sklearn谱聚类Spectral Clustering(一)运行:以coco标签为例

浅浅的花香味﹌ 2022-02-05 12:59 680阅读 0赞

背景：我们需要对多标签的问题，标签进行谱聚类，然后看相应的聚类结果。

官方API描述：[https://scikit-learn.org/stable/modules/generated/sklearn.cluster.SpectralClustering.html\#sklearn.cluster.SpectralClustering][https_scikit-learn.org_stable_modules_generated_sklearn.cluster.SpectralClustering.html_sklearn.cluster.SpectralClustering]

**目录**

一、安装sklearn

1.1 scikit-learn概览

1.2 安装

二、简单谱聚类

2.1 谱聚类详解

2.2 简单运行

2.3 iris数据集

三、谱聚类函数

3.1 SpectralClustering

3.2 输入

3.3 输出

四、用coco标签进行谱聚类

4.1 coco互相关矩阵保存

4.3 加载

4.4 直接进行预测

4.5 affinity matrix有向图

4.6 调整获取最好参数

--------------------

# 一、安装sklearn #

## 1.1 scikit-learn概览 ##

sklearn全称为scikit-learn

**Scikit-learn(sklearn)的定位是通用机器学习库**，而**TensorFlow(tf)的定位主要是深度学习库**。一个显而易见的不同：tf并未提供sklearn那种强大的特征工程，如维度压缩、特征选择等。究其根本，我认为是因为机器学习模型的两种不同的处理数据的方式：

*  **传统机器学习：利用特征工程(feature engineering)，人为对数据进行提炼清洗**
 *  **深度学习：利用表示学习(representation learning)，机器学习模型自身对数据进行提炼**

## 1.2 安装 ##

torch031环境下，pip install sklearn

(torch031) \[xingxiangrui@gzbh-mms-gpu55.gzbh.baidu.com chun-ML\_GCN\]$ pip install sklearn

env环境下

env/bin/python -m pip install sklearn

Collecting sklearn
      Using cached https://files.pythonhosted.org/packages/1e/7a/dbb3be0ce9bd5c8b7e3d87328e79063f8b263b2b1bfa4774cb1147bfcd3f/sklearn-0.0.tar.gz
    Collecting scikit-learn (from sklearn)
      Downloading https://files.pythonhosted.org/packages/5e/82/c0de5839d613b82bddd088599ac0bbfbbbcbd8ca470680658352d2c435bd/scikit_learn-0.20.3-cp36-cp36m-manylinux1_x86_64.whl (5.4MB)
        100% |################################| 5.4MB 20kB/s
    Requirement already satisfied: numpy>=1.8.2 in ./env/lib/python3.6/site-packages (from scikit-learn->sklearn) (1.16.3)
    Requirement already satisfied: scipy>=0.13.3 in ./env/lib/python3.6/site-packages (from scikit-learn->sklearn) (1.2.1)
    Building wheels for collected packages: sklearn
      Running setup.py bdist_wheel for sklearn ... done
      Stored in directory: /home/xingxiangrui/.cache/pip/wheels/76/03/bb/589d421d27431bcd2c6da284d5f2286c8e3b2ea3cf1594c074
    Successfully built sklearn
    Installing collected packages: scikit-learn, sklearn
    Successfully installed scikit-learn-0.20.3 sklearn-0.0

# 二、简单谱聚类 #

## 2.1 谱聚类详解 ##

[Graph特征提取方法:谱聚类(Spectral Clustering)详解 ][Graph_Spectral Clustering_]

## 2.2 简单运行 ##

参考样例

[https://www.bbsmax.com/A/NMAzABqJ9p/][https_www.bbsmax.com_A_NMAzABqJ9p]

[https://blog.csdn.net/fjssharpsword/article/details/79198054][https_blog.csdn.net_fjssharpsword_article_details_79198054]

[https://blog.csdn.net/weixin\_40042143/article/details/82462804][https_blog.csdn.net_weixin_40042143_article_details_82462804]

