机器学习：BIRCH聚类、谱聚类

1、BIRCH聚类

BIRCH的全称是利用层次方法的平衡迭代规约和聚类（Balanced Iterative Reducing and Clustering Using Hierarchies）。BIRCH算法利用了一个树结构来快速的聚类，这个数结构类似于平衡B+树，一般将它称之为聚类特征树(Clustering Feature Tree，简称CF Tree)。这颗树的每一个节点是由若干个聚类特征(Clustering Feature，简称CF)组成。
一般来说，BIRCH算法适用于样本量较大和类别数比较大的情况，需要进行调参。

BIRCH算法的主要优点有：

1. 节约内存，所有的样本都在磁盘上，CF Tree仅仅存了CF节点和对应的指针。
2. 聚类速度快，只需要一遍扫描训练集就可以建立CF Tree，CF Tree的增删改都很快。
3. 可以识别噪音点，还可以对数据集进行初步分类的预处理。

BIRCH算法的主要缺点有：

1. 由于CF Tree对每个节点的CF个数有限制，导致聚类的结果可能和真实的类别分布不同。
2. 对高维特征的数据聚类效果不好。
3. 如果数据集的分布簇不是类似于超球体，或者说不是凸的，则聚类效果不好。

# BIRCH聚类，使用默认参数
from sklearn.datasets.samples_generator import make_blobs
from sklearn.cluster import Birch
from sklearn.metrics import calinski_harabaz_score
import matplotlib.pyplot as plt

# 随机生成数据
x, y = make_blobs(n_samples=1000, centers=[[-2, -2], [-1, -1], [0, 0], [1, 1]], cluster_std=[0.3, 0.4, 0.5, 0.3], random_state=2)

# BIRCH聚类
birch = Birch(n_clusters=None, threshold=0.5, branching_factor=50).fit(x)

# 预测
y_pred = birch.predict(x)

# 可视化
plt.scatter(x[:, 0], x[:, 1], c=y_pred)
plt.show()

# 使用calinski_harabaz_score作为模型评估标准
print(calinski_harabaz_score(x, y_pred))

# BIRCH聚类，调参
from sklearn.datasets.samples_generator import make_blobs
from sklearn.cluster import Birch
from sklearn.metrics import calinski_harabaz_score
from sklearn.model_selection import GridSearchCV
import matplotlib.pyplot as plt

# 随机生成数据
x, y = make_blobs(n_samples=1000, centers=[[-2, -2], [-1, -1], [0, 0], [1, 1]], cluster_std=[0.3, 0.4, 0.5, 0.3], random_state=2)

# 类别数
n_clusters = [2, 3, 4, 5]

# 叶子节点每个CF的最大样本半径阈值
thresholds = [0.3, 0.4, 0.5, 0.6]

# CF树内部节点的最大CF
branching_factors = [30, 40, 50, 60]

# 调参，得到最优的参数组合
def get_best_params():
    max_chs = 0
    for n in n_clusters:
        for t in thresholds:
            for b in branching_factors:
                birch = Birch(n_clusters=n, threshold=t, branching_factor=b).fit(x)
                y_pred = birch.predict(x)
                chs = calinski_harabaz_score(x, y_pred)  # 用Calinski-Harabasez分数作为评估标准
                if chs > max_chs:
                    max_chs = chs
                    best_n = n
                    best_t = t
                    best_b = b
    return best_n, best_t, best_b, max_chs

best_n, best_t, best_b, max_chs = get_best_params()

print('best n_cluster: ', best_n)
print('best threshold: ', best_t)
print('best branching_factor: ', best_b)
print('max Calinski-Harabasez_score: ', max_chs)

birch = Birch(n_clusters=best_n, threshold=best_t, branching_factor=best_b).fit(x)
y_pred = birch.predict(x)

plt.scatter(x[:, 0], x[:, 1], c=y_pred)
plt.show()

best n_cluster: 4
best threshold: 0.6
best branching_factor: 30
max Calinski-Harabasez_score: 3111.9410181233275

2、谱聚类Spectral Clustering

# 谱聚类
from sklearn.datasets.samples_generator import make_blobs
from sklearn.cluster import SpectralClustering
from sklearn.metrics import calinski_harabaz_score
import matplotlib.pyplot as plt

# 随机生成数据
x, y = make_blobs(n_samples=500, n_features=6, centers=5, cluster_std=[0.8, 0.5, 0.8, 0.5, 0.6], random_state=2)

# 参数
n_clusters = [3, 4, 5, 6]
gamma = [0.01, 0.1, 1, 10]

# 调参
def get_best_params():
    max_chs = 0
    for n in n_clusters:
        for g in gamma:
            y_pred = SpectralClustering(n_clusters=n, gamma=g).fit_predict(x)
            chs = calinski_harabaz_score(x, y_pred)
            if chs > max_chs:
                max_chs = chs
                best_n = n
                best_gamma = g
    return best_n, best_gamma, max_chs

best_n, best_gamma, max_ = get_best_params()
print('best clusters: ', best_n)
print('best gamma: ', best_gamma)
print('max chs: ', max_chs)

best clusters: 5
best gamma: 0.01
max chs: 3111.9410181233275