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ClusteringMeasurements[{{e1,e2,…},…},meas]

返回聚类样例 ei 的度量 meas.

ClusteringMeasurements[clusters,gt,meas]

假定真实聚类 gt.

更多信息和选项
Details and Options Details and Options
范例  
基本范例  
范围  
数据格式  
度量  
选项  
DistanceFunction  
FeatureExtractor  
应用  
可能存在的问题  
互动范例  
参见
相关指南
历史
按以下格式引用：

ClusteringMeasurements

ClusteringMeasurements[{{e1,e2,…},…},meas]

返回聚类样例 ei 的度量 meas.

ClusteringMeasurements[clusters,gt,meas]

假定真实聚类 gt.

更多信息和选项

  • ClusteringMeasurements 用于分析聚类过程的结果. 可以单独处理聚类数据，也可以将其与真实信息进行比较.
  • 可能的聚类规范 clusters 包括：
  • {{e1,e2,…},…}聚类样例的列表
    <|l1{e1,e2,…},…|>标签为 li 的聚类样例的关联
    {e1l1,e2l2,…}样例列表及其对应的聚类标签
    {e1,e2,…}{l1,l2,…}分开的样例列表和标签列表
    {e1,e2,…}cfun通过 ClassifierFunction 得到的隐式分类
  • 可能的真实分类规范 gt 包括：
  • {{e1,e2,…},…}示例聚类 (example cluster) 的列表
    <|l1{e1,e2,…},…|>样例列表关联，并用聚类作为标签
    {e1l1,e2l2,…}样例列表及其对应的聚类
    {e1,e2,…}{l1,l2,…}分开的样例和聚类的列表
    {l1,l2,…}每个示例的聚类标签列表
  • 度量 meas 可采用以下形式：
  • "Summary"度量汇总表
    "name"特定度量 "name"
    {"name1","name2",…}度量列表
    All所有可能的度量
    "Properties"可能的度量名称的列表
  • 度量可分为内部度量和外部度量.
  • 内部度量通常假设好的簇具有高分离度和低分散度.
  • 常见的分离度（簇间距离）的定义：
  • 常见的色散（簇内距离）的定义：
  • 符号 〈ei〉 和 〈e〉 表示聚类和整个数据集的平均值.
  • 支持的内部度量 meas 包括：
  • "CalinskiHarabasz"平均分离度和平均质心色散的比值（最大化）
    "DaviesBouldin"一对簇的质心色散和与质心分离度的平均最大比值（最小化）
    "Dunn"最小的最小分离度与数据集最大色散的比值（最大化）
    "RSquared"平均色散的均值与数据集质心色散的比值（肘部法则）
    "Silhouette"簇间距离与最近的簇的簇间距离之间的差的均值（最大化）
    "StandardDeviation"平均色散的均值（肘部法则）
  • 为每个聚类或每个样例返回结果的内部度量包括：
  • "DaviesBouldinScore"最大聚类相似度
    "RSquaredScore"聚类与整个数据集的色散之比
    "SilhouetteScore"簇间距离与最近的簇的簇间距离之间的差
    "SilhouetteScoreList"每个样例的轮廓值
    "StandardDeviationScore"平均色散
  • 外部度量将样例 ei 的聚类分配与其真实值 gt 进行比较.
  • 支持的外部度量包括：
  • "Purity"簇中按最多的真实值分配的样例的比例（最大化）
    "Rand"正确共享或不共享相同的真实值分配的 (ei,ej) 数据对的比例（最大化）
  • 为每个聚类或每个样例返回结果的外部度量包括：
  • "PurityScore"每个簇中共享相同真实值分配的样例的最大比例
    "RandScore"每个簇中正确共享或不共享相同的真实值分配的 (ei,ej) 数据对的比例
  • ClusteringMeasurements[…,{"prop1","prop2",…}] 可用于计算多个属性.
  • ClusteringMeasurements 支持以下选项：
  • DistanceFunction Automatic要使用的距离函数
    FeatureExtractor Identity怎样从样例中提取特征
  • 默认情况下，以下距离函数被用于不同类型的元素：
  • EuclideanDistance数值数据
    ImageDistance图像
    JaccardDissimilarity布尔数据
    EditDistance文本和名义序列
    Abs[DateDifference[#1,#2]]&日期和时间
    ColorDistance颜色
    GeoDistance地理空间数据
    Boole[SameQ[#1,#2]]&名义数据
    HammingDistance名义向量数据
    WarpingDistance数值序列

