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# Linear Support Vector Machine: Soft Margin
#----------------------------------
#
# This function shows how to use TensorFlow to
# create a soft margin SVM
#
# We will use the iris data, specifically:
# x1 = Sepal Length
# x2 = Petal Width
# Class 1 : I. setosa
# Class -1: not I. setosa
#
# We know here that x and y are linearly seperable
# for I. setosa classification.
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_vals = np.array([1 if y==0 else -1 for y in iris.target])
# Split data into train/test sets
train_indices = np.random.choice(len(x_vals), int(len(x_vals)*0.8), replace=False)
test_indices = np.array(list(set(range(len(x_vals))) - set(train_indices)))
x_vals_train = x_vals[train_indices]
x_vals_test = x_vals[test_indices]
y_vals_train = y_vals[train_indices]
y_vals_test = y_vals[test_indices]
# Declare batch size
batch_size = 100
# Initialize placeholders
x_data = tf.placeholder(shape=[None, 2], dtype=tf.float32)
y_target = tf.placeholder(shape=[None, 1], dtype=tf.float32)
# Create variables for linear regression
A = tf.Variable(tf.random_normal(shape=[2,1]))
b = tf.Variable(tf.random_normal(shape=[1,1]))
# Declare model operations
model_output = tf.subtract(tf.matmul(x_data, A), b)
# Declare vector L2 'norm' function squared
l2_norm = tf.reduce_sum(tf.square(A))
# Declare loss function
# Loss = max(0, 1-pred*actual) + alpha * L2_norm(A)^2
# L2 regularization parameter, alpha
alpha = tf.constant([0.01])
# Margin term in loss
classification_term = tf.reduce_mean(tf.maximum(0., tf.subtract(1., tf.multiply(model_output, y_target))))
# Put terms together
loss = tf.add(classification_term, tf.multiply(alpha, l2_norm))
# Declare prediction function
prediction = tf.sign(model_output)
accuracy = tf.reduce_mean(tf.cast(tf.equal(prediction, y_target), 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 = []
train_accuracy = []
test_accuracy = []
for i in range(500):
rand_index = np.random.choice(len(x_vals_train), size=batch_size)
rand_x = x_vals_train[rand_index]
rand_y = np.transpose([y_vals_train[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)
train_acc_temp = sess.run(accuracy, feed_dict={x_data: x_vals_train, y_target: np.transpose([y_vals_train])})
train_accuracy.append(train_acc_temp)
test_acc_temp = sess.run(accuracy, feed_dict={x_data: x_vals_test, y_target: np.transpose([y_vals_test])})
test_accuracy.append(test_acc_temp)
if (i+1)%100==0:
print('Step #' + str(i+1) + ' A = ' + str(sess.run(A)) + ' b = ' + str(sess.run(b)))
print('Loss = ' + str(temp_loss))
# Extract coefficients
[[a1], [a2]] = sess.run(A)
[[b]] = sess.run(b)
slope = -a2/a1
y_intercept = b/a1
# Extract x1 and x2 vals
x1_vals = [d[1] for d in x_vals]
# Get best fit line
best_fit = []
for i in x1_vals:
best_fit.append(slope*i+y_intercept)
# Separate I. setosa
setosa_x = [d[1] for i,d in enumerate(x_vals) if y_vals[i]==1]
setosa_y = [d[0] for i,d in enumerate(x_vals) if y_vals[i]==1]
not_setosa_x = [d[1] for i,d in enumerate(x_vals) if y_vals[i]==-1]
not_setosa_y = [d[0] for i,d in enumerate(x_vals) if y_vals[i]==-1]
# Plot data and line
plt.plot(setosa_x, setosa_y, 'o', label='I. setosa')
plt.plot(not_setosa_x, not_setosa_y, 'x', label='Non-setosa')
plt.plot(x1_vals, best_fit, 'r-', label='Linear Separator', linewidth=3)
plt.ylim([0, 10])
plt.legend(loc='lower right')
plt.title('Sepal Length vs Pedal Width')
plt.xlabel('Pedal Width')
plt.ylabel('Sepal Length')
plt.show()
# Plot train/test accuracies
plt.plot(train_accuracy, 'k-', label='Training Accuracy')
plt.plot(test_accuracy, 'r--', label='Test Accuracy')
plt.title('Train and Test Set Accuracies')
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()
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x_vals_train
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y_vals_test.shape
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[[a1], [a2]] = sess.run(A)
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sess.run(A)
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