores = list() for fold in folds: train_set = list(folds) train_set.remove(fold) train_set = sum(train_set, []) test_set = list() for row in fold: row_copy = list(row) test_set.append(row_copy) row_copy[-1] = None predicted = algorithm(train_set, test_set, *args) actual = [row[-1] for row in fold] accuracy = accuracy_metric(actual, predicted) scores.append(accuracy) return scores # Make a prediction with weights def predict(row, weights): activation = weights[0] for i in range(len(row)-1): activation += weights[i + 1] * row[i] return 1.0 if activation >= 0.0 else 0.0 # Estimate Perceptron weights using stochastic gradient descent def train_weights(train, l_rate, n_epoch): weights = [0.0 for i in range(len(train[0]))] for epoch in range(n_epoch): for row in train: prediction = predict(row, weights) error = row[-1] - prediction weights[0] = weights[0] + l_rate * error for i in range(len(row)-1): weights[i + 1] = weights[i + 1] + l_rate * error * row[i] return weights # Perceptron Algorithm With Stochastic Gradient Descent def perceptron(train, test, l_rate, n_epoch): predictions = list() weights = train_weights(train, l_rate, n_epoch) for row in test: prediction = predict(row, weights) predictions.append(prediction) return(predictions) # Test the Perceptron algorithm on the sonar dataset seed(1) # load and prepare data filename = 'sonar.all-data.csv' dataset = load_csv(filename) for i in range(len(dataset[0])-1): str_column_to_float(dataset, i) # convert string class to integers str_column_to_int(dataset, len(dataset[0])-1) # evaluate algorithm n_folds = 3 l_rate = 0.01 n_epoch = 500 scores = evaluate_algorithm(dataset, perceptron, n_folds, l_rate, n_epoch) print('Scores: %s' % scores) print('Mean Accuracy: %.3f%%' % (sum(scores)/float(len(scores))))
O/P : Scores: [81.15942028985508, 69.56521739130434, 62.31884057971014] Mean Accuracy: 71.014%