add svm

Author: LockGit

README.md

@@ -482,4 +482,21 @@ print '快慢指针方式,单链表中间节点为:%s,索引为:%s，只遍历
 ```
 
 
+### 支持向量机 svm.py
+```
+迟早会忘记的svm
+分类算法，寻找一个最优超平面
+demo为线性可分离数据
+
+参考1：https://zh.wikipedia.org/zh-hans/支持向量机
+参考2：http://blog.csdn.net/viewcode/article/details/12840405
+参考3：http://blog.csdn.net/lisi1129/article/details/70209945?locationNum=8&fps=1
+
+依赖：
+pip install numpy
+pip install matplotlib
+
+执行：python svm.py
+```
+![](https://github.com/LockGit/Py/blob/master/img/svm.png)
 

img/svm.png

@@ -0,0 +1,137 @@
+# -*- coding: utf-8 -*-
+# @Author: lock
+# @Date:   2017-12-21 09:58:01
+# @Last Modified by:   lock
+# @Last Modified time: 2017-12-21 17:41:07
+# 分类算法之SVM,比KNN算法更加复杂
+# demo最简单的线性可分离数据
+# 参考：http://blog.csdn.net/lisi1129/article/details/70209945?locationNum=8&fps=1
+
+import numpy as np
+from matplotlib import pyplot
+import math
+import sys
+ 
+class SVM(object):
+    def __init__(self, visual=True):
+        self.visual = visual
+        self.colors = {1:'r', -1:'b'}
+        if self.visual:
+            self.fig = pyplot.figure()
+            self.ax = self.fig.add_subplot(1,1,1)
+ 
+    def train(self, data):
+        self.data = data
+        opt_dict = {}
+    
+        transforms = [[1,1],
+                      [-1,1],
+                      [-1,-1],
+                      [1,-1]]
+                      
+        # 找到数据集中最大值和最小值
+        self.max_feature_value = float('-inf')   # 正无穷
+        self.min_feature_value = float('inf')    # 负无穷
+        for y in self.data:
+            for features in self.data[y]:
+                for feature in features:
+                    if feature > self.max_feature_value:
+                        self.max_feature_value = feature
+                    if feature < self.min_feature_value:
+                        self.min_feature_value = feature
+        print(self.max_feature_value, self.min_feature_value)
+        
+        # 和梯度下降一样，定义每一步的大小；开始快，然后慢，越慢越耗时
+        step_sizes = [self.max_feature_value * 0.1, self.max_feature_value * 0.01, self.max_feature_value * 0.001]
+        
+        b_range_multiple = 5
+        b_multiple = 5
+        lastest_optimum = self.max_feature_value * 10
+        
+        for step in step_sizes:
+            w = np.array([lastest_optimum,lastest_optimum])
+            optimized = False
+            while not optimized:
+                for b in np.arange(self.max_feature_value*b_range_multiple*-1, self.max_feature_value*b_range_multiple, step*b_multiple):
+                    for transformation in transforms:
+                        w_t = w * transformation
+                        found_option = True
+                        for i in self.data:
+                            for x in self.data[i]:
+                                y = i
+                                if not y*(np.dot(w_t, x)+b) >= 1:
+                                    found_option = False
+                                #print(x,':',y*(np.dot(w_t, x)+b))  逐渐收敛
+                                    
+                        if found_option:
+                            opt_dict[np.linalg.norm(w_t)] = [w_t,b]
+ 
+                if w[0] < 0:
+                    optimized = True
+                else:
+                    w = w - step
+        
+            norms = sorted([n for n in opt_dict])
+            opt_choice = opt_dict[norms[0]]
+            self.w = opt_choice[0]
+            self.b = opt_choice[1]
+            print(self.w, self.b)
+            lastest_optimum = opt_choice[0][0] + step*2
+ 
+
+    def predict(self, features):
+        classification = np.sign( np.dot(features, self.w) + self.b )
+        
+        if classification != 0 and self.visual:
+            self.ax.scatter(features[0], features[1], s=300, marker='*', c=self.colors[classification])
+ 
+        return classification
+ 
+ 
+    # 显示picture
+    def visualize(self):
+        for i in self.data:
+            for x in self.data[i]:
+                self.ax.scatter(x[0], x[1], s=50, c=self.colors[i])
+ 
+        # 超平面
+        def hyperplane(x,w,b,v):
+            return (-w[0]*x-b+v) / w[1]
+ 
+        data_range = (self.min_feature_value*0.9, self.max_feature_value*1.1)
+ 
+        hyp_x_min = data_range[0]
+        hyp_x_man = data_range[1]
+ 
+        psv1 = hyperplane(hyp_x_min, self.w, self.b, 1)
+        psv2 = hyperplane(hyp_x_man, self.w, self.b, 1)
+        self.ax.plot([hyp_x_min, hyp_x_man], [psv1, psv2], c=self.colors[1])
+ 
+        nsv1 = hyperplane(hyp_x_min, self.w, self.b, -1)
+        nsv2 = hyperplane(hyp_x_man, self.w, self.b, -1)
+        self.ax.plot([hyp_x_min, hyp_x_man], [nsv1, nsv2], c=self.colors[-1])
+ 
+        db1 = hyperplane(hyp_x_min, self.w, self.b, 0)
+        db2 = hyperplane(hyp_x_man, self.w, self.b, 0)
+        self.ax.plot([hyp_x_min, hyp_x_man], [db1, db2], 'y--')
+ 
+        pyplot.show()
+ 
+if __name__ == '__main__':
+    data_set = {-1:np.array([[1,7],
+                             [2,8],
+                             [3,8]]),
+                 1:np.array([[5,1],
+                             [6,-1],
+                             [7,3]])}
+    print(data_set)
+ 
+    svm = SVM()
+    svm.train(data_set)
+ 
+    # 预测
+    for predict_feature in [[0,10],[2,6],[1,3], [4,3], [5.5,7.5], [8,3]]:
+        print(svm.predict(predict_feature))
+ 
+    svm.visualize()
+