代码：

#-*-coding:utf-8 -*-
    """
    created by xingxinangrui on 2019.5.5
    this is the simple demo that use sk-learn to run spectral clustering
    """
    #demo one use iris dataset
    import numpy as np
    from sklearn import datasets
    
    X = datasets.load_iris()
    # print(X)
    # 查看默认的谱聚类效果
    from sklearn.cluster import SpectralClustering
    
    spectral = SpectralClustering()
    pred_y = spectral.fit_predict(X.data)
    from sklearn import metrics
    
    print("Calinski-Harabasz Score", metrics.calinski_harabaz_score(X.data, pred_y))
    """
    Calinski-Harabasz Score 438.286953256
    """
    
    # 默认使用的是高斯核，需要对n_cluster和gamma进行调参，选择合适的参数
    scores = []
    s = dict()
    for index, gamma in enumerate((0.01, 0.1, 1, 10)):
        for index, k in enumerate((3, 4, 5, 6)):
            pred_y = SpectralClustering(n_clusters=k).fit_predict(X.data)
            print("Calinski-Harabasz Score with gamma=", gamma, "n_cluster=", k, "score=",
                  metrics.calinski_harabaz_score(X.data, pred_y))
            tmp = dict()
            tmp['gamma'] = gamma
            tmp['n_cluster'] = k
            tmp['score'] = metrics.calinski_harabaz_score(X.data, pred_y)
            s[metrics.calinski_harabaz_score(X.data, pred_y)] = tmp
            scores.append(metrics.calinski_harabaz_score(X.data, pred_y))
    print(np.max(scores))
    print("max score:")
    print(s.get(np.max(scores)))

运行结果

[xingxiangrui@gzbh-mms-gpu55.gzbh.baidu.com chun-ML_GCN]$ env/bin/python sk_spectral_cluster/demo_spectral_clustering.py
    Calinski-Harabasz Score 412.6798087360221
    Calinski-Harabasz Score with gamma= 0.01 n_cluster= 3 score= 556.1176919037501
    Calinski-Harabasz Score with gamma= 0.01 n_cluster= 4 score= 467.76231583239655
    Calinski-Harabasz Score with gamma= 0.01 n_cluster= 5 score= 432.63682714748126
    Calinski-Harabasz Score with gamma= 0.01 n_cluster= 6 score= 410.18904618455855
    Calinski-Harabasz Score with gamma= 0.1 n_cluster= 3 score= 556.11769190375
    Calinski-Harabasz Score with gamma= 0.1 n_cluster= 4 score= 467.76231583239655
    Calinski-Harabasz Score with gamma= 0.1 n_cluster= 5 score= 437.95873781534283
    Calinski-Harabasz Score with gamma= 0.1 n_cluster= 6 score= 410.4013080804197
    Calinski-Harabasz Score with gamma= 1 n_cluster= 3 score= 556.1176919037501
    Calinski-Harabasz Score with gamma= 1 n_cluster= 4 score= 467.76231583239655
    Calinski-Harabasz Score with gamma= 1 n_cluster= 5 score= 437.95873781534283
    Calinski-Harabasz Score with gamma= 1 n_cluster= 6 score= 404.45914748471347
    Calinski-Harabasz Score with gamma= 10 n_cluster= 3 score= 556.1176919037501
    Calinski-Harabasz Score with gamma= 10 n_cluster= 4 score= 467.76231583239655
    Calinski-Harabasz Score with gamma= 10 n_cluster= 5 score= 437.9587378153427
    Calinski-Harabasz Score with gamma= 10 n_cluster= 6 score= 401.6775659923456
    556.1176919037501
    max score:
    {'gamma': 10, 'n_cluster': 3, 'score': 556.1176919037501}

## 2.3 iris数据集 ##

用莺尾花数据集（IRIS数据集）

Iris数据集是常用的分类实验数据集，由Fisher, 1936收集整理。Iris也称鸢尾花卉数据集，是一类多重变量分析的数据集。数据集包含150个数据集，分为3类，每类50个数据，每个数据包含4个属性。可通过花萼长度，花萼宽度，花瓣长度，花瓣宽度4个属性预测鸢尾花卉属于（Setosa，Versicolour，Virginica）三个种类中的哪一类。

iris以鸢尾花的特征作为数据来源，常用在分类操作中。该数据集由3种不同类型的鸢尾花的50个样本数据构成。其中的一个种类与另外两个种类是线性可分离的，后两个种类是非线性可分离的。

