上节我们简单进行了KNN算法的说明，想想假期结束再回味一下！
Knn算法基本原理：
假设我有如下两个数据集：
dataset = {'black':[ [1,2], [2,3], [3,1] ], 'red':[ [6,5], [7,7], [8,6] ] }
KNN分类算法超级简单：只需使用初中所学的两点距离公式（欧拉距离公式），计算绿点到各组的距离，看绿点和哪组更接近。K代表取离绿点最近的k个点，这k个点如果其中属于红点个数占多数，我们就认为绿点应该划分为红组，反之，则划分为黑组。如果有两组数据(如上图)，k值最小应为3（X轴坐标3.5）。
除了K-Nearest Neighbor之外还有其它分组的方法，如Radius-Based Neighbor。此方法后面在做介绍。
实现代码如下：
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import math
import numpy as np
from matplotlib import pyplot
from collections import Counter
import warnings
# k-Nearest Neighbor算法
def k_nearest_neighbors(data, predict, k=5):
if len(data) >= k:
warnings.warn("k is too small")
# 计算predict点到各点的距离
distances = []
for group in data:
for features in data[group]:
#euclidean_distance = np.sqrt(np.sum((np.array(features)-np.array(predict))**2)) # 计算欧拉距离，这个方法没有下面一行代码快
euclidean_distance = np.linalg.norm(np.array(features)-np.array(predict))
distances.append([euclidean_distance, group])
sorted_distances =[i[1] for i in sorted(distances)]
top_nearest = sorted_distances[:k]
#print(top_nearest) ['red','black','red']
group_res = Counter(top_nearest).most_common(1)[0][0]
confidence = Counter(top_nearest).most_common(1)[0][1]*1.0/k
# confidences是对本次分类的确定程度，例如(red,red,red)，(red,red,black)都分为red组，但是前者显的更自信
return group_res, confidence
if __name__=='__main__':
dataset = {'black':[ [1,2], [2,3], [3,1] ], 'red':[ [6,5], [7,7], [8,6] ]}
new_features = [3.5,5.2] # 判断这个样本属于哪个组
for i in dataset:
for ii in dataset[i]:
pyplot.scatter(ii[0], ii[1], s=50, color=i)
which_group,confidence = k_nearest_neighbors(dataset, new_features, k=3)
print(which_group, confidence)
pyplot.scatter(new_features[0], new_features[1], s=100, color=which_group)
pyplot.show()
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结果如下所示：
归为红色一类的概率为：0.66666666
我们使用实际数据进行应用
数据集（Breast Cancer）：https://archive.ics.uci.edu/ml/datasets/Breast+Cancer+Wisconsin+%28Original%29
点击download： Data Folder/breast-cancer-wisconsin.data(复制粘贴到txt文件再重命名)
| 代码如下：（if __name__=='__main__':前面代码一样） |
import math
import numpy as np
from collections import Counter
import warnings
import pandas as pd
import random
# k-Nearest Neighbor算法
def k_nearest_neighbors(data, predict, k=5):
if len(data) >= k:
warnings.warn("k is too small")
# 计算predict点到各点的距离
distances = []
for group in data:
for features in data[group]:
euclidean_distance = np.linalg.norm(np.array(features)-np.array(predict))
distances.append([euclidean_distance, group])
sorted_distances =[i[1] for i in sorted(distances)]
top_nearest = sorted_distances[:k]
group_res = Counter(top_nearest).most_common(1)[0][0]
confidence = Counter(top_nearest).most_common(1)[0][1]*1.0/k
return group_res, confidence
if __name__=='__main__':
df=pd.read_csv('iris.csv')#加载数据
#print （df.head（））
#print(df.shape)
df.replace('?', np.nan, inplace=True) # -99999
df.dropna(inplace=True) # 去掉无效数据
#print(df.shape)
df.drop(['id'], 1, inplace=True)#去掉id 这一列（第一列名字为id）
# 把数据分成两部分，训练数据和测试数据
full_data = df.astype(float).values.tolist()
random.shuffle(full_data)
test_size= 0.2 # 测试数据占20%
train_data = full_data[:-int(test_size*len(full_data))]
test_data = full_data[-int(test_size*len(full_data)):]
train_set = {2:[], 4:[]}
test_set = {2:[], 4:[]}
for i in train_data:
train_set[i[-1]].append(i[:-1])
for i in test_data:
test_set[i[-1]].append(i[:-1])
correct = 0
total = 0
for group in test_set:
for data in test_set[group]:
res,confidence = k_nearest_neighbors(train_set, data, k = 5) # 你可以调整这个k看看准确率的变化，你也可以使用matplotlib画出k对应的准确率，找到最好的k值
if group == res:
correct += 1
else:
print(confidence)
total += 1
print(correct/total) # 准确率
print(k_nearest_neighbors(train_set, [4,2,1,1,1,2,3,2,1], k = 5)) # 预测一条记录
结果如下所示：
使用scikit-learn 中K临近算法
代码如下：
import numpy as np
from sklearn import preprocessing, cross_validation, neighbors # cross_validation已deprecated，使用model_selection替代
import pandas as pd
df=pd.read_csv('iris.csv')#加载exel数据
#print(df.head())
#print(df.shape)
df.replace('?', np.nan, inplace=True) # -99999
df.dropna(inplace=True)
#print(df.shape)
df.drop(['id'], 1, inplace=True)
X = np.array(df.drop(['class'], 1))
Y = np.array(df['class'])
X_trian,X_test,Y_train,Y_test = cross_validation.train_test_split(X, Y, test_size=0.2)
clf = neighbors.KNeighborsClassifier()
clf.fit(X_trian, Y_train)
accuracy = clf.score(X_test, Y_test)
print(accuracy)
sample = np.array([4,2,1,1,1,2,3,2,1])
print(sample.reshape(1, -1))
print(clf.predict(sample.reshape(1, -1)))
结果如下：（里面有个警告但不妨碍结果）
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scikit-learn中的算法和我们上面实现的算法原理完全一样，只是它的效率更高，支持的参数更全。 (以上内容学习于大熊猫) |