范例

打开所有单元 关闭所有单元

基本范例  (2)

获取聚类度量的汇总：

Wolfram Language code: ClusteringMeasurements[{{{0.79, 0.56}, {0.71, 0.48}}, {{0.48, 0.033}, {0.66, -0.18}, {0.71, -0.021}}, {{-0.88, 0.12}, {-0.90, 0.092}}}, "Summary"]

计算一组聚类的轮廓分数：

Wolfram Language code: ClusteringMeasurements[<|"A" -> {RGBColor[0.876608492574193, 0.9473400809250909, 0.25067253612711804], RGBColor[0.9272661633421619, 0.9363261805264331, 0.32353349989516933], RGBColor[0.8243947208728843, 0.9364356599106853, 0.435400674336722], RGBColor[0.9057946589188117, 0.9381773467978105, 0.016447357477133107]}, "B" -> {RGBColor[0.5219642502018771, 0.5017220835545622, 0.9175588985597154], RGBColor[0.08280489339492836, 0.41421577414235555, 0.9357625935021598], RGBColor[0.21636803014287387, 0.23382792797523244, 0.5159899501126328], RGBColor[0.40815049823996064, 0.5740819900353236, 0.9231104239323873], RGBColor[0.08642430807107115, 0.281127551566819, 0.6649469000247543], RGBColor[0.3506031248835497, 0.42471407043932174, 0.8278435761417782], RGBColor[0.16525562567118945, 0.5125318540604438, 0.8296464274479893]}, "C" -> {RGBColor[0.08622342695413243, 0.71879922942928, 0.765413236947557], RGBColor[0.4238352228971154, 0.6931876506845667, 0.7117293054980371], RGBColor[0.4712616494486832, 0.8178536200085944, 0.8565962988336242], RGBColor[0.1496529618394109, 0.701645179917191, 0.7804714896485088], RGBColor[0.6973467249643173, 0.8294373633128278, 0.8957452203075256], RGBColor[0.7093533212993834, 0.8150926594568284, 0.7811722698229906], RGBColor[0.04515994704540893, 0.935387695243086, 0.21554127051988736], RGBColor[0.1505455345874276, 0.9945961988546483, 0.47401708153690225]}|>, "SilhouetteScore"]

用条形图可视化分数：

Wolfram Language code: BarChart[%, ChartLabels -> Automatic]

计算并绘制单个样例的轮廓分数：

Wolfram Language code: ClusteringMeasurements[{{RGBColor[0.876608492574193, 0.9473400809250909, 0.25067253612711804], RGBColor[0.9272661633421619, 0.9363261805264331, 0.32353349989516933], RGBColor[0.8243947208728843, 0.9364356599106853, 0.435400674336722], RGBColor[0.9057946589188117, 0.9381773467978105, 0.016447357477133107]}, {RGBColor[0.5219642502018771, 0.5017220835545622, 0.9175588985597154], RGBColor[0.08280489339492836, 0.41421577414235555, 0.9357625935021598], RGBColor[0.21636803014287387, 0.23382792797523244, 0.5159899501126328], RGBColor[0.40815049823996064, 0.5740819900353236, 0.9231104239323873], RGBColor[0.08642430807107115, 0.281127551566819, 0.6649469000247543], RGBColor[0.3506031248835497, 0.42471407043932174, 0.8278435761417782], RGBColor[0.16525562567118945, 0.5125318540604438, 0.8296464274479893]}, {RGBColor[0.08622342695413243, 0.71879922942928, 0.765413236947557], RGBColor[0.4238352228971154, 0.6931876506845667, 0.7117293054980371], RGBColor[0.4712616494486832, 0.8178536200085944, 0.8565962988336242], RGBColor[0.1496529618394109, 0.701645179917191, 0.7804714896485088], RGBColor[0.6973467249643173, 0.8294373633128278, 0.8957452203075256], RGBColor[0.7093533212993834, 0.8150926594568284, 0.7811722698229906], RGBColor[0.04515994704540893, 0.935387695243086, 0.21554127051988736], RGBColor[0.1505455345874276, 0.9945961988546483, 0.47401708153690225]}}, "SilhouetteScoreList"]
Wolfram Language code: BarChart[%, ChartStyle -> {ColorData[96], None}]

范围  (9)

数据格式  (5)

用列表明确指定簇：

Wolfram Language code: ClusteringMeasurements[{{{0.79, 0.56}, {0.71, 0.48}}, {{0.48, 0.033}, {0.66, -0.18}, {0.71, -0.021}}, {{-0.88, 0.12}, {-0.90, 0.092}}}, "DaviesBouldin"]

