svm代碼實(shí)現(xiàn)
# -*- coding: utf-8 -*-
"""
-------------------------------------------------
File Name： svm
Description :
Author : Tingur
date： 2018/11/27
Ref: https://github.com/Madhu009/Deep-math-machine-learning.ai/blob/master/SVM-FromScratch.ipynb
-------------------------------------------------
"""
import numpy as np
import matplotlib.pyplot as plt
import math
from sklearn.datasets.samples_generator import make_blobs
# step 1: generate data
(X, y) = make_blobs(n_samples=50,
n_features=2,
centers=2,
cluster_std=1.05,
random_state=40)
# print(X.shape)
# print(X) #[[ 7.12731332 -4.4394424 ] [ 6.68873898 -2.44840134]
# print(y) # 1 1 0 1 0 0 1 0 1 0 1 1 0 ...
X1 = np.c_[np.ones((X.shape[0])), X]
# print(X1)
# display data
# plt.scatter(X1[:,1], X1[:,2],marker='o', c=y)
# plt.axis([-5,10,-12,-1])
# plt.show()
# step 2: cluster the data
# for svm, we set the data cluster value to -1 and 1
positive_data = list()
negative_data = list()
for i, v in enumerate(y):
if v == 0:
negative_data.append(X[i])
else:
positive_data.append(X[i])
data_dict = {1: np.array(positive_data), -1: np.array(negative_data)}
print(data_dict)
# step 3: svm training
w = [] # weights 2 dimesional vector
b = [] # bias
max_feature_value = float('-inf')
min_feature_value = float('+inf')
for yi in data_dict:
if np.amax(data_dict[yi]) > max_feature_value:
max_feature_value = np.amax(data_dict[yi])
if np.amin(data_dict[yi]) < min_feature_value:
min_feature_value = np.amin(data_dict[yi])
print(max_feature_value, min_feature_value)
learning_rates = [max_feature_value * 0.1,
max_feature_value * 0.01,
max_feature_value * 0.001]
def svm_training(data_dict):
i = 1
global w
global b
length_w_vector = {}
transforms = [[1, 1], [-1, 1], [-1, -1], [1, -1]]
b_step_size = 2
b_multiple = 5
w_optimum = max_feature_value * 0.5
for rate in learning_rates:
w = np.array([w_optimum, w_optimum])
optimized = False
while not optimized:
for b in np.arange(-1 * (max_feature_value * b_step_size), max_feature_value * b_step_size,
rate * b_multiple):
for transformation in transforms:
w_t = w * transformation
correctly_classified = True
for yi in data_dict:
for xi in data_dict[yi]:
if yi * (np.dot(w_t, xi) + b) < 1:
correctly_classified = False
if correctly_classified:
length_w_vector[np.linalg.norm(w_t)] = [w_t, b]
if w[0] < 0:
optimized = True
else:
w = w - rate
norms = sorted([n for n in length_w_vector])
minimum_w_length = length_w_vector[norms[0]]
w = minimum_w_length[0]
b = minimum_w_length[1]
w_optimum = w[0] + rate * 2
svm_training(data_dict)
print("w: ", w)
print("b: ", b)
# step 4: plot the svm result
colors = {1:'r',-1:'b'}
fig = plt.figure()
ax = fig.add_subplot(1,1,1)
def visualize(data_dict):
# [[ax.scatter(x[0],x[1],s=100,color=colors[i]) for x in data_dict[i]] for i in data_dict]
plt.scatter(X1[:, 1], X1[:, 2], marker='o', c=y)
# hyperplane = x.w+b
# v = x.w+b
# psv = 1
# nsv = -1
# dec = 0
def hyperplane_value(x, w, b, v):
return (-w[0] * x - b + v) / w[1]
datarange = (min_feature_value * 0.9, max_feature_value * 1.)
hyp_x_min = datarange[0]
hyp_x_max = datarange[1]
# (w.x+b) = 1
# positive support vector hyperplane
psv1 = hyperplane_value(hyp_x_min, w, b, 1)
psv2 = hyperplane_value(hyp_x_max, w, b, 1)
ax.plot([hyp_x_min, hyp_x_max], [psv1, psv2], 'k')
# (w.x+b) = -1
# negative support vector hyperplane
nsv1 = hyperplane_value(hyp_x_min, w, b, -1)
nsv2 = hyperplane_value(hyp_x_max, w, b, -1)
ax.plot([hyp_x_min, hyp_x_max], [nsv1, nsv2], 'k')
# (w.x+b) = 0
# positive support vector hyperplane
db1 = hyperplane_value(hyp_x_min, w, b, 0)
db2 = hyperplane_value(hyp_x_max, w, b, 0)
ax.plot([hyp_x_min, hyp_x_max], [db1, db2], 'y--')
plt.axis([-5, 10, -12, -1])
plt.show()
visualize(data_dict)
源碼地址
效果
image.png
