python改进k-means聚类算法，基于能量距离，并将其运用在肺癌基因上，聚类分成三类，分别从样本量以10，30，50，100，200，300，400递推绘制聚类效果图及准确率，并说明数据来源和python代码实现

改进k-means聚类算法基于能量距离的实现：

数据来源：UCI机器学习库中的肺癌基因数据集。

代码实现：

首先，需要导入必要的库：

import numpy as np
import pandas as pd
import random
import math
import matplotlib.pyplot as plt

接下来，读取肺癌基因数据集：

data = pd.read_csv('lung_cancer.csv')

接着，进行数据预处理，将数据集中的标签列删除，并将数据集转换为numpy数组：

data = data.drop('label', axis=1)
data = np.array(data)

然后，实现能量距离计算公式：

def energy_distance(x1, x2, sigma):
    n = x1.shape[0]
    res = 0
    for i in range(n):
        res += (math.exp(-(x1[i]-x2[i])**2/(2*sigma**2)) - math.exp(-(x1[i]-x2[i])**2/(2*(2*sigma)**2)))**2
    return res

接下来，实现改进的k-means聚类算法：

def k_means_energy(data, k, max_iter, sigma):
    n = data.shape[0]
    m = data.shape[1]
    centroids = np.zeros((k, m))
    for i in range(k):
        centroids[i] = data[random.randint(0, n-1)]
    cluster = np.zeros(n)
    for i in range(max_iter):
        for j in range(n):
            min_dist = float('inf')
            for l in range(k):
                dist = energy_distance(data[j], centroids[l], sigma)
                if dist < min_dist:
                    min_dist = dist
                    cluster[j] = l
        for l in range(k):
            centroids[l] = np.mean(data[cluster==l], axis=0)
    return cluster

最后，实现绘制聚类效果图和计算准确率的函数：

def plot_cluster_result(cluster, data, k):
    colors = ['r', 'g', 'b', 'c', 'm', 'y', 'k', 'w']
    for i in range(k):
        plt.scatter(data[cluster==i,0], data[cluster==i,1], c=colors[i%8], s=10)
    plt.show()

def calculate_accuracy(cluster, true_labels):
    n = cluster.shape[0]
    correct = 0
    for i in range(n):
        if cluster[i] == true_labels[i]:
            correct += 1
    return correct/n

接着，可以使用以上实现的函数进行聚类，并绘制效果图和计算准确率：

true_labels = pd.read_csv('lung_cancer.csv')['label']
true_labels = np.array(true_labels)
k = 3
max_iter = 100
sigma = 1
sample_sizes = [10, 30, 50, 100, 200, 300, 400]
accuracies = []
for sample_size in sample_sizes:
    indices = random.sample(range(data.shape[0]), sample_size)
    sample_data = data[indices]
    cluster = k_means_energy(sample_data, k, max_iter, sigma)
    plot_cluster_result(cluster, sample_data, k)
    accuracy = calculate_accuracy(cluster, true_labels[indices])
    accuracies.append(accuracy)
    print('Sample size:', sample_size, 'Accuracy:', accuracy)
plt.plot(sample_sizes, accuracies)
plt.xlabel('Sample size')
plt.ylabel('Accuracy')
plt.show()

最终，可以得到不同样本量下的聚类效果图和准确率曲线图。