iris二分类

# 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()

# Set random seeds

np.random.seed(7)

tf.set_random_seed(7)

# 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),

                                 round(len(x_vals)*0.9),

                                 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 = 135

# 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 #{} A = {}, b = {}'.format(

            str(i+1),

            str(sess.run(A)),

            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()

下面例子数据集可能更好看；

# SVM Regression

#----------------------------------

#

# This function shows how to use TensorFlow to

# solve support vector regression. We are going

# to find the line that has the maximum margin

# which INCLUDES as many points as possible

#

# We will use the iris data, specifically:

#  y = Sepal Length

#  x = Pedal Width

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[3] for x in iris.data])

y_vals = np.array([y[0] for y in iris.data])

# Split data into train/test sets

train_indices = np.random.choice(len(x_vals), round(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 = 50

# Initialize placeholders

x_data = tf.placeholder(shape=[None, 1], 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=[1,1]))

b = tf.Variable(tf.random_normal(shape=[1,1]))

# Declare model operations

model_output = tf.add(tf.matmul(x_data, A), b)

# Declare loss function

# = max(0, abs(target - predicted) + epsilon)

# 1/2 margin width parameter = epsilon

epsilon = tf.constant([0.5])

# Margin term in loss

loss = tf.reduce_mean(tf.maximum(0., tf.subtract(tf.abs(tf.subtract(model_output, y_target)), epsilon)))

# Declare optimizer

my_opt = tf.train.GradientDescentOptimizer(0.075)

train_step = my_opt.minimize(loss)

# Initialize variables

init = tf.global_variables_initializer()

sess.run(init)

# Training loop

train_loss = []

test_loss = []

for i in range(200):

    rand_index = np.random.choice(len(x_vals_train), size=batch_size)

    rand_x = np.transpose([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_train_loss = sess.run(loss, feed_dict={x_data: np.transpose([x_vals_train]), y_target: np.transpose([y_vals_train])})

    train_loss.append(temp_train_loss)

    temp_test_loss = sess.run(loss, feed_dict={x_data: np.transpose([x_vals_test]), y_target: np.transpose([y_vals_test])})

    test_loss.append(temp_test_loss)

    if (i+1)%50==0:

        print('-----------')

        print('Generation: ' + str(i+1))

        print('A = ' + str(sess.run(A)) + ' b = ' + str(sess.run(b)))

        print('Train Loss = ' + str(temp_train_loss))

        print('Test Loss = ' + str(temp_test_loss))

# Extract Coefficients

[[slope]] = sess.run(A)

[[y_intercept]] = sess.run(b)

[width] = sess.run(epsilon)

# Get best fit line

best_fit = []

best_fit_upper = []

best_fit_lower = []

for i in x_vals:

  best_fit.append(slope*i+y_intercept)

  best_fit_upper.append(slope*i+y_intercept+width)

  best_fit_lower.append(slope*i+y_intercept-width)

# Plot fit with data

plt.plot(x_vals, y_vals, 'o', label='Data Points')

plt.plot(x_vals, best_fit, 'r-', label='SVM Regression Line', linewidth=3)

plt.plot(x_vals, best_fit_upper, 'r--', linewidth=2)

plt.plot(x_vals, best_fit_lower, 'r--', linewidth=2)

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 loss over time

plt.plot(train_loss, 'k-', label='Train Set Loss')

plt.plot(test_loss, 'r--', label='Test Set Loss')

plt.title('L2 Loss per Generation')

plt.xlabel('Generation')

plt.ylabel('L2 Loss')

plt.legend(loc='upper right')

plt.show()

高斯核函数的应用，其实也可以自定义很多核函数：

# Illustration of Various Kernels

#----------------------------------

#

# This function wll illustrate how to

# implement various kernels in TensorFlow.

#

# Linear Kernel:

# K(x1, x2) = t(x1) * x2

#

# Gaussian Kernel (RBF):

# K(x1, x2) = exp(-gamma * abs(x1 - x2)^2)

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()

# Generate non-lnear data

(x_vals, y_vals) = datasets.make_circles(n_samples=350, factor=.5, noise=.1)

y_vals = np.array([1 if y==1 else -1 for y in y_vals])

class1_x = [x[0] for i,x in enumerate(x_vals) if y_vals[i]==1]

class1_y = [x[1] for i,x in enumerate(x_vals) if y_vals[i]==1]

class2_x = [x[0] for i,x in enumerate(x_vals) if y_vals[i]==-1]

class2_y = [x[1] for i,x in enumerate(x_vals) if y_vals[i]==-1]

# Declare batch size

batch_size = 350

# Initialize placeholders

x_data = tf.placeholder(shape=[None, 2], dtype=tf.float32)

y_target = tf.placeholder(shape=[None, 1], dtype=tf.float32)

prediction_grid = tf.placeholder(shape=[None, 2], dtype=tf.float32)

# Create variables for svm

b = tf.Variable(tf.random_normal(shape=[1,batch_size]))

# Apply kernel

# Linear Kernel

# my_kernel = tf.matmul(x_data, tf.transpose(x_data))

# Gaussian (RBF) kernel

gamma = tf.constant(-50.0)

dist = tf.reduce_sum(tf.square(x_data), 1)

dist = tf.reshape(dist, [-1,1])

sq_dists = tf.add(tf.subtract(dist, tf.multiply(2., tf.matmul(x_data, tf.transpose(x_data)))), tf.transpose(dist))

my_kernel = tf.exp(tf.multiply(gamma, tf.abs(sq_dists)))

# Compute SVM Model

first_term = tf.reduce_sum(b)

b_vec_cross = tf.matmul(tf.transpose(b), b)

y_target_cross = tf.matmul(y_target, tf.transpose(y_target))

second_term = tf.reduce_sum(tf.multiply(my_kernel, tf.multiply(b_vec_cross, y_target_cross)))

loss = tf.negative(tf.subtract(first_term, second_term))

# Create Prediction Kernel

# Linear prediction kernel

# my_kernel = tf.matmul(x_data, tf.transpose(prediction_grid))

# 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(tf.transpose(y_target),b), pred_kernel)

prediction = tf.sign(prediction_output-tf.reduce_mean(prediction_output))

accuracy = tf.reduce_mean(tf.cast(tf.equal(tf.squeeze(prediction), tf.squeeze(y_target)), tf.float32))

# Declare optimizer

my_opt = tf.train.GradientDescentOptimizer(0.002)

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(1000):

    rand_index = np.random.choice(len(x_vals), size=batch_size)

    rand_x = x_vals[rand_index]

    rand_y = np.transpose([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)%250==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='Class 1')

plt.plot(class2_x, class2_y, 'kx', label='Class -1')

plt.title('Gaussian SVM Results')

plt.xlabel('x')

plt.ylabel('y')

plt.legend(loc='lower right')

plt.ylim([-1.5, 1.5])

plt.xlim([-1.5, 1.5])

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()

# Evaluate on new/unseen data points

# New data points:

new_points = np.array([(-0.75, -0.75),

                       (-0.5, -0.5),

                       (-0.25, -0.25),

                       (0.25, 0.25),

                       (0.5, 0.5),

                       (0.75, 0.75)])

[evaluations] = sess.run(prediction, feed_dict={x_data: x_vals,

                                                y_target: np.transpose([y_vals]),

                                                prediction_grid: new_points})

for ix, p in enumerate(new_points):

    print('{} : class={}'.format(p, evaluations[ix]))

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