SPSS聚类分析实战指南：K均值与系统聚类详解

Introduction

Cluster analysis, often perceived as an esoteric statistical technique, is fundamentally a method for discovering inherent groupings within data. The ancient adage "birds of a feather flock together" perfectly encapsulates its core principle. Technically, it is a multivariate statistical method used to classify a set of observations into subsets (called clusters) so that observations in the same cluster are similar in some sense. This technique is indispensable across diverse fields such as economics, medical research, and market studies, where classification based on multiple variables—rather than a single factor—is required for a comprehensive understanding. For instance, categorizing supermarket products effectively necessitates considering variables like usage, price range, and origin simultaneously. Cluster analysis provides a quantitative framework to describe relationships between items and establish grouping rules tailored to specific needs.

聚类分析又称群分析，是多元统计学中应用广泛的数据分类方法，通过将具有相似性的元素归为同一类别来实现数据分组。，常被视为一种深奥的统计技术，其本质是一种发现数据内在分组的方法。古老的谚语“物以类聚，人以群分”完美概括了其核心原理。从技术上讲，它是一种多元统计方法，用于将一组观测值分类为子集（称为聚类），使得同一聚类内的观测值在某种意义上具有相似性。这项技术在经济学、医学研究和市场研究等众多领域不可或缺，在这些领域中，通常需要基于多个变量（而非单一因素）进行分类，以获得全面的理解。例如，要对超市商品进行有效分类，必须同时考虑用途、价格档次和产地等多个变量。聚类分析又称群分析，是多元统计学中应用广泛的数据分类方法，通过将具有相似性的元素归为同一类别来实现数据分组。提供了一个量化框架来描述项目之间的关系，并根据特定需求建立分组规则。

Key Concepts in Cluster Analysis

At its heart, cluster analysis is an exploratory data analysis tool. There is no single "correct" outcome; obtaining an objective and robust clustering result typically requires experimentation with different methods and parameters. It's a process of interpretation rather than definitive proof.

聚类分析又称群分析，是多元统计学中应用广泛的数据分类方法，通过将具有相似性的元素归为同一类别来实现数据分组。本质上是一种探索性数据分析工具。不存在单一的“正确”结果；要获得客观且稳健的聚类结果，通常需要尝试不同的方法和参数。这是一个解释的过程，而非确证性的证明。

SPSS, a widely used statistical software, provides two primary clustering methods, each with distinct characteristics and applications.

SPSS作为一款广泛使用的统计软件，提供了两种主要的聚类方法，每种方法都有其独特的特点和应用场景。

1. K-Means Clustering (K-Center Point Clustering)

K-Means Clustering, also known as K-Center Point clustering, is based on algorithms like MacQueen's. It is designed for efficiency with large datasets, capable of handling hundreds of thousands of records.

K均值聚类，也称为K中心点聚类，基于MacQueen等算法。它专为处理大型数据集而设计，效率高，能够处理数十万条记录。

Core Mechanism: The process starts by the user specifying the desired number of clusters (K). The algorithm then selects K initial cluster centers (seeds). It proceeds iteratively, alternating between two steps: (1) assigning each data point to the cluster whose center is nearest (using Euclidean distance), and (2) recalculating the center (mean) of each newly formed cluster. This iteration continues until cluster assignments stabilize.

核心机制：该过程首先由用户指定期望的聚类数量（K）。然后算法选择K个初始聚类中心（种子点）。随后进行迭代，交替执行两个步骤：(1) 将每个数据点分配到中心点最近的聚类（使用欧氏距离），(2) 重新计算每个新形成聚类的中心（均值）。此迭代持续进行，直到聚类分配稳定为止。

Key Characteristics & Limitations:

• Requires Pre-specified K: The user must decide the number of clusters beforehand.
• Computational Efficiency: It is faster for large samples, hence termed "Quick Cluster."
• Sample Clustering Only: It can only cluster cases (rows), not variables (columns).
• Variable Type Restriction: It requires all input variables to be continuous.

主要特点与限制：

• 需要预先指定K：用户必须事先决定聚类的数量。
• 计算效率高：对于大样本速度更快，因此被称为“快速聚类”。
• 仅用于样品聚类：只能对样品（行）进行聚类，不能对变量（列）聚类。
• 变量类型限制：要求所有输入变量均为连续变量。

Application Example: Clustering 20 samples. A potential result might be: Samples 1, 5, 16 form Cluster 1; samples 8, 9, 17, 19 form Cluster 2; samples 3, 11, 13 form Cluster 3; and the remaining samples form Cluster 4.

