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机器学习(四) 分类算法--K近邻算法 KNN (上)

一、K近邻算法基础

KNN------- K近邻算法--------K-Nearest Neighbors

思想极度简单

应用数学知识少（近乎为零）

效果好（缺点？）

可以解释机器学习算法使用过程中很多细节问题

更完整的刻画机器学习应用的流程

import numpy as np
import matplotlib.pyplot as plt

实现我们自己的 kNN
创建简单测试用例
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_train
array([[ 3.39353321,  2.33127338],
       [ 3.11007348,  1.78153964],
       [ 1.34380883,  3.36836095],
       [ 3.58229404,  4.67917911],
       [ 2.28036244,  2.86699026],
       [ 7.42343694,  4.69652288],
       [ 5.745052  ,  3.5339898 ],
       [ 9.17216862,  2.51110105],
       [ 7.79278348,  3.42408894],
       [ 7.93982082,  0.79163723]])
y_train
array([0, 0, 0, 0, 0, 1, 1, 1, 1, 1])

kNN的过程

from math import sqrt
distances = []
for x_train in X_train:
    d = sqrt(np.sum((x_train - x)**2))
    distances.append(d)
distances
[4.812566907609877,
 5.229270827235305,
 6.749798999160064,
 4.6986266144110695,
 5.83460014556857,
 1.4900114024329525,
 2.354574897431513,
 1.3761132675144652,
 0.3064319992975,
 2.5786840957478887]
distances = [sqrt(np.sum((x_train - x)**2))
             for x_train in X_train]
distances
[4.812566907609877,
 5.229270827235305,
 6.749798999160064,
 4.6986266144110695,
 5.83460014556857,
 1.4900114024329525,
 2.354574897431513,
 1.3761132675144652,
 0.3064319992975,
 2.5786840957478887]
np.argsort(distances)
array([8, 7, 5, 6, 9, 3, 0, 1, 4, 2])
nearest = np.argsort(distances)
k = 6
topK_y = [y_train[neighbor] for neighbor in nearest[:k]]
topK_y
[1, 1, 1, 1, 1, 0]
from collections import Counter
votes = Counter(topK_y)
votes
Counter({0: 1, 1: 5})
votes.most_common(1)
[(1, 5)]
predict_y = votes.most_common(1)[0][0]
predict_y
1

二、scikit-learn 中的机器学习算法封装
KNN/KNNN.py

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

kNN_function/KNN.py

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]

三、训练数据集、测试数据集

判断机器学习算法的性能

playML/KNN.py

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

playML/model_selection.py

import numpy as np


def train_test_split(X, y, test_ratio=0.2, seed=None):
    """将数据 X 和 y 按照test_ratio分割成X_train, X_test, y_train, y_test"""
    assert X.shape[0] == y.shape[0], 
        "the size of X must be equal to the size of y"
    assert 0.0 <= test_ratio <= 1.0, 
        "test_ration must be valid"

    if seed:
        np.random.seed(seed)

    shuffled_indexes = np.random.permutation(len(X))

    test_size = int(len(X) * test_ratio)
    test_indexes = shuffled_indexes[:test_size]
    train_indexes = shuffled_indexes[test_size:]

    X_train = X[train_indexes]
    y_train = y[train_indexes]

    X_test = X[test_indexes]
    y_test = y[test_indexes]

    return X_train, X_test, y_train, y_test

playML/__init__.py

四、分类的准确度
playML/metrics.py

import numpy as np

def accuracy_score(y_true, y_predict):
    '''计算y_true和y_predict之间的准确率'''
    assert y_true.shape[0] == y_predict.shape[0], 
        "the size of y_true must be equal to the size of y_predict"

    return sum(y_true == y_predict) / len(y_true)

model_selection.py-->KNNClassifier 类里面添加这样一个方法

from .metrics import accuracy_score

    def score(self, X_test, y_test):
        """根据测试数据集 X_test 和 y_test 确定当前模型的准确度"""

        y_predict = self.predict(X_test)
        return accuracy_score(y_test, y_predict)