对数据进行k-means聚类并进行三维可视化

import csv import matplotlib.pyplot as plt import numpy as np import xlrd from sklearn import preprocessing from mpl_toolkits.mplot3d import Axes3D # 标准化数据集 X from xlsxwriter import worksheet 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=4, 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) closest_i = np.argmin(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) data = [] # 读取数据 wk = xlrd.open_workbook(r'D:\用kmeans算法的排名.xlsx') sheets = wk.sheet_by_name('sheet1') ws = wk.sheet_by_index(0) # 获取总行数 nrows = ws.nrows for i in range(1, nrows): row = sheets.cell_value(i, 0) row1 = sheets.cell_value(i, 1) row2 = sheets.cell_value(i, 2) data.append([row, row1, row2]) min_max_scaler = preprocessing.MinMaxScaler(feature_range=(0,1)) A = np.array(data) X=min_max_scaler.fit_transform(A) num, dim = X.shape clf = Kmeans(k=4) y_pred = clf.predict(X) print(y_pred) color = ['r', 'g', 'b', 'c', 'y', 'm', 'k'] ax = plt.subplot(111, projection='3d') f = open('D:\结果.csv', 'w', encoding='utf-8', newline='') csv_writer = csv.writer(f) for p in range(0,num): y=y_pred[p] csv_writer.writerow([y]) ax.scatter(int(A[p, 0]), int(A[p, 1]), int(A[p, 2]), c=color[int(y)]) f.close() plt.show()