機器學習之K近鄰演算法 kNN(1)
阿新 • • 發佈:2019-02-04
可以說kNN是機器學習中非常特殊的沒有模型的演算法,為了和其他演算法統一,可以認為新聯資料集就是模型本身
1. kNN演算法基本實現
import numpy as np
import matplotlib.pyplot as plt
from math import sqrt
from collections import Counter
# 特徵集合
raw_data_x = [[3.393533211, 2.331273381],
[3.110073483, 1.781539638],
[1.343808831, 3.368360954 ],
[3.582294042, 4.679179110],
[2.280362439, 2.866990263],
[7.423469421, 4.694522875],
[5.745051997, 3.533989803],
[9.172168622, 2.511101045],
[7.792783481, 3.424088941],
[7.939820817, 0.791637231]]
# 每一個特徵的類別
raw_data_y = [0 , 0, 0, 0, 0, 1, 1, 1, 1, 1]
# 訓練集
x_train = np.array(raw_data_x)
y_train = np.array(raw_data_y)
# 來了一個新的資料 要判斷它的特徵值
new = np.array([8.093607318, 3.365731514])
# 原資料
plt.scatter(x_train[y_train == 0, 0], x_train[y_train == 0, 1], color='g')
plt.scatter(x_train[y_train == 1, 0], x_train[y_train == 1, 1], color='r' )
# 新資料
plt.scatter(new[0], new[1], color='b')
# plt.show()
# 由圖可知,它一定輸入特徵值為 1
# kNN的過程
distances = []
# np.sum((x - new) ** 2) 等價於 (x[0] - new[0]) ** 2 + (x[1] - new[1]) ** 2
for x in x_train:
d = sqrt(np.sum((x - new) ** 2))
distances.append(d)
# 一句話搞定
# distances = [sqrt(np.sum((x - new) ** 2)) for x in x_train]
nearest = np.argsort(distances)
K = 6
# 最近距離y座標
topK_y = [y_train[i] for i in nearest[:K]]
# 投票過程
votes = Counter(topK_y)
# 預測結果值
predict_y = votes.most_common(1)[0][0]
print(predict_y)
2.函式
很容易把上述的過程整理出來寫出一個函式
import numpy as np
from math import sqrt
from collections import Counter
def kNN_classify(k, x_train, y_train, new):
# 校驗引數
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] == new.shape[0], "th feature number of x must be equal to x_train"
# 距離陣列
distance = [sqrt(np.sum((x - new) ** 2)) for x in x_train]
nearest = np.argsort(distance)
topK_y = [y_train[i] for i in nearest[:k]]
# 投票
votes = Counter(topK_y)
return votes.most_common(1)[0][0]
3.使用sklearn中的kNN演算法
from sklearn.neighbors import KNeighborsClassifier
import numpy as np
# 特徵集合
raw_data_x = [[3.393533211, 2.331273381],
[3.110073483, 1.781539638],
[1.343808831, 3.368360954],
[3.582294042, 4.679179110],
[2.280362439, 2.866990263],
[7.423469421, 4.694522875],
[5.745051997, 3.533989803],
[9.172168622, 2.511101045],
[7.792783481, 3.424088941],
[7.939820817, 0.791637231]]
# 每一個特徵的類別
raw_data_y = [0, 0, 0, 0, 0, 1, 1, 1, 1, 1]
# 訓練集
x_train = np.array(raw_data_x)
y_train = np.array(raw_data_y)
new = np.array([[8.093607318, 3.365731514]])
kNN_classifier = KNeighborsClassifier(n_neighbors=6)
kNN_classifier.fit(x_train, y_train)
print(kNN_classifier.predict(new))
4.模擬sklearn的方式使用面向物件的方式實現
import numpy as np
from math import sqrt
from collections import Counter
class KNNClassifier:
def __init__(self, k):
""""初始化kNN分類器"""
assert 1 <= k, "k must be valid "
self.k = k
self._x_train = None
self._y_train = None
def fit(self, x_train, y_train):
""""根據訓練資料集x_train,y_train訓練kNN分類器"""
assert x_train.shape[0] == y_train.shape[0], "the size of x_train must equal to the size of y_train"
assert self.k <= x_train.shape[0], "th feature number of x must be equal to x_train"
self._x_train = x_train
self._y_train = y_train
return self
def predict(self, new):
""""給定待預測資料集new,返回表示NEW的結果向量"""
assert self._x_train is not None and self._y_train is not None, "must fit before predict!"
assert new.shape[1] == self._x_train.shape[1], "the feature number of new must be equal to x_train"
y_predict = [self._predict(x) for x in new]
return np.array(y_predict)
def _predict(self, x):
""""給定單個待預測資料x,返回x_predict的預測結果值"""
assert x.shape[0] == self._x_train.shape[1], "the feature number of x must be equal to x_train"
# 距離陣列
distance = [sqrt(np.sum((i - x) ** 2)) for i in self._x_train]
nearest = np.argsort(distance)
topK_y = [self._y_train[i] for i in nearest[:self.k]]
# 投票
votes = Counter(topK_y)
return votes.most_common(1)[0][0]