该数据集包含了5个属性：

*  & Sepal.Length（花萼长度），单位是cm;
 *  & Sepal.Width（花萼宽度），单位是cm;
 *  & Petal.Length（花瓣长度），单位是cm;
 *  & Petal.Width（花瓣宽度），单位是cm;
 *  & 种类：Iris Setosa（山鸢尾）、Iris Versicolour（杂色鸢尾），以及Iris Virginica（维吉尼亚鸢尾）。

数据集输入之后，我们将数据集print

dataset iris:
    {'data': array([[5.1, 3.5, 1.4, 0.2],
           [4.9, 3. , 1.4, 0.2],
           [6.4, 3.2, 4.5, 1.5],
           [6.9, 3.1, 4.9, 1.5],
           [5.5, 2.3, 4. , 1.3],
    。。。
           [6.3, 2.5, 5. , 1.9],
           [6.5, 3. , 5.2, 2. ],
           [6.2, 3.4, 5.4, 2.3],
           [5.9, 3. , 5.1, 1.8]]), 'target': array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
           0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
           0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
           1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
           1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
           2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
           2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]), 'target_names': array(['setosa', 'versicolor', 'virginica'], dtype='<U10'), 'DESCR': '.. _iris_dataset:\n\nIris plants dataset\

打出纬度：

#demo one use iris dataset
    import numpy as np
    from sklearn import datasets
    
    X = datasets.load_iris()
    print('dataset iris .data shape:')
    #print(X)
    print(np.array(X.data).shape)
    
    # 查看默认的谱聚类效果
    from sklearn.cluster import SpectralClustering
    
    spectral = SpectralClustering()
    pred_y = spectral.fit_predict(X.data)
    print("pred_y")
    print(pred_y)
    print("pred_y.shape")
    print(np.array(pred_y).shape)
    
    """
    dataset iris .data shape:
    (150, 4)
    pred_y
    [6 0 0 0 6 6 0 0 0 0 6 0 0 0 6 6 6 6 6 6 6 6 0 6 0 0 6 6 6 0 0 6 6 6 0 0 6
     6 0 6 6 0 0 6 6 0 6 0 6 0 3 3 3 5 3 5 3 2 3 5 2 5 5 3 5 3 5 5 3 5 7 5 7 3
     3 3 3 3 3 5 5 5 5 7 5 3 3 3 5 5 5 3 5 2 5 5 5 3 2 5 4 7 4 7 4 1 5 4 4 4 4
     7 4 7 7 4 4 1 1 7 4 7 1 7 4 4 7 7 4 4 4 1 4 7 7 1 4 4 7 4 4 4 7 4 4 4 7 4
     4 7]
    pred_y.shape
    (150,)
    """

即按每行元素进行聚类，聚类得到结果输出为一个list，每个元素对应一个list

# 三、谱聚类函数 #

## 3.1 SpectralClustering ##

函数参数及用法：

[http://www.cnblogs.com/pinard/p/6235920.html][http_www.cnblogs.com_pinard_p_6235920.html]

[https://blog.csdn.net/fjssharpsword/article/details/79198054][https_blog.csdn.net_fjssharpsword_article_details_79198054]

[https://blog.csdn.net/weixin\_40042143/article/details/82462804][https_blog.csdn.net_weixin_40042143_article_details_82462804]

[https://www.bbsmax.com/A/NMAzABqJ9p/][https_www.bbsmax.com_A_NMAzABqJ9p]

from sklearn.cluster import SpectralClustering
    
    spectral = SpectralClustering()
    pred_y = spectral.fit_predict(X.data)

或者：

pred_y = SpectralClustering(n_clusters=k).fit_predict(X.data)
            print("Calinski-Harabasz Score with gamma=", gamma, "n_cluster=", k, "score=",
                  metrics.calinski_harabaz_score(X.data, pred_y))