用关联明确指定簇：

Wolfram Language code: ClusteringMeasurements[<|1 -> {{0.79, 0.56}, {0.71, 0.48}}, 2 -> {{0.48, 0.033}, {0.66, -0.18}, {0.71, -0.021}}, 3 -> {{-0.88, 0.12}, {-0.9, 0.092}}|>, "DaviesBouldin"]

用样例和分配之间的规则列表指定簇：

Wolfram Language code: ClusteringMeasurements[{{0.79, 0.56} -> 1, {0.71, 0.48} -> 1, {0.48, 0.033} -> 2, {0.66, -0.18} -> 2, {0.71, -0.021} -> 2, {-0.88, 0.12} -> 3, {-0.9, 0.092} -> 3}, "DaviesBouldin"]

用样例和分配之间的规则指定簇：

Wolfram Language code: ClusteringMeasurements[{{0.79, 0.56}, {0.71, 0.48}, {0.48, 0.033}, {0.66, -0.18}, {0.71, -0.021}, {-0.88, 0.12}, {-0.9, 0.092}} -> {1, 1, 2, 2, 2, 3, 3}, "DaviesBouldin"]

用样例和 ClassifierFunction[…] 之间的规则指定簇：

Wolfram Language code: data = {{0.79, 0.56}, {0.71, 0.48}, {0.48, 0.033}, {0.66, -0.18}, {0.71, -0.021}, {-0.88, 0.12}, {-0.9, 0.092}};
Wolfram Language code: cfun = ClusterClassify[data]
Wolfram Language code: ClusteringMeasurements[data -> cfun, "DaviesBouldin"]

度量  (4)

计算聚类属性：

Wolfram Language code: ClusteringMeasurements[{{RGBColor[0.876608492574193, 0.9473400809250909, 0.25067253612711804], RGBColor[0.9272661633421619, 0.9363261805264331, 0.32353349989516933], RGBColor[0.8243947208728843, 0.9364356599106853, 0.435400674336722]}, {RGBColor[0.5219642502018771, 0.5017220835545622, 0.9175588985597154], RGBColor[0.08280489339492836, 0.41421577414235555, 0.9357625935021598], RGBColor[0.21636803014287387, 0.23382792797523244, 0.5159899501126328], RGBColor[0.40815049823996064, 0.5740819900353236, 0.9231104239323873]}, {RGBColor[0.08622342695413243, 0.71879922942928, 0.765413236947557], RGBColor[0.4238352228971154, 0.6931876506845667, 0.7117293054980371], RGBColor[0.1496529618394109, 0.701645179917191, 0.7804714896485088]}, {RGBColor[0.3779129543048858, 0.9299217761823355, 0.05300428332934981], RGBColor[0.47933167047242464, 0.8484812906095962, 0.25070732863307543], RGBColor[0.2639731675000303, 0.8447135871358933, 0.17741459618375854], RGBColor[0.10553834214315283, 0.7432472973816968, 0.23144281661937094]}, {RGBColor[0.12261520318947783, 0.02938259624263395, 0.1917186445336998]}}, "Dunn"]

计算一组属性：

Wolfram Language code: ClusteringMeasurements[{{RGBColor[0.876608492574193, 0.9473400809250909, 0.25067253612711804], RGBColor[0.9272661633421619, 0.9363261805264331, 0.32353349989516933], RGBColor[0.8243947208728843, 0.9364356599106853, 0.435400674336722]}, {RGBColor[0.5219642502018771, 0.5017220835545622, 0.9175588985597154], RGBColor[0.08280489339492836, 0.41421577414235555, 0.9357625935021598], RGBColor[0.21636803014287387, 0.23382792797523244, 0.5159899501126328], RGBColor[0.40815049823996064, 0.5740819900353236, 0.9231104239323873]}, {RGBColor[0.08622342695413243, 0.71879922942928, 0.765413236947557], RGBColor[0.4238352228971154, 0.6931876506845667, 0.7117293054980371], RGBColor[0.1496529618394109, 0.701645179917191, 0.7804714896485088]}, {RGBColor[0.3779129543048858, 0.9299217761823355, 0.05300428332934981], RGBColor[0.47933167047242464, 0.8484812906095962, 0.25070732863307543], RGBColor[0.2639731675000303, 0.8447135871358933, 0.17741459618375854], RGBColor[0.10553834214315283, 0.7432472973816968, 0.23144281661937094]}, {RGBColor[0.12261520318947783, 0.02938259624263395, 0.1917186445336998]}}, {"Dunn", "RSquared"}]

