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)
五、超参数
超参数：在算法运行前需要决定的参数
模型参数：算法过程中学习的参数
KNN算法没有模型参数
KNN算法中的 K 是 典型的 超参数
寻找好的超参数：
领域知识、经验数值、实验搜索
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