## 3.2 输入 ##

输入

#gengrate our dataset
    X, y = datasets.make_blobs(n_samples=500, n_features=6, centers=5, cluster_std=[0.4, 0.3, 0.4, 0.3, 0.4], random_state=11)
    
    #print dataset shape
    print("X.shape and y.shape:")
    print(np.array(X).shape)
    print(np.array(y).shape)
    print("X is", X)

随机生成的X，500个数据点，每个数据点为6维

X.shape and y.shape:
    (500, 6)
    (500,)
    X is [[-7.76324808 -8.84656238  4.27901582  2.24092088 -9.01179124 -0.38420006]
     [-6.7332813  -9.41315963 -0.7936109   4.74079464 -1.07047174 -0.74584275]
     [-6.95129282 -9.51077056 -0.84525704  4.10274755 -1.28878541  0.14329266]
     ...
     [-3.52246694 -6.80041267  4.91296278  6.27507964 -3.01961225 -3.42770556]
     [ 7.76663892  7.82404263 -6.8318606   2.88728932 -9.76742041 -7.50407371]
     [ 8.40228838  7.63184647 -6.50528954  3.36423644 -9.48793872 -7.73365915]]

例如对于iris数据集，输入为：

## 3.3 输出 ##

与输入的维度有关，多少个样本点得到对应的输出。对于5维为  0到4,  对于3维为  0到2

Calinski-Harabasz Score with gamma= 0.01 n_clusters= 5 score: 23410.638949991386
    (500,)
    y_pred is [0 3 3 2 3 3 1 2 3 3 0 0 3 3 3 2 3 1 1 1 4 4 0 1 4 2 2 2 3 0 0 1 3 3 1 0 0
     2 4 2 2 1 1 3 2 4 0 0 1 4 4 0 2 2 0 1 4 4 2 2 0 4 4 4 1 3 2 4 4 2 4 1 1 0
     3 1 2 1 2 0 3 2 4 4 2 3 3 3 3 0 2 3 3 4 2 1 1 3 0 3 2 0 2 0 1 2 0 0 3 1 3
     0 2 2 2 4 0 2 2 3 0 3 1 3 3 0 0 1 0 2 4 2 3 4 1 1 1 1 3 1 4 0 4 4 4 4 4 0
     2 1 4 0 1 0 2 4 1 1 1 4 3 1 0 2 4 0 2 2 1 4 4 3 1 2 2 1 2 4 4 2 2 3 2 3 1
     3 0 3 4 1 4 1 4 3 2 0 3 2 0 1 4 4 0 4 0 2 4 3 2 4 1 0 1 3 2 0 4 4 2 4 1 1
     0 1 0 0 3 0 3 1 3 1 0 4 1 2 3 1 3 3 4 3 1 1 3 2 1 0 2 2 0 3 2 4 3 1 4 1 1
     0 1 0 1 1 1 4 0 0 2 3 4 4 2 0 1 3 1 0 3 0 2 4 3 1 0 1 4 2 0 4 0 4 4 1 4 4
     4 2 1 0 0 1 0 3 0 1 1 0 3 2 3 4 3 2 1 4 1 1 1 3 0 2 1 3 1 0 0 1 2 4 3 2 1
     3 3 2 0 2 2 0 0 3 3 0 4 2 1 4 2 4 0 3 1 4 3 3 0 1 2 4 1 0 4 2 2 2 0 4 3 2
     4 0 3 0 4 2 4 0 0 0 0 0 3 3 4 1 4 2 0 4 3 1 3 2 4 3 3 1 0 1 1 4 4 3 0 4 0
     3 3 2 3 4 3 1 0 4 2 2 4 4 4 2 2 3 0 4 1 3 0 0 1 2 0 3 0 1 2 0 3 0 3 4 1 1
     3 4 0 4 4 0 2 3 3 4 3 2 2 3 0 1 2 4 1 1 3 4 2 2 2 2 3 2 3 2 4 4 2 2 0 1 0
     0 1 3 3 3 1 1 0 1 4 4 2 2 0 4 1 4 2 2]
    Calinski-Harabasz Score with gamma= 0.1 n_clusters= 3 score: 1979.7709609161868
    (500,)