计算得出全局度量的汇总：

Wolfram Language code: ClusteringMeasurements[{{RGBColor[0.876608492574193, 0.9473400809250909, 0.25067253612711804], RGBColor[0.9272661633421619, 0.9363261805264331, 0.32353349989516933], RGBColor[0.8243947208728843, 0.9364356599106853, 0.435400674336722]}, {RGBColor[0.5219642502018771, 0.5017220835545622, 0.9175588985597154], RGBColor[0.08280489339492836, 0.41421577414235555, 0.9357625935021598], RGBColor[0.21636803014287387, 0.23382792797523244, 0.5159899501126328], RGBColor[0.40815049823996064, 0.5740819900353236, 0.9231104239323873]}, {RGBColor[0.08622342695413243, 0.71879922942928, 0.765413236947557], RGBColor[0.4238352228971154, 0.6931876506845667, 0.7117293054980371], RGBColor[0.1496529618394109, 0.701645179917191, 0.7804714896485088]}, {RGBColor[0.3779129543048858, 0.9299217761823355, 0.05300428332934981], RGBColor[0.47933167047242464, 0.8484812906095962, 0.25070732863307543], RGBColor[0.2639731675000303, 0.8447135871358933, 0.17741459618375854], RGBColor[0.10553834214315283, 0.7432472973816968, 0.23144281661937094]}, {RGBColor[0.12261520318947783, 0.02938259624263395, 0.1917186445336998]}}, "Summary"]

获取可用属性列表：

Wolfram Language code: ClusteringMeasurements[{{RGBColor[0.876608492574193, 0.9473400809250909, 0.25067253612711804], RGBColor[0.9272661633421619, 0.9363261805264331, 0.32353349989516933], RGBColor[0.8243947208728843, 0.9364356599106853, 0.435400674336722]}, {RGBColor[0.5219642502018771, 0.5017220835545622, 0.9175588985597154], RGBColor[0.08280489339492836, 0.41421577414235555, 0.9357625935021598], RGBColor[0.21636803014287387, 0.23382792797523244, 0.5159899501126328], RGBColor[0.40815049823996064, 0.5740819900353236, 0.9231104239323873]}, {RGBColor[0.08622342695413243, 0.71879922942928, 0.765413236947557], RGBColor[0.4238352228971154, 0.6931876506845667, 0.7117293054980371], RGBColor[0.1496529618394109, 0.701645179917191, 0.7804714896485088]}, {RGBColor[0.3779129543048858, 0.9299217761823355, 0.05300428332934981], RGBColor[0.47933167047242464, 0.8484812906095962, 0.25070732863307543], RGBColor[0.2639731675000303, 0.8447135871358933, 0.17741459618375854], RGBColor[0.10553834214315283, 0.7432472973816968, 0.23144281661937094]}, {RGBColor[0.12261520318947783, 0.02938259624263395, 0.1917186445336998]}}, "Properties"]

指定真实值的情况下获取可用属性列表：

Wolfram Language code: ClusteringMeasurements[{{RGBColor[0.876608492574193, 0.9473400809250909, 0.25067253612711804], RGBColor[0.9272661633421619, 0.9363261805264331, 0.32353349989516933], RGBColor[0.8243947208728843, 0.9364356599106853, 0.435400674336722]}, {RGBColor[0.5219642502018771, 0.5017220835545622, 0.9175588985597154], RGBColor[0.08280489339492836, 0.41421577414235555, 0.9357625935021598], RGBColor[0.21636803014287387, 0.23382792797523244, 0.5159899501126328], RGBColor[0.40815049823996064, 0.5740819900353236, 0.9231104239323873]}, {RGBColor[0.08622342695413243, 0.71879922942928, 0.765413236947557], RGBColor[0.4238352228971154, 0.6931876506845667, 0.7117293054980371], RGBColor[0.1496529618394109, 0.701645179917191, 0.7804714896485088]}, {RGBColor[0.3779129543048858, 0.9299217761823355, 0.05300428332934981], RGBColor[0.47933167047242464, 0.8484812906095962, 0.25070732863307543], RGBColor[0.2639731675000303, 0.8447135871358933, 0.17741459618375854], RGBColor[0.10553834214315283, 0.7432472973816968, 0.23144281661937094]}, {RGBColor[0.12261520318947783, 0.02938259624263395, 0.1917186445336998]}}, <|1 -> {RGBColor[0.876608492574193, 0.9473400809250909, 0.25067253612711804], RGBColor[0.9272661633421619, 0.9363261805264331, 0.32353349989516933], RGBColor[0.8243947208728843, 0.9364356599106853, 0.435400674336722]}, 2 -> {RGBColor[0.5219642502018771, 0.5017220835545622, 0.9175588985597154], RGBColor[0.08280489339492836, 0.41421577414235555, 0.9357625935021598], RGBColor[0.40815049823996064, 0.5740819900353236, 0.9231104239323873]}, 3 -> {RGBColor[0.08622342695413243, 0.71879922942928, 0.765413236947557], RGBColor[0.4238352228971154, 0.6931876506845667, 0.7117293054980371], RGBColor[0.1496529618394109, 0.701645179917191, 0.7804714896485088]}, 4 -> {RGBColor[0.3779129543048858, 0.9299217761823355, 0.05300428332934981], RGBColor[0.47933167047242464, 0.8484812906095962, 0.25070732863307543], RGBColor[0.2639731675000303, 0.8447135871358933, 0.17741459618375854], RGBColor[0.10553834214315283, 0.7432472973816968, 0.23144281661937094]}, 5 -> {RGBColor[0.12261520318947783, 0.02938259624263395, 0.1917186445336998], RGBColor[0.21636803014287387, 0.23382792797523244, 0.5159899501126328]}|>, "Properties"]

