Background: Sequence analysis is a set of tools increasingly used in demography and other social sciences to analyse longitudinal categorical data. Typically, single (e.g., education trajectories) or multiple parallel temporal processes (e.g., work and family) are analysed by using crisp clustering algorithms that reduce complexity by partitioning cases into exhaustive and mutually exclusive groups. Crisp partitions can be problematic when clusters are not clearly separated, as is often the case in social-science applications. An effective alternative strategy is fuzzy clustering, allowing cases to belong to different clusters with a different degree of membership. Objective: We extend the scarce literature on fuzzy clustering of sequences to the analysis of multiple trajectories jointly unfolding over time. We illustrate how to properly apply fuzzy algorithms in this case. We propose some criteria (the fuzzy silhouette coefficients) to support the choice of the number of clusters to extract, and we introduce the gradient index plot to enhance the substantive interpretation of (multichannel) fuzzy-clustering results. Methods: We first describe the general features of fuzzy clustering applied to sequence data. We then use an illustrative example of multidomain sequence analysis applied to family and work trajectories to present the fuzzy silhouette coefficient and the gradient index plot. Contribution: These research materials provide practitioners with analytical and graphical tools that facilitate the use of fuzzy-clustering algorithms to address research questions concerning the link between the unfolding of multiple trajectories in sequence analysis, for demographic research and beyond.

中文翻译：

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用于分析序列数据模糊簇的工具（Raffaella Piccarreta、Emanuela Struffolino）


背景：序列分析是一组越来越多地用于人口学和其他社会科学的工具，用于分析纵向分类数据。通常，通过使用清晰的聚类算法来分析单个（例如，教育轨迹）或多个并行时间过程（例如，工作和家庭），该算法通过将案例划分为详尽且互斥的组来降低复杂性。当簇没有明确分离时，清晰的分区可能会出现问题，这在社会科学应用中经常出现。一种有效的替代策略是模糊聚类，允许案例属于具有不同隶属度的不同聚类。目的：我们将关于序列模糊聚类的稀缺文献扩展到对随时间共同展开的多个轨迹的分析。我们将说明如何在这种情况下正确应用模糊算法。我们提出了一些标准（模糊轮廓系数）来支持选择要提取的聚类数量，并引入梯度指数图来增强（多通道）模糊聚类结果的实质性解释。方法：我们首先描述应用于序列数据的模糊聚类的一般特征。然后，我们使用应用于家庭和工作轨迹的多域序列分析的说明性示例来呈现模糊轮廓系数和梯度指数图。贡献：这些研究材料为从业者提供了分析和图形工具，有助于使用模糊聚类算法来解决有关序列分析中多个轨迹展开之间联系的研究问题，用于人口统计研究等。