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

 

  1. import numpy as np
  2. import matplotlib.pyplot as plt
  4. 实现我们自己的 kNN
  5. 创建简单测试用例
  6. raw_data_X = [[3.393533211, 2.331273381],
  7.               [3.110073483, 1.781539638],
  8.               [1.343808831, 3.368360954],
  9.               [3.582294042, 4.679179110],
  10.               [2.280362439, 2.866990263],
  11.               [7.423436942, 4.696522875],
  12.               [5.745051997, 3.533989803],
  13.               [9.172168622, 2.511101045],
  14.               [7.792783481, 3.424088941],
  15.               [7.939820817, 0.791637231]
  16.              ]
  17. raw_data_y = [0, 0, 0, 0, 0, 1, 1, 1, 1, 1]
  18. X_train = np.array(raw_data_X)
  19. y_train = np.array(raw_data_y)
  20. X_train
  21. array([[ 3.39353321,  2.33127338],
  22.        [ 3.11007348,  1.78153964],
  23.        [ 1.34380883,  3.36836095],
  24.        [ 3.58229404,  4.67917911],
  25.        [ 2.28036244,  2.86699026],
  26.        [ 7.42343694,  4.69652288],
  27.        [ 5.745052  ,  3.5339898 ],
  28.        [ 9.17216862,  2.51110105],
  29.        [ 7.79278348,  3.42408894],
  30.        [ 7.93982082,  0.79163723]])
  31. y_train
  32. array([0, 0, 0, 0, 0, 1, 1, 1, 1, 1])

 

  1. from math import sqrt
  2. distances = []
  3. for x_train in X_train:
  4.     d = sqrt(np.sum((x_train - x)**2))
  5.     distances.append(d)
  6. distances
  7. [4.812566907609877,
  8.  5.229270827235305,
  9.  6.749798999160064,
  10.  4.6986266144110695,
  11.  5.83460014556857,
  12.  1.4900114024329525,
  13.  2.354574897431513,
  14.  1.3761132675144652,
  15.  0.3064319992975,
  16.  2.5786840957478887]
  17. distances = [sqrt(np.sum((x_train - x)**2))
  18.              for x_train in X_train]
  19. distances
  20. [4.812566907609877,
  21.  5.229270827235305,
  22.  6.749798999160064,
  23.  4.6986266144110695,
  24.  5.83460014556857,
  25.  1.4900114024329525,
  26.  2.354574897431513,
  27.  1.3761132675144652,
  28.  0.3064319992975,
  29.  2.5786840957478887]
  30. np.argsort(distances)
  31. array([8, 7, 5, 6, 9, 3, 0, 1, 4, 2])
  32. nearest = np.argsort(distances)
  33. k = 6
  34. topK_y = [y_train[neighbor] for neighbor in nearest[:k]]
  35. topK_y
  36. [1, 1, 1, 1, 1, 0]
  37. from collections import Counter
  38. votes = Counter(topK_y)
  39. votes
  40. Counter({0: 1, 1: 5})
  41. votes.most_common(1)
  42. [(1, 5)]
  43. predict_y = votes.most_common(1)[0][0]
  44. predict_y
  45. 1

 二、scikit-learn 中的机器学习算法封装
KNN/KNNN.py

  1. import numpy as np
  2. from math import sqrt
  3. from collections import Counter
  6. class KNNClassifier:
  8.     def __init__(self, k):
  9.         """初始化kNN分类器"""
  10.         assert k >= 1, "k must be valid"
  11.         self.k = k
  12.         self._X_train = None
  13.         self._y_train = None
  15.     def fit(self, X_train, y_train):
  16.         """根据训练数据集X_train和y_train训练kNN分类器"""
  17.         assert X_train.shape[0] == y_train.shape[0], \
  18.             "the size of X_train must be equal to the size of y_train"
  19.         assert self.k <= X_train.shape[0], \
  20.             "the size of X_train must be at least k."
  22.         self._X_train = X_train
  23.         self._y_train = y_train
  24.         return self
  26.     def predict(self, X_predict):
  27.         """给定待预测数据集X_predict，返回表示X_predict的结果向量"""
  28.         assert self._X_train is not None and self._y_train is not None, \
  29.                 "must fit before predict!"
  30.         assert X_predict.shape[1] == self._X_train.shape[1], \
  31.                 "the feature number of X_predict must be equal to X_train"
  33.         y_predict = [self._predict(x) for x in X_predict]
  34.         return np.array(y_predict)
  36.     def _predict(self, x):
  37.         """给定单个待预测数据x，返回x的预测结果值"""
  38.         assert x.shape[0] == self._X_train.shape[1], \
  39.             "the feature number of x must be equal to X_train"
  41.         distances = [sqrt(np.sum((x_train - x) ** 2))
  42.                      for x_train in self._X_train]
  43.         nearest = np.argsort(distances)
  45.         topK_y = [self._y_train[i] for i in nearest[:self.k]]
  46.         votes = Counter(topK_y)
  48.         return votes.most_common(1)[0][0]
  50.     def __repr__(self):
  51.         return "KNN(k=%d)" % self.k