    y_pred is [1 1 1 2 1 1 0 2 1 1 1 1 1 1 1 2 1 0 0 0 1 1 1 0 1 2 2 2 1 1 1 0 1 1 0 1 1
     2 1 2 2 0 0 1 2 1 1 1 0 1 1 1 2 2 1 0 1 1 2 2 1 1 1 1 0 1 2 1 1 2 1 0 0 1
     1 0 2 0 2 1 1 2 1 1 2 1 1 1 1 1 2 1 1 1 2 0 0 1 1 1 2 1 2 1 0 2 1 1 1 0 1
     1 2 2 2 1 1 2 2 1 1 1 0 1 1 1 1 0 1 2 1 2 1 1 0 0 0 0 1 0 1 1 1 1 1 1 1 1
     2 0 1 1 0 1 2 1 0 0 0 1 1 0 1 2 1 1 2 2 0 1 1 1 0 2 2 0 2 1 1 2 2 1 2 1 0
     1 1 1 1 0 1 0 1 1 2 1 1 2 1 0 1 1 1 1 1 2 1 1 2 1 0 1 0 1 2 1 1 1 2 1 0 0
     1 0 1 1 1 1 1 0 1 0 1 1 0 2 1 0 1 1 1 1 0 0 1 2 0 1 2 2 1 1 2 1 1 0 1 0 0
     1 0 1 0 0 0 1 1 1 2 1 1 1 2 1 0 1 0 1 1 1 2 1 1 0 1 0 1 2 1 1 1 1 1 0 1 1
     1 2 0 1 1 0 1 1 1 0 0 1 1 2 1 1 1 2 0 1 0 0 0 1 1 2 0 1 0 1 1 0 2 1 1 2 0
     1 1 2 1 2 2 1 1 1 1 1 1 2 0 1 2 1 1 1 0 1 1 1 1 0 2 1 0 1 1 2 2 2 1 1 1 2
     1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 0 1 2 1 1 1 0 1 2 1 1 1 0 1 0 0 1 1 1 1 1 1
     1 1 2 1 1 1 0 1 1 2 2 1 1 1 2 2 1 1 1 0 1 1 1 0 2 1 1 1 0 2 1 1 1 1 1 0 0
     1 1 1 1 1 1 2 1 1 1 1 2 2 1 1 0 2 1 0 0 1 1 2 2 2 2 1 2 1 2 1 1 2 2 1 0 1
     1 0 1 1 1 0 0 1 0 1 1 2 2 1 1 0 1 2 2]

# 四、用coco标签进行谱聚类 #

## 4.1 coco互相关矩阵保存 ##

将coco的互相关矩阵存下来，用pickle存入

correlations = {}
        correlations.update(pp=A_B) #p(A/B)
        correlations.update(fp=notA_B) # P(not A/B)
        correlations.update(pf=A_notB)
        correlations.update(ff=notA_notB)
        with open('sk_spectral_cluster/coco_correlations.pkl', 'wb') as f:
            print("write correlations in sk_spectral_cluster/coco_correlations.pkl")
            pickle.dump(correlations, f)
        with open('sk_spectral_cluster/coco_names.pkl','wb') as name_file:
            print("write correlations in sk_spectral_cluster/coco_names.pkl")
            pickle.dump(names, name_file)

## 4.3 加载 ##

加载出来

# ----------------------load coco_correlations.pkl and load coco_names.pkl--------
    with open('sk_spectral_cluster/coco_correlations.pkl', 'rb') as f:
        print("loading coco_correlations.pkl ")
        correlations= pickle.load(f)
    
    with open('sk_spectral_cluster/coco_names.pkl', 'rb') as f:
        print("loading coco_names.pkl")
        names=pickle.load(f)
    
    coco_correlation_A_B=correlations['pp']
    print('coco label corrrelation matrix (80*80) : \n' , coco_correlation_A_B)

