一.K邻近算法概念
二.代码实现
# 0. 引入依赖
import numpy as np
import pandas as pd# 这里直接引入sklearn里的数据集，iris鸢尾花
from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split # 切分数据集为训练集和测试集
from sklearn.metrics import accuracy_score # 计算分类预测的准确率# 1. 数据加载和预处理
iris = load_iris()
# print(iris)df = pd.DataFrame(data = iris.data, columns = iris.feature_names)
df['class'] = iris.target
df['class'] = df['class'].map({0: iris.target_names[0], 1: iris.target_names[1], 2: iris.target_names[2]})
df.head(10)
# df.describe()
# print(df)x = iris.data
y = iris.target.reshape(-1,1)
# print(x.shape, y.shape)# 划分训练集和测试集
# test_size：测试比例，random_state：随机划分，stratify：按照y的分布等比例分割
x_train, x_test, y_train, y_test = train_test_split(x, y, test_size=0.3, random_state=35, stratify=y)
# print(x_train.shape, y_train.shape)
# print(x_test.shape, y_test.shape)# 2. 核心算法实现
# 距离函数定义
def l1_distance(a, b):return np.sum(np.abs(a - b), axis=1) # 曼哈顿距离def l2_distance(a, b):return np.sqrt(np.sum((a - b) ** 2, axis=1)) # 欧氏距离# 分类器实现
class kNN(object):# 定义一个初始化方法，__init__ 是类的构造方法def __init__(self, n_neighbors=1, dist_func=l1_distance):self.n_neighbors = n_neighborsself.dist_func = dist_func# 训练模型方法def fit(self, x, y):self.x_train = xself.y_train = y# 模型预测方法def predict(self, x):# 初始化预测分类数组：初始化一个0数组，x.shape[0]：行数，1：列数，dtype：定义此数据类型y_pred = np.zeros((x.shape[0], 1), dtype=self.y_train.dtype)# 遍历输入的x数据点，取出每一个数据点的序号i和数据x_test。enumerate：可同时拿出两个(序号和值)for i, x_test in enumerate(x):# x_test跟所有训练数据计算距离distances = self.dist_func(self.x_train, x_test)# 得到的距离按照由近到远排序，取出索引值nn_index = np.argsort(distances)# 选取最近的k个点，保存它们对应的分类类别，n_neighbors：表示取k个邻近的值nn_y = self.y_train[nn_index[0:self.n_neighbors]].ravel()# 统计类别中出现频率最高的那个，赋给y_pred[i]y_pred[i] = np.argmax(np.bincount(nn_y))return y_pred"""a = np.array([[3,2,4,2],[2,1,4,23],[12,3,2,3],[2,3,15,23],[1,3,2,3],[13,3,2,2],[213,16,3,63],[23,62,23,23],[23,16,23,43]])b = np.array([[1,1,1,1]])print("a-b:",a-b) # 下面的a-b：a表示数组，b表示向量np.sum(np.abs(a - b), axis=1)dist = np.sqrt( np.sum((a-b) ** 2, axis=1) )nn_index = np.argsort(dist)print("dist: ", dist)print("nn_index: ", nn_index)nn_y = y_train[nn_index[:9]].ravel()print("未转换前的y：",y_train[:8])print("nn_y：", nn_y)print("y计数：",np.bincount(nn_y))print("取出现次数最多的y：",np.argmax(np.bincount(nn_y)))
"""# 3. 测试
# 定义一个knn实例
knn = kNN(n_neighbors = 3)
# 训练模型
knn.fit(x_train, y_train)
# 传入测试数据，做预测
y_pred = knn.predict(x_test)
print("y测试值: ", y_test.ravel())
print("y预测值: ", y_pred.ravel())
# 求出预测准确率
accuracy = accuracy_score(y_test, y_pred)
print("预测准确率: ", accuracy)# 定义一个knn实例
knn = kNN()
# 训练模型
knn.fit(x_train, y_train)
# 保存结果list
result_list = []
# 针对不同的参数选取，做预测
for p in [1, 2]:knn.dist_func = l1_distance if p == 1 else l2_distance# 考虑不同的k取值，步长为2(取奇数1,3,5,7,9)for k in range(1, 10, 2):knn.n_neighbors = k# 传入测试数据，做预测y_pred = knn.predict(x_test)# 求出预测准确率accuracy = accuracy_score(y_test, y_pred)result_list.append([k, '曼哈顿距离' if p == 1 else '欧氏距离', accuracy])
df = pd.DataFrame(result_list, columns=['k', '距离函数', '预测准确率'])
print(df)y测试值: [2 1 2 2 0 0 2 0 1 1 2 0 1 1 1 2 2 0 1 2 1 0 0 0 1 2 0 2 0 0 2 1 0 2 1 0 2 1 2 2 1 1 1 0 0]
y预测值: [2 1 2 2 0 0 2 0 1 1 1 0 1 1 1 2 2 0 1 2 1 0 0 0 1 2 0 2 0 0 2 1 0 2 1 0 2 1 2 1 1 2 1 0 0]
预测准确率: 0.9333333333333333
k 距离函数 预测准确率
0 1 曼哈顿距离 0.933333
1 3 曼哈顿距离 0.933333
2 5 曼哈顿距离 0.977778
3 7 曼哈顿距离 0.955556
4 9 曼哈顿距离 0.955556
5 1 欧氏距离 0.933333
6 3 欧氏距离 0.933333
7 5 欧氏距离 0.977778
8 7 欧氏距离 0.977778
9 9 欧氏距离 0.977778
