LVQ模型Python实现

叁歲伎倆 2022-02-27 23:52 559阅读 0赞

*  [https://github.com/Sean16SYSU/MachineLearningImplement][https_github.com_Sean16SYSU_MachineLearningImplement]

## 简述 ##

LVQ模型是聚类的经典模型，跟Kmeans有点像。但是作为一个聚类，这个模型是一个有监督的模型。

### 算法流程 ###

1.  输入的数据集X, y，还有学习率（在0,1之间） η \\eta η
2.  初始，选k个点，作为原型向量
3.  然后开始循环
    
    1.  在样本集中随机选个点。
    2.  找到在原型向量中离它最近的点
    3.  然后来比较这两个点之间的y是否一样。一样就正向更新节点，不一样就反向更新节点
    4.   p i = p i ( + / − ) η ∗ ( x j − p i ) p\_i = p\_i (+ / -) \\eta \* (x\_j- p\_i) pi=pi(\+/−)η∗(xj−pi) 中间选是加或者减。
4.  迭代一定的次数，或者变化足够小之后，就退出迭代

## 实验部分 ##

*  导入数据

from sklearn import datasets
    iris = datasets.load_iris()

*  数据规模测试

iris.data.shape, iris.target.shape

((150, 4), (150,))

*  随机挑选节点作为训练集合

import numpy as np
    
    def random_split(X, y, train_rate=0.3):
        y_ = np.array(list(zip(y, range(len(y)))))
        np.random.shuffle(y_)
        
        train_n = int(len(y) * train_rate)
        
        y_train = y_[:train_n]
        y_test = y_[train_n:]
        
        index_train = y_train[:, 1]
        index_test = y_test[:, 1]
        
        return X[index_train], y_train[:, 0], X[index_test], y_test[:, 0]

*  LVQ函数和LVQ的聚类函数

def LVQ(X, y, k, MAX_TIME=100, ita=0.2):
        init_index = np.random.choice(len(y), k)
        px = X[init_index]
        py = y[init_index]
        for _ in range(MAX_TIME):
            j = np.random.choice(len(y), 1)
            xj, yj = X[j], y[j]
            i = np.argmin([np.linalg.norm(xj - pi) for pi in px])
            pyi = py[i]
            
            if pyi == yj:
                px[i] = px[i] + ita * (xj - px[i])
            else:
                px[i] = px[i] - ita * (xj - px[i])
        
        return px
    
    def PVQ_clustering(X, px):
        return np.array(list(map(lambda x: np.argmin([np.linalg.norm(x - pi) for pi in px]), X)))

*  拆分数据集并训练

train_x, train_y, test_x, test_y = random_split(iris.data, iris.target)
    px = LVQ(train_x, train_y, 3)
    y = PVQ_clustering(test_x, px)

*  画图

import matplotlib.pyplot as plt
    from sklearn.decomposition import PCA
    
    X_reduced = PCA(n_components=2).fit_transform(test_x)
    plt.scatter(X_reduced[:, 0], X_reduced[:, 1], c=y, cmap=plt.cm.Set1)

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2ExOTk5MDQxMg_size_16_color_FFFFFF_t_70]

*  实际值

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2ExOTk5MDQxMg_size_16_color_FFFFFF_t_70 1]

*  算法估量：这里只考虑外部指标

def evaluate(y, t):
        a, b, c, d = [0 for i in range(4)]
        for i in range(len(y)):
            for j in range(i+1, len(y)):
                if y[i] == y[j] and y[j] == t[j]:
                    a += 1
                elif y[i] == y[j] and y[j] != t[j]:
                    b += 1
                elif y[i] != y[j] and y[j] == t[j]:
                    c += 1
                elif y[i] != y[j] and y[j] != t[j]:
                    d += 1
        return a, b, c, d
    a, b, c, d = evaluate(y, test_y)

def external_index(a, b, c, d, m):
        JC = a / (a + b + c)
        FMI = np.sqrt(a**2 / ((a + b) * (a + c)))
        RI = 2 * ( a + d ) / ( m * (m + 1) )
        return JC, FMI, RI
    external_index(a, b, c, d, len(y))

*  将最后的结果展示下

<table> 
 <thead> 
  <tr> 
   <th>External index</th> 
   <th>Value</th> 
  </tr> 
 </thead> 
 <tbody> 
  <tr> 
   <td>JC</td> 
   <td>0.1485971596813301</td> 
  </tr> 
  <tr> 
   <td>FMI</td> 
   <td>0.26021571720401077</td> 
  </tr> 
  <tr> 
   <td>RI</td> 
   <td>0.5394429469901169</td> 
  </tr> 
 </tbody> 
</table>

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2ExOTk5MDQxMg_size_16_color_FFFFFF_t_70 2][]

[https_github.com_Sean16SYSU_MachineLearningImplement]: https://github.com/Sean16SYSU/MachineLearningImplement
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[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2ExOTk5MDQxMg_size_16_color_FFFFFF_t_70 1]: /images/20220228/82576dfd4ed94ca2a091104a36c7558c.png
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