## 4.4 直接进行预测 ##

运用前面所讲的SpectralClustering 函数

#-----------------------spectral clustering----------------------------------------
    
    y_pred = SpectralClustering().fit_predict(coco_correlation_A_B)
    print ("Calinski-Harabasz Score:")
    print(metrics.calinski_harabaz_score(coco_correlation_A_B, y_pred))
    print("y_pred",y_pred)

但是会出现一定的warning

/env/lib/python3.6/site-packages/sklearn/cluster/spectral.py:462: 
    UserWarning: The spectral clustering API has changed. ``fit``now constructs an affinity matrix from data. 
    To use a custom affinity matrix, set ``affinity=precomputed``.
      warnings.warn("The spectral clustering API has changed. ``fit``"

聚类结果

Calinski-Harabasz Score:
    8.367635511918138
    y_pred [1 2 6 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 7 2 7 7 2
     2 2 4 0 4 0 0 0 4 2 2 0 2 2 2 2 0 2 0 4 0 0 2 4 2 5 5 5 0 5 2 3 3 2 3 3 0
     2 0 2 2 2 2]

## 4.5 affinity matrix有向图 ##

此warning非常有用，给出了如果想要使用affinity matrix，直接代码中添加程序，affinity=precomputed

adjacent matrix和affinity matrix之间的区别:

[https://blog.csdn.net/songkun123/article/details/80720938][https_blog.csdn.net_songkun123_article_details_80720938]

adjacent表示点与点之间的关系，affinity可以理解为点与边之间的关系。

更改代码

y_pred = SpectralClustering(affinity=precomputed).fit_predict(coco_correlation_A_B)

不可行，precomputed未定义不可用，可能需要将affinity matrix定义出来才可以运用。还是需要理解谱聚类中参数细节才可以运用这个。

## 4.6 调整获取最好参数 ##

根据 calinski\_harabaz\_score 来获取最佳参数。

# ---------------choose parameters by calinski_harabaz_score
    scores = []
    best_parameters = dict()
    for index, gamma in enumerate((0.01, 0.1, 1, 10)):
        for index, k in enumerate((3, 4, 5, 6, 7, 8, 9, 10)):
            pred_y = SpectralClustering(n_clusters=k,gamma=gamma).fit_predict(coco_correlation_A_B)
            print("Calinski-Harabasz Score with gamma=", gamma, "n_cluster=", k, "score=",
                  metrics.calinski_harabaz_score(coco_correlation_A_B, pred_y))
            tmp = dict()
            tmp['gamma'] = gamma
            tmp['n_cluster'] = k
            tmp['score'] = metrics.calinski_harabaz_score(coco_correlation_A_B, pred_y)
            best_parameters[metrics.calinski_harabaz_score(coco_correlation_A_B, pred_y)] = tmp
            scores.append(metrics.calinski_harabaz_score(coco_correlation_A_B, pred_y))
            print("pred_y:",pred_y)
    print(np.max(scores))
    print("max score:")
    print(best_parameters.get(np.max(scores)))

