kNN算法效果好，细想简单，作为初接触机器学习算法的同学来说，是很好的一个切入点。

kNN算法的核心思想就是如果一个样本在特征空间中的k个最相邻的样本中的大多数属于某一个类别，则该样本也属于这个类别，并具有这个类别上样本的特性。

kNN主要用来解决监督学习中的分类问题。

下面通过一个例子，来看看kNN算法的具体过程

首先我们给出一个数据集，raw_data_X表示样本特征集合，raw_data_y为样本所属的类别：

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]

在这里我们把原始数据集作为训练集

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

然后kNN要做的事情是，新来一个数据x，对它进行分类，具体便是计算x与x_train的距离，看x与哪些样本的距离离的最近

x = np.array([8.093607318, 3.365731514])
distances = [sqrt(np.sum((x_train - x)**2)) for x_train in X_train]

接下来找到离新来的x点最近的6个点的y值是多少

np.argsort(distances)
k = 6
nearest = np.argsort(distances)
topK_y = [y_train[i] for i in nearest[:k]]

然后投票选出x的类别

votes = Counter(topK_y)
return votes.most_common(1)[0][0]

这样我们就会得到结果1，表示对新来的x，kNN将其分类为1。

在这里用到的argsort是Numpy里一个函数，可以返回排序的序号下标，方便我们投票使用。下面是完整的Python代码

import numpy as np
from math import sqrt
from collections import Counter


def kNN_classify(k, X_train, y_train, x):
    assert 1 <= k <= X_train.shape[0], "k must be valid"
    assert X_train.shape[0] == y_train.shape[0], \
        "the size of X_train must equal to the size of y_train"
    assert X_train.shape[1] == x.shape[0], \
        "the feature number of x must be equal to X_train"

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

    topK_y = [y_train[i] for i in nearest[:k]]
    votes = Counter(topK_y)

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

封装成一个类

import numpy as np
from math import sqrt
from collections import Counter


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