选项  (2)

DistanceFunction  (1)

自定义距离函数：

Wolfram Language code: ClusteringMeasurements[{{"king", "kingdom", "kingly"}, {"dutchess", "duchy"}}, "Dunn", DistanceFunction -> EditDistance]

FeatureExtractor  (1)

自定义特征提取器，对样例进行预处理：

Wolfram Language code: extractor = NetDrop[NetModel["ShuffleNet-V2 Trained on ImageNet Competition Data"], -2];
Wolfram Language code: ClusteringMeasurements[{{[image], [image], [image]}, {[image], [image], [image]}}, "Dunn", FeatureExtractor -> extractor]

应用  (2)

求合成数据集的最优簇数：

Wolfram Language code: SeedRandom[1234];clusters = Map[m  RandomVariate[MultinormalDistribution[m, .01IdentityMatrix[2]], 20], RandomReal[{-1, 1}, {5, 2}]];
Wolfram Language code: ListPlot[clusters, PlotTheme -> "Minimal"]

随机排列，合并不同的组：

Wolfram Language code: data = RandomSample@Catenate[clusters];

k 取不同的值，计算 k-均值聚类：

Wolfram Language code: groupings = Table[FindClusters[data, n, Method -> "KMeans"], {n, 1, 10}];

测量每一组聚类的邓恩指数（Dunn index）：

Wolfram Language code: ClusteringMeasurements[#, "Dunn"]& /@ groupings

最佳聚类为 5 个聚类：

Wolfram Language code: ListPlot[%, Filling -> Bottom]

聚类过程能够恢复所有原始的分组：

Wolfram Language code: ListPlot[groupings[[5]], PlotTheme -> "Minimal"]

可视化聚类中每个点的轮廓图（Silhouette）分数：

Wolfram Language code: SeedRandom[2345];data = Catenate@Map[m  RandomVariate[MultinormalDistribution[m, .01IdentityMatrix[2]], 20], RandomReal[{-1, 1}, {5, 2}]];

计算给定 k 的 k 均值聚类：

Wolfram Language code: FindClusters[data, 4, Method -> "KMeans"]//Short

可视化 Silhouette 分数：

Wolfram Language code: BarChart[ClusteringMeasurements[%, "SilhouetteScoreList"], ChartStyle -> {ColorData[97], None}]

计算不同 k 值的 k 均值聚类：

Wolfram Language code: groupings = Table[FindClusters[data, n, Method -> "KMeans"], {n, {3, 4, 5, 6, 7}}];

用相应的 Silhouette 剖面图绘制每一组聚类：

Wolfram Language code: Table[ GraphicsRow[{ ListPlot[groupings[[i]], PlotTheme -> "Minimal", PlotStyle -> PointSize[Medium]], BarChart[ReverseSort /@ ClusteringMeasurements[groupings[[i]], "SilhouetteScoreList"], ChartStyle -> {ColorData[97], None}, PlotRange -> {-.5, 1}]}, ImageSize -> Medium], {i, 1, Length[groupings], 1}]

可能存在的问题  (1)

