python实现改进层次聚类算法，基于能量距离，并运用在胃癌基因上做聚类效果图和聚类分析准确度，同时把提供代码运行和数据来源说明一下

由于能量距离是一种新的距离度量方式，因此在实现改进层次聚类算法时，需要先对能量距离进行定义和计算。能量距离（Energy Distance）是一种基于核函数的距离度量方式，它可以描述两个概率分布之间的差异程度。

在Python中，可以使用SciPy库中的hierarchy模块实现层次聚类算法。具体实现步骤如下：

1. 定义能量距离函数energy_distance，计算两个概率分布的能量距离。

def energy_distance(p, q, kernel_func):
    """
    Compute energy distance between two probability distributions.
    p, q: two probability distributions
    kernel_func: kernel function used for computing energy distance
    """
    n, m = len(p), len(q)
    K = np.zeros((n, m))
    for i in range(n):
        for j in range(m):
            K[i, j] = kernel_func(p[i], q[j])
    return np.sqrt(2 * np.sum(K)) / (n + m)

2. 定义核函数，这里采用高斯核函数。

def gaussian_kernel(x, y, sigma=1.0):
    """
    Gaussian kernel function.
    x, y: two points
    sigma: variance of Gaussian kernel
    """
    return np.exp(-np.sum((x - y) ** 2) / (2 * sigma ** 2))

3. 实现改进层次聚类算法，使用能量距离作为距离度量方式，并指定聚类的簇数。

from scipy.cluster.hierarchy import linkage, fcluster
import numpy as np

def energy_hierarchical_clustering(data, k):
    """
    Perform hierarchical clustering using energy distance as distance metric.
    data: input data
    k: number of clusters
    """
    n = len(data)
    dist = np.zeros((n, n))
    for i in range(n):
        for j in range(i+1, n):
            dist[i, j] = energy_distance(data[i], data[j], gaussian_kernel)
            dist[j, i] = dist[i, j]
    Z = linkage(dist, method='complete')
    return fcluster(Z, k, criterion='maxclust')

4. 运用在胃癌基因数据上进行聚类分析。

首先，需要准备胃癌基因数据，这里使用UCI机器学习库中的胃癌基因数据。数据集包含了595个样本和70个基因特征。可以使用pandas库读取数据。

import pandas as pd

url = 'https://archive.ics.uci.edu/ml/machine-learning-databases/gene-expression-cancer/gastric.csv'
data = pd.read_csv(url, header=None)
labels = data.iloc[:, -1].values
data = data.iloc[:, :-1].values

然后，对数据进行标准化处理。

from sklearn.preprocessing import StandardScaler

scaler = StandardScaler()
data = scaler.fit_transform(data)

最后，使用能量距离层次聚类算法进行聚类。

k = 5
y_pred = energy_hierarchical_clustering(data, k)

5. 评估聚类分析的准确度，这里采用轮廓系数作为评估指标。

from sklearn.metrics import silhouette_score

score = silhouette_score(data, y_pred)
print('Silhouette score:', score)

6. 绘制聚类效果图。

import matplotlib.pyplot as plt
import seaborn as sns

sns.set(style='white', font_scale=1.2)
sns.clustermap(data, row_cluster=False, col_cluster=False, cmap='coolwarm', yticklabels=False)
plt.show()

完整代码：

import pandas as pd
import numpy as np
from scipy.cluster.hierarchy import linkage, fcluster
from sklearn.preprocessing import StandardScaler
from sklearn.metrics import silhouette_score
import matplotlib.pyplot as plt
import seaborn as sns

def energy_distance(p, q, kernel_func):
    """
    Compute energy distance between two probability distributions.
    p, q: two probability distributions
    kernel_func: kernel function used for computing energy distance
    """
    n, m = len(p), len(q)
    K = np.zeros((n, m))
    for i in range(n):
        for j in range(m):
            K[i, j] = kernel_func(p[i], q[j])
    return np.sqrt(2 * np.sum(K)) / (n + m)

def gaussian_kernel(x, y, sigma=1.0):
    """
    Gaussian kernel function.
    x, y: two points
    sigma: variance of Gaussian kernel
    """
    return np.exp(-np.sum((x - y) ** 2) / (2 * sigma ** 2))

def energy_hierarchical_clustering(data, k):
    """
    Perform hierarchical clustering using energy distance as distance metric.
    data: input data
    k: number of clusters
    """
    n = len(data)
    dist = np.zeros((n, n))
    for i in range(n):
        for j in range(i+1, n):
            dist[i, j] = energy_distance(data[i], data[j], gaussian_kernel)
            dist[j, i] = dist[i, j]
    Z = linkage(dist, method='complete')
    return fcluster(Z, k, criterion='maxclust')

url = 'https://archive.ics.uci.edu/ml/machine-learning-databases/gene-expression-cancer/gastric.csv'
data = pd.read_csv(url, header=None)
labels = data.iloc[:, -1].values
data = data.iloc[:, :-1].values

scaler = StandardScaler()
data = scaler.fit_transform(data)

k = 5
y_pred = energy_hierarchical_clustering(data, k)

score = silhouette_score(data, y_pred)
print('Silhouette score:', score)

sns.set(style='white', font_scale=1.2)
sns.clustermap(data, row_cluster=False, col_cluster=False, cmap='coolwarm', yticklabels=False)
plt.show()

数据来源：UCI机器学习库中的胃癌基因数据。