应用示例：对20个样品进行聚类分析又称群分析，是多元统计学中应用广泛的数据分类方法，通过将具有相似性的元素归为同一类别来实现数据分组。。一个可能的结果是：样品1、5、16聚为第一类；样品8、9、17、19聚为第二类；样品3、11、13聚为第三类；其余样品聚为第四类。

Result Validation - ANOVA Table: After clustering, it's crucial to check if the chosen variables meaningfully differentiate the clusters. Including irrelevant variables can degrade results. Using the ANOVA table option in SPSS, you can perform a one-way analysis of variance to test if the mean values of each variable differ significantly across the formed clusters. A significant result suggests the variable contributes to the cluster separation.

结果验证 - ANOVA表：聚类后，必须检查所选变量是否能有效区分不同聚类。引入无关变量会降低聚类效果。使用SPSS中的ANOVA表选项，可以进行单因素方差分析，以检验每个变量在已形成的各类间的均值是否存在显著差异。显著的结果表明该变量对聚类区分有贡献。

2. Hierarchical Clustering (Systematic Clustering)

Hierarchical Clustering builds a hierarchy of clusters, which can be visualized as a tree structure (dendrogram). It can cluster both cases and variables, and it accepts both continuous and categorical variables. A key application for variable clustering is dimension reduction, where highly correlated variables are grouped together.

系统聚类也称为分层聚类法，通过逐步合并最接近的类别来实现聚类，可处理样品和变量聚类，支持连续和分类变量。会建立一个聚类的层次结构，可以可视化为树状结构（树状图聚类分析的可视化图表，纵坐标表示距离，通过横线显示类别划分，需要结合尺子测量来确定不同距离下的类别数量。）。它既可以聚类样品，也可以聚类变量，并且接受连续变量和分类变量。变量聚类的一个关键应用是降维，即将高度相关的变量分组在一起。

Core Mechanism: The process starts with each observation (or variable) as its own cluster. At each step, the two closest clusters (based on a chosen distance measure for cases or a similarity measure for variables) are merged. This process repeats until all observations are merged into a single cluster. The entire sequence is recorded, allowing the analyst to choose the appropriate number of clusters by "cutting" the tree at a desired level.

核心机制：该过程开始时，每个观测值（或变量）自成一类。在每一步中，将两个最接近的聚类（基于为样品选择的距离度量或为变量选择的相似性度量）进行合并。此过程重复进行，直到所有观测值合并为一个聚类。整个过程被记录下来，允许分析者通过在期望的层级“切割”树状图聚类分析的可视化图表，纵坐标表示距离，通过横线显示类别划分，需要结合尺子测量来确定不同距离下的类别数量。来选择适当的聚类数量。

Interpreting Hierarchical Clustering Outputs

The results of hierarchical clustering are primarily interpreted through two graphical tools.

系统聚类也称为分层聚类法，通过逐步合并最接近的类别来实现聚类，可处理样品和变量聚类，支持连续和分类变量。的结果主要通过两种图形工具进行解读。

The Icicle Plot

An Icicle Plot provides a vertical representation of the clustering process. Reading typically starts from the bottom.

冰柱图聚类分析结果的可视化工具，从图底端开始分析，通过白色间隙显示聚类过程，帮助理解样本如何被逐步分类。以垂直方式展示聚类过程。解读通常从底部开始。

Interpretation: At the very bottom (where the column count equals the total number of items), each item is a separate cluster (represented by a vertical white space between bars). As you move upward, clusters merge. The number of distinct vertical columns at any horizontal level indicates the number of clusters present at that stage of the agglomeration process. For example, if you have 10 samples, the bottom shows 10 columns (9 white spaces). Further up, you might see 8 white spaces, indicating 9 clusters, and so on.

解读：在最底部（列数等于项目总数），每个项目是一个独立的聚类（由条形图之间的垂直白色间隙表示）。向上移动时，聚类开始合并。在任何水平层级上，不同的垂直列的数量表示在该聚合阶段存在的聚类数量。例如，如果有10个样品，底部会显示10列（9个白色间隙）。再往上，你可能看到8个白色间隙，表示9个类，依此类推。

The Dendrogram (Tree Diagram)

The Dendrogram is the most common visualization. The vertical axis represents the distance or dissimilarity at which clusters are merged.

树状图聚类分析的可视化图表，纵坐标表示距离，通过横线显示类别划分，需要结合尺子测量来确定不同距离下的类别数量。是最常见的可视化方式。纵轴代表聚类合并时的距离或相异性。

Interpretation: To determine the number of clusters, imagine drawing a horizontal line across the dendrogram at a chosen distance level. The number of vertical lines this horizontal line intersects equals the number of clusters at that level. The structure of the tree shows which items are grouped together most closely. The choice of where to cut the tree (i.e., how many clusters to retain) is not automated; it requires substantive knowledge of the data and the research context to decide what level of granularity is most meaningful.

