tensorflow实现svm多分类 iris 3分类——本质上在使用梯度下降法求解线性回归(loss是定制的而已)
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# Multi-class (Nonlinear) SVM Example # # This function wll illustrate how to # implement the gaussian kernel with # multiple classes on the iris dataset. # # Gaussian Kernel: # K(x1, x2) = exp(-gamma * abs(x1 - x2)^2) # # X : (Sepal Length, Petal Width) # Y: (I. setosa, I. virginica, I. versicolor) (3 classes) # # Basic idea: introduce an extra dimension to do # one vs all classification. # # The prediction of a point will be the category with # the largest margin or distance to boundary. import matplotlib.pyplot as plt import numpy as np import tensorflow as tf from sklearn import datasets from tensorflow.python.framework import ops ops.reset_default_graph() # Create graph sess = tf.Session() # Load the data # iris.data = [(Sepal Length, Sepal Width, Petal Length, Petal Width)] iris = datasets.load_iris() x_vals = np.array([[x[0], x[3]] for x in iris.data]) y_vals1 = np.array([1 if y == 0 else -1 for y in iris.target]) y_vals2 = np.array([1 if y == 1 else -1 for y in iris.target]) y_vals3 = np.array([1 if y == 2 else -1 for y in iris.target]) y_vals = np.array([y_vals1, y_vals2, y_vals3]) class1_x = [x[0] for i, x in enumerate(x_vals) if iris.target[i] == 0] class1_y = [x[1] for i, x in enumerate(x_vals) if iris.target[i] == 0] class2_x = [x[0] for i, x in enumerate(x_vals) if iris.target[i] == 1] class2_y = [x[1] for i, x in enumerate(x_vals) if iris.target[i] == 1] class3_x = [x[0] for i, x in enumerate(x_vals) if iris.target[i] == 2] class3_y = [x[1] for i, x in enumerate(x_vals) if iris.target[i] == 2] # Declare batch size batch_size = 50 # Initialize placeholders x_data = tf.placeholder(shape=[None, 2], dtype=tf.float32) y_target = tf.placeholder(shape=[3, None], dtype=tf.float32) prediction_grid = tf.placeholder(shape=[None, 2], dtype=tf.float32) # Create variables for svm b = tf.Variable(tf.random_normal(shape=[3, batch_size])) # Gaussian (RBF) kernel gamma = tf.constant(-10.0) dist = tf.reduce_sum(tf.square(x_data), 1) dist = tf.reshape(dist, [-1, 1]) sq_dists = tf.multiply(2., tf.matmul(x_data, tf.transpose(x_data))) my_kernel = tf.exp(tf.multiply(gamma, tf.abs(sq_dists))) # Declare function to do reshape/batch multiplication def reshape_matmul(mat, _size): v1 = tf.expand_dims(mat, 1) v2 = tf.reshape(v1, [3, _size, 1]) return tf.matmul(v2, v1) # Compute SVM Model first_term = tf.reduce_sum(b) b_vec_cross = tf.matmul(tf.transpose(b), b) y_target_cross = reshape_matmul(y_target, batch_size) second_term = tf.reduce_sum(tf.multiply(my_kernel, tf.multiply(b_vec_cross, y_target_cross)), [1, 2]) loss = tf.reduce_sum(tf.negative(tf.subtract(first_term, second_term))) # Gaussian (RBF) prediction kernel rA = tf.reshape(tf.reduce_sum(tf.square(x_data), 1), [-1, 1]) rB = tf.reshape(tf.reduce_sum(tf.square(prediction_grid), 1), [-1, 1]) pred_sq_dist = tf.add(tf.subtract(rA, tf.multiply(2., tf.matmul(x_data, tf.transpose(prediction_grid)))), tf.transpose(rB)) pred_kernel = tf.exp(tf.multiply(gamma, tf.abs(pred_sq_dist))) prediction_output = tf.matmul(tf.multiply(y_target, b), pred_kernel) prediction = tf.argmax(prediction_output - tf.expand_dims(tf.reduce_mean(prediction_output, 1), 1), 0) accuracy = tf.reduce_mean(tf.cast(tf.equal(prediction, tf.argmax(y_target, 0)), tf.float32)) # Declare optimizer my_opt = tf.train.GradientDescentOptimizer(0.01) train_step = my_opt.minimize(loss) # Initialize variables init = tf.global_variables_initializer() sess.run(init) # Training loop loss_vec = [] batch_accuracy = [] for i in range(100): rand_index = np.random.choice(len(x_vals), size=batch_size) rand_x = x_vals[rand_index] rand_y = y_vals[:, rand_index] sess.run(train_step, feed_dict={x_data: rand_x, y_target: rand_y}) temp_loss = sess.run(loss, feed_dict={x_data: rand_x, y_target: rand_y}) loss_vec.append(temp_loss) acc_temp = sess.run(accuracy, feed_dict={x_data: rand_x, y_target: rand_y, prediction_grid: rand_x}) batch_accuracy.append(acc_temp) if (i + 1) % 25 == 0: print(\'Step #\' + str(i+1)) print(\'Loss = \' + str(temp_loss)) # Create a mesh to plot points in x_min, x_max = x_vals[:, 0].min() - 1, x_vals[:, 0].max() + 1 y_min, y_max = x_vals[:, 1].min() - 1, x_vals[:, 1].max() + 1 xx, yy = np.meshgrid(np.arange(x_min, x_max, 0.02), np.arange(y_min, y_max, 0.02)) grid_points = np.c_[xx.ravel(), yy.ravel()] grid_predictions = sess.run(prediction, feed_dict={x_data: rand_x, y_target: rand_y, prediction_grid: grid_points}) grid_predictions = grid_predictions.reshape(xx.shape) # Plot points and grid plt.contourf(xx, yy, grid_predictions, cmap=plt.cm.Paired, alpha=0.8) plt.plot(class1_x, class1_y, \'ro\', label=\'I. setosa\') plt.plot(class2_x, class2_y, \'kx\', label=\'I. versicolor\') plt.plot(class3_x, class3_y, \'gv\', label=\'I. virginica\') plt.title(\'Gaussian SVM Results on Iris Data\') plt.xlabel(\'Pedal Length\') plt.ylabel(\'Sepal Width\') plt.legend(loc=\'lower right\') plt.ylim([-0.5, 3.0]) plt.xlim([3.5, 8.5]) plt.show() # Plot batch accuracy plt.plot(batch_accuracy, \'k-\', label=\'Accuracy\') plt.title(\'Batch Accuracy\') plt.xlabel(\'Generation\') plt.ylabel(\'Accuracy\') plt.legend(loc=\'lower right\') plt.show() # Plot loss over time plt.plot(loss_vec, \'k-\') plt.title(\'Loss per Generation\') plt.xlabel(\'Generation\') plt.ylabel(\'Loss\') plt.show() # Evaluations on new/unseen data
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