一、KNN算法是什么？

knn是最简单的机器学习算法，也是最不需要数学知识的算法。
算法步骤：

1. 给定训练数据，啥也不用干，存起来。
2. 给定新的数据，把新数据和每一条训练数据进行求欧氏距离，然后把求得的距离进行从小到大排序，
3. 选取前K个最小的距离，然后看一下这k个中哪一个标签的最多。
4. 新数据就会被分类到最多的标签中。

import numpy as np
from math import sqrt
from collections import Counter
import matplotlib.pyplot as plt

class KNNClassifier:

    def __init__(self, k):
        """初始化kNN分类器"""
        assert k >= 1, "k must be valid"
        self.k = k
        self._X_train = None
        self._y_train = None

    def fit(self, X_train, y_train):
        """根据训练数据集X_train和y_train训练kNN分类器"""
        assert X_train.shape[0] == y_train.shape[0], \
            "the size of X_train must be equal to the size of y_train"
        assert self.k <= X_train.shape[0], \
            "the size of X_train must be at least k."

        self._X_train = X_train
        self._y_train = y_train
        return self

    def predict(self, X_predict):
        """给定待预测数据集X_predict，返回表示X_predict的结果向量"""
        assert self._X_train is not None and self._y_train is not None, \
            "must fit before predict!"
        assert X_predict.shape[1] == self._X_train.shape[1], \
            "the feature number of X_predict must be equal to X_train"

        y_predict = [self._predict(x) for x in X_predict]
        return np.array(y_predict)

    def _predict(self, x):
        """给定单个待预测数据x，返回x的预测结果值"""
        assert x.shape[0] == self._X_train.shape[1], \
            "the feature number of x must be equal to X_train"

        distances = [sqrt(np.sum((x_train - x) ** 2))
                     for x_train in self._X_train]
        nearest = np.argsort(distances)

        topK_y = [self._y_train[i] for i in nearest[:self.k]]
        votes = Counter(topK_y)

        return votes.most_common(1)[0][0]

    def __repr__(self):
        return "KNN(k=%d)" % self.k


raw_data_X = [[3.393533211, 2.331273381],
              [3.110073483, 1.781539638],
              [1.343808831, 3.368360954],
              [3.582294042, 4.679179110],
              [2.280362439, 2.866990263],
              [7.423436942, 4.696522875],
              [5.745051997, 3.533989803],
              [9.172168622, 2.511101045],
              [7.792783481, 3.424088941],
              [7.939820817, 0.791637231]
              ]
raw_data_y = [0, 0, 0, 0, 0, 1, 1, 1, 1, 1]



X_train = np.array(raw_data_X)
y_train = np.array(raw_data_y)

x = np.array([8.093607318, 3.365731514])
X_predict = x.reshape(1, -1)
knn_clf = KNNClassifier(3)
knn_clf.fit(X_train, y_train)
y_predict = knn_clf.predict(X_predict)
print(y_predict[0])


plt.scatter(X_train[y_train==0,0],X_train[y_train==0,1])
plt.scatter(X_train[y_train==1,0],X_train[y_train==1,1])
plt.scatter(X_predict[0][0],X_predict[0][1])
plt.show()