kNN_function/KNN.py

  1. import numpy as np
  2. from math import sqrt
  3. from collections import Counter
  6. def kNN_classify(k, X_train, y_train, x):
  8.     assert 1 <= k <= X_train.shape[0], "k must be valid"
  9.     assert X_train.shape[0] == y_train.shape[0], \
  10.         "the size of X_train must equal to the size of y_train"
  11.     assert X_train.shape[1] == x.shape[0], \
  12.         "the feature number of x must be equal to X_train"
  14.     distances = [sqrt(np.sum((x_train - x)**2)) for x_train in X_train]
  15.     nearest = np.argsort(distances)
  17.     topK_y = [y_train[i] for i in nearest[:k]]
  18.     votes = Counter(topK_y)
  20.     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

  1. import numpy as np
  2. from math import sqrt
  3. from collections import Counter
  6. class KNNClassifier:
  8.     def __init__(self, k):
  9.         """初始化kNN分类器"""
  10.         assert k >= 1, "k must be valid"
  11.         self.k = k
  12.         self._X_train = None
  13.         self._y_train = None
  15.     def fit(self, X_train, y_train):
  16.         """根据训练数据集X_train和y_train训练kNN分类器"""
  17.         assert X_train.shape[0] == y_train.shape[0], \
  18.             "the size of X_train must be equal to the size of y_train"
  19.         assert self.k <= X_train.shape[0], \
  20.             "the size of X_train must be at least k."
  22.         self._X_train = X_train
  23.         self._y_train = y_train
  24.         return self
  26.     def predict(self, X_predict):
  27.         """给定待预测数据集X_predict，返回表示X_predict的结果向量"""
  28.         assert self._X_train is not None and self._y_train is not None, \
  29.                 "must fit before predict!"
  30.         assert X_predict.shape[1] == self._X_train.shape[1], \
  31.                 "the feature number of X_predict must be equal to X_train"
  33.         y_predict = [self._predict(x) for x in X_predict]
  34.         return np.array(y_predict)
  36.     def _predict(self, x):
  37.         """给定单个待预测数据x，返回x的预测结果值"""
  38.         assert x.shape[0] == self._X_train.shape[1], \
  39.             "the feature number of x must be equal to X_train"
  41.         distances = [sqrt(np.sum((x_train - x) ** 2))
  42.                      for x_train in self._X_train]
  43.         nearest = np.argsort(distances)
  45.         topK_y = [self._y_train[i] for i in nearest[:self.k]]
  46.         votes = Counter(topK_y)
  48.         return votes.most_common(1)[0][0]
  50.     def __repr__(self):
  51.         return "KNN(k=%d)" % self.k

 

 playML/model_selection.py

  1. import numpy as np
  4. def train_test_split(X, y, test_ratio=0.2, seed=None):
  5.     """将数据 X 和 y 按照test_ratio分割成X_train, X_test, y_train, y_test"""
  6.     assert X.shape[0] == y.shape[0], \
  7.         "the size of X must be equal to the size of y"
  8.     assert 0.0 <= test_ratio <= 1.0, \
  9.         "test_ration must be valid"
  10.  
  11.     if seed:
  12.         np.random.seed(seed)
  14.     shuffled_indexes = np.random.permutation(len(X))
  16.     test_size = int(len(X) * test_ratio)
  17.     test_indexes = shuffled_indexes[:test_size]
  18.     train_indexes = shuffled_indexes[test_size:]
  20.     X_train = X[train_indexes]
  21.     y_train = y[train_indexes]
  23.     X_test = X[test_indexes]
  24.     y_test = y[test_indexes]
  26.     return X_train, X_test, y_train, y_test

playML/__init__.py

 

 

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