解读：要确定聚类数量，可以想象在选定的距离水平上画一条横线穿过树状图聚类分析的可视化图表，纵坐标表示距离，通过横线显示类别划分，需要结合尺子测量来确定不同距离下的类别数量。。这条横线相交的垂直线的数量就等于该水平下的聚类数量。树的结构显示了哪些项目被最紧密地分组在一起。在何处切割树状图聚类分析的可视化图表，纵坐标表示距离，通过横线显示类别划分，需要结合尺子测量来确定不同距离下的类别数量。（即保留多少个聚类）并非自动决定；这需要基于对数据和研究背景的实质性了解，来判断何种粒度水平最有意义。

Main Analysis: Bridging the Gap Between Operation and Interpretation

A common challenge in applied statistics, and cluster analysis is no exception, is the disconnect between software operation and result interpretation. SPSS makes the mechanics of clustering—clicking through dialog boxes—remarkably simple. The real difficulty lies in mastering the underlying principles. Knowing which method (K-Means vs. Hierarchical) to choose, how to prepare and standardize data, determining the optimal number of clusters, and, most importantly, interpreting the clusters in a substantively meaningful way all require a systematic understanding of statistical theory.

应用统计学中的一个常见挑战是软件操作与结果解读之间的脱节，聚类分析又称群分析，是多元统计学中应用广泛的数据分类方法，通过将具有相似性的元素归为同一类别来实现数据分组。也不例外。SPSS使得聚类的操作过程——点击对话框——异常简单。真正的困难在于掌握其基本原理。知道选择哪种方法（K均值 vs. 系统聚类也称为分层聚类法，通过逐步合并最接近的类别来实现聚类，可处理样品和变量聚类，支持连续和分类变量。）、如何准备和标准化数据、确定最佳聚类数量，以及最重要的是，以具有实质意义的方式解读聚类结果，所有这些都需要对统计理论有系统性的理解。

This foundational knowledge transforms the analyst from a mere button-clicker into a competent decision-maker. It enables you to:

• Justify your methodological choices.
• Diagnose potential issues (e.g., using inappropriate variables).
• Extract actionable insights from the cluster labels.

这种基础知识将分析者从单纯的按钮点击者转变为有能力的决策者。它使你能够：

• 为你选择的方法提供理由。
• 诊断潜在问题（例如，使用了不合适的变量）。
• 从聚类标签中提取可操作的见解。

(Note: Due to length considerations, the detailed step-by-step walkthrough of the provided case studies and the promotional content for specific books and courses have been condensed. The core technical explanation and framework above provide the essential understanding of cluster analysis in SPSS.)

（注：考虑到篇幅，所提供的案例研究的详细逐步讲解以及特定书籍和课程的推广内容已进行浓缩。上述核心技术解释和框架提供了对SPSS中聚类分析又称群分析，是多元统计学中应用广泛的数据分类方法，通过将具有相似性的元素归为同一类别来实现数据分组。的基本理解。）

Conclusion

Cluster analysis is a powerful, intuitive, yet nuanced tool for exploratory data analysis. Moving beyond the "black box" of software procedures to grasp the logic behind K-Means and Hierarchical methods—including their assumptions, outputs (like ANOVA tables, icicle plots, and dendrograms), and appropriate interpretation—is key to leveraging its full potential. Successful application always hinges on the thoughtful integration of statistical technique with domain-specific knowledge.

聚类分析又称群分析，是多元统计学中应用广泛的数据分类方法，通过将具有相似性的元素归为同一类别来实现数据分组。是一种强大、直观但微妙的探索性数据分析工具。要超越软件过程的“黑箱”，理解K均值和系统聚类也称为分层聚类法，通过逐步合并最接近的类别来实现聚类，可处理样品和变量聚类，支持连续和分类变量。方法背后的逻辑——包括它们的假设、输出（如ANOVA表、冰柱图聚类分析结果的可视化工具，从图底端开始分析，通过白色间隙显示聚类过程，帮助理解样本如何被逐步分类。和树状图聚类分析的可视化图表，纵坐标表示距离，通过横线显示类别划分，需要结合尺子测量来确定不同距离下的类别数量。）以及正确的解读——是发挥其全部潜力的关键。成功的应用始终取决于统计技术与领域知识的深思熟虑的结合。