运行结果

env/bin/python sk_spectral_cluster/coco_spectral_cluster.py
    loading coco_correlations.pkl
    loading coco_names.pkl
    coco label corrrelation matrix (80*80) :
     [[1.00000000e+00 8.26410144e-01 7.04392284e-01 ... 4.03311258e-01
      4.45312500e-01 5.40000000e-01]
     [4.18382255e-02 1.00000000e+00 1.02719033e-01 ... 1.12582781e-02
      0.00000000e+00 5.71428571e-03]
     [1.34192234e-01 3.86532575e-01 1.00000000e+00 ... 3.84105960e-02
      7.81250000e-03 8.57142857e-03]
     ...
     [1.34812060e-02 7.43331876e-03 6.73948408e-03 ... 1.00000000e+00
      2.34375000e-02 8.57142857e-03]
     [1.26178775e-03 0.00000000e+00 1.16198001e-04 ... 1.98675497e-03
      1.00000000e+00 2.57142857e-02]
     [8.36764511e-03 1.74901618e-03 6.97188008e-04 ... 3.97350993e-03
      1.40625000e-01 1.00000000e+00]]
    Calinski-Harabasz Score without affinity:
    7.791262553375102
    y_pred [2 4 1 4 4 1 4 1 4 1 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 1 4 4 4 4 4 0 4 0 0 4
     4 4 6 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 4 3 4 7 7 7 5 7 4 6 6 4 6 6 5
     4 5 4 4 4 4]
    Calinski-Harabasz Score with n_cluster= 3 score= 9.492174347024601
    pred_y: [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
     0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 2 0 0 1 0 2 2 2 0 2 0 0 0 0 0 0 2
     0 0 0 0 0 0]
    Calinski-Harabasz Score with n_cluster= 4 score= 8.725501530904658
    pred_y: [1 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
     3 3 0 3 1 3 0 0 0 3 3 3 3 3 3 3 3 3 3 2 2 3 3 1 3 2 2 2 3 2 3 0 0 3 0 0 2
     3 3 3 3 3 3]
    Calinski-Harabasz Score with n_cluster= 5 score= 7.40234200110186
    pred_y: [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 3 3 0
     0 0 4 0 4 0 4 0 4 0 0 0 0 0 0 0 0 0 0 4 0 0 0 1 0 0 0 0 0 0 0 2 2 0 2 2 0
     0 0 0 0 0 0]
    Calinski-Harabasz Score with n_cluster= 6 score= 9.752144844448322
    pred_y: [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 4 4 0
     0 0 2 0 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 5 0 0 2 0 5 5 5 0 5 0 3 3 0 3 3 5
     0 0 0 0 0 0]
    Calinski-Harabasz Score with n_cluster= 7 score= 8.785937326387648
    pred_y: [1 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 2 0
     0 0 3 0 3 0 0 0 3 0 0 0 0 0 0 0 0 0 0 3 0 0 0 3 0 4 4 4 0 4 0 5 5 0 5 5 4
     0 0 0 0 0 0]
    Calinski-Harabasz Score with n_cluster= 8 score= 7.506167403594684
    pred_y: [1 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 6 6 0
     0 0 4 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 7 7 0 2 0 5 5 5 7 5 0 4 4 0 4 4 7
     0 7 0 0 0 0]
    Calinski-Harabasz Score with n_cluster= 9 score= 7.752484557844312
    pred_y: [1 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 7 7 0
     0 0 3 0 2 5 5 5 5 0 0 0 0 0 0 0 0 0 0 4 4 4 0 2 0 8 8 8 4 8 0 3 3 0 3 3 4
     0 4 0 0 0 0]
    Calinski-Harabasz Score with n_cluster= 10 score= 7.382406625549057
    pred_y: [1 2 5 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 6 2 6 6 2
     2 2 8 7 3 7 7 7 7 9 9 2 9 2 2 2 2 2 7 0 0 0 2 3 2 4 4 4 0 4 2 8 8 2 8 8 0
     2 0 2 2 2 2]
    9.752144844448322
    max score:
    {'n_cluster': 6, 'score': 9.752144844448322}

[https_scikit-learn.org_stable_modules_generated_sklearn.cluster.SpectralClustering.html_sklearn.cluster.SpectralClustering]: https://scikit-learn.org/stable/modules/generated/sklearn.cluster.SpectralClustering.html#sklearn.cluster.SpectralClustering
[Graph_Spectral Clustering_]: https://blog.csdn.net/weixin_36474809/article/details/89669623
[https_www.bbsmax.com_A_NMAzABqJ9p]: https://www.bbsmax.com/A/NMAzABqJ9p/
[https_blog.csdn.net_fjssharpsword_article_details_79198054]: https://blog.csdn.net/fjssharpsword/article/details/79198054
[https_blog.csdn.net_weixin_40042143_article_details_82462804]: https://blog.csdn.net/weixin_40042143/article/details/82462804
[http_www.cnblogs.com_pinard_p_6235920.html]: http://www.cnblogs.com/pinard/p/6235920.html
[https_blog.csdn.net_songkun123_article_details_80720938]: https://blog.csdn.net/songkun123/article/details/80720938