外部度量需要指定真实值：

Wolfram Language code: ClusteringMeasurements[{{RGBColor[0.876608492574193, 0.9473400809250909, 0.25067253612711804], RGBColor[0.9272661633421619, 0.9363261805264331, 0.32353349989516933], RGBColor[0.8243947208728843, 0.9364356599106853, 0.435400674336722]}, {RGBColor[0.5219642502018771, 0.5017220835545622, 0.9175588985597154], RGBColor[0.08280489339492836, 0.41421577414235555, 0.9357625935021598], RGBColor[0.21636803014287387, 0.23382792797523244, 0.5159899501126328]}, {RGBColor[0.40815049823996064, 0.5740819900353236, 0.9231104239323873], RGBColor[0.08622342695413243, 0.71879922942928, 0.765413236947557], RGBColor[0.4238352228971154, 0.6931876506845667, 0.7117293054980371]}}, "Purity"]
Wolfram Language code: ClusteringMeasurements[{{RGBColor[0.876608492574193, 0.9473400809250909, 0.25067253612711804], RGBColor[0.9272661633421619, 0.9363261805264331, 0.32353349989516933], RGBColor[0.8243947208728843, 0.9364356599106853, 0.435400674336722]}, {RGBColor[0.5219642502018771, 0.5017220835545622, 0.9175588985597154], RGBColor[0.08280489339492836, 0.41421577414235555, 0.9357625935021598], RGBColor[0.21636803014287387, 0.23382792797523244, 0.5159899501126328]}, {RGBColor[0.40815049823996064, 0.5740819900353236, 0.9231104239323873], RGBColor[0.08622342695413243, 0.71879922942928, 0.765413236947557], RGBColor[0.4238352228971154, 0.6931876506845667, 0.7117293054980371]}}, {{RGBColor[0.876608492574193, 0.9473400809250909, 0.25067253612711804], RGBColor[0.9272661633421619, 0.9363261805264331, 0.32353349989516933], RGBColor[0.8243947208728843, 0.9364356599106853, 0.435400674336722]}, {RGBColor[0.5219642502018771, 0.5017220835545622, 0.9175588985597154], RGBColor[0.08280489339492836, 0.41421577414235555, 0.9357625935021598], RGBColor[0.21636803014287387, 0.23382792797523244, 0.5159899501126328], RGBColor[0.40815049823996064, 0.5740819900353236, 0.9231104239323873]}, {RGBColor[0.08622342695413243, 0.71879922942928, 0.765413236947557], RGBColor[0.4238352228971154, 0.6931876506845667, 0.7117293054980371]}}, "Purity"]

互动范例  (1)

对点列表进行聚类以交互方式测量 Calinski–Harabasz 指数：

Wolfram Language code: Manipulate[ Show[ ListPlot[groups = Values@KeySort@GroupBy[{...}, Nearest[pt -> Automatic]], PlotTheme -> "NoAxes", PlotLabel -> StringForm["Calinski-Harabasz Index: ``", ClusteringMeasurements[groups, "CalinskiHarabasz"]]], VoronoiMesh[pt, 2{{-1, 1}, {-1, 1}}, PlotTheme -> "Lines", MeshCellStyle -> {1} -> Gray], PlotRange -> {{-1, 1}, {-1, 1}}, ImageSize -> Medium, Frame -> True ], {{pt, .3{{-1, 0}, {0, -1}, {1, 1}}}, Locator, LocatorAutoCreate -> 2}, {groups, ControlType -> None}, AppearanceElements -> None ]
Wolfram Research (2022)，ClusteringMeasurements，Wolfram 语言函数，https://reference.wolfram.com/language/ref/ClusteringMeasurements.html.

文本

Wolfram Research (2022)，ClusteringMeasurements，Wolfram 语言函数，https://reference.wolfram.com/language/ref/ClusteringMeasurements.html.

CMS

Wolfram 语言. 2022. "ClusteringMeasurements." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/ClusteringMeasurements.html.

APA

Wolfram 语言. (2022). ClusteringMeasurements. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/ClusteringMeasurements.html 年

BibTeX

@misc{reference.wolfram_2026_clusteringmeasurements, author="Wolfram Research", title="{ClusteringMeasurements}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/ClusteringMeasurements.html}", note=[Accessed: 15-August-2026]}

BibLaTeX

@online{reference.wolfram_2026_clusteringmeasurements, organization={Wolfram Research}, title={ClusteringMeasurements}, year={2022}, url={https://reference.wolfram.com/language/ref/ClusteringMeasurements.html}, note=[Accessed: 15-August-2026]}