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KNN.py
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KNN.py
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import random
from sklearn import datasets
import sklearn
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
# 正规化数据集 X
def normalize(X, axis=-1, p=2):
lp_norm = np.atleast_1d(np.linalg.norm(X, p, axis))
lp_norm[lp_norm == 0] = 1
return X / np.expand_dims(lp_norm, axis)
# 计算一个样本与数据集中所有样本的欧氏距离的平方
def euclidean_distance(one_sample, X):
one_sample = one_sample.reshape(1, -1)
X = X.reshape(X.shape[0], -1)
distances = np.power(np.tile(one_sample, (X.shape[0], 1)) - X, 2).sum(axis=1)
return distances
class Kmeans():
"""Kmeans聚类算法.
Parameters:
-----------
k: int
聚类的数目.
max_iterations: int
最大迭代次数.
varepsilon: float
判断是否收敛, 如果上一次的所有k个聚类中心与本次的所有k个聚类中心的差都小于varepsilon,
则说明算法已经收敛
"""
def __init__(self, k=2, max_iterations=500, varepsilon=0.0001):
self.k = k
self.max_iterations = max_iterations
self.varepsilon = varepsilon
# 从所有样本中随机选取self.k样本作为初始的聚类中心
def init_random_centroids(self, X):
n_samples, n_features = np.shape(X)
centroids = np.zeros((self.k, n_features))
for i in range(self.k):
centroid = X[np.random.choice(range(n_samples))]
centroids[i] = centroid
return centroids
# 返回距离该样本最近的一个中心索引[0, self.k)
def _closest_centroid(self, sample, centroids):
distances = euclidean_distance(sample, centroids)
#计算每一个样本与质心之间的距离
closest_i = np.argmin(distances)
#print(distances)
return closest_i
# 将所有样本进行归类，归类规则就是将该样本归类到与其最近的中心
def create_clusters(self, centroids, X):
n_samples = np.shape(X)[0]
clusters = [[] for _ in range(self.k)]
for sample_i, sample in enumerate(X):
centroid_i = self._closest_centroid(sample, centroids)
clusters[centroid_i].append(sample_i)
return clusters
# 对中心进行更新
def update_centroids(self, clusters, X):
n_features = np.shape(X)[1]
centroids = np.zeros((self.k, n_features))
for i, cluster in enumerate(clusters):
centroid = np.mean(X[cluster], axis=0)
centroids[i] = centroid
return centroids
# 将所有样本进行归类，其所在的类别的索引就是其类别标签
def get_cluster_labels(self, clusters, X):
y_pred = np.zeros(np.shape(X)[0])
for cluster_i, cluster in enumerate(clusters):
for sample_i in cluster:
y_pred[sample_i] = cluster_i
return y_pred
# 对整个数据集X进行Kmeans聚类，返回其聚类的标签
def predict(self, X):
# 从所有样本中随机选取self.k样本作为初始的聚类中心
centroids = self.init_random_centroids(X)
# 迭代，直到算法收敛(上一次的聚类中心和这一次的聚类中心几乎重合)或者达到最大迭代次数
for _ in range(self.max_iterations):
# 将所有进行归类，归类规则就是将该样本归类到与其最近的中心
clusters = self.create_clusters(centroids, X)
former_centroids = centroids
# 计算新的聚类中心
centroids = self.update_centroids(clusters, X)
# 如果聚类中心几乎没有变化，说明算法已经收敛，退出迭代
diff = centroids - former_centroids
if diff.any() < self.varepsilon:
break
return self.get_cluster_labels(clusters, X)
def main():
# Load the dataset
X, y = datasets.make_blobs(n_samples=10000,
n_features=3,
centers=[[3,3, 3], [0,0,0], [1,1,1], [2,2,2]],
cluster_std=[0.2, 0.1, 0.2, 0.2],
random_state =9)
# 用Kmeans算法进行聚类
clf = Kmeans(k=4)
y_pred = clf.predict(X)
# 可视化聚类效果
fig = plt.figure(figsize=(12, 8))
ax = Axes3D(fig, rect=[0, 0, 1, 1], elev=30, azim=20)
plt.scatter(X[y==0][:, 0], X[y==0][:, 1], X[y==0][:, 2])
plt.scatter(X[y==1][:, 0], X[y==1][:, 1], X[y==1][:, 2])
plt.scatter(X[y==2][:, 0], X[y==2][:, 1], X[y==2][:, 2])
plt.scatter(X[y==3][:, 0], X[y==3][:, 1], X[y==3][:, 2])
plt.show()
if __name__ == "__main__":
main()