Clustering methods must be tailored to the dataset it operates on, as there is no objective or universal definition of ``cluster,'' but nevertheless arbitrariness in the clustering method must be minimized. This paper develops a quantitative ``stability'' method of determining clusters, where stable or persistent clustering signals are used to indicate real structures have been identified in the underlying dataset. This method is based on modulating clustering methods by controlling a parameter -- through a thermodynamic analogy, the modulation parameter is considered ``time'' and the evolving clustering methodologies can be considered a ``heat flow.'' When the information entropy of the heat flow is stable over a wide range of times -- either globally or in the local sense which we define -- we interpret this stability as an indication that essential features of the data have been found, and create clusters on this basis.

翻译：聚类方法必须针对其操作的数据集进行定制，因为“簇”并无客观或通用定义，但聚类方法中的任意性必须最小化。本文提出一种定量的“稳定性”方法来确定簇，其中稳定或持久的聚类信号被用于指示已从底层数据集中识别出真实结构。该方法通过控制参数来调节聚类方法——通过热力学类比，将调节参数视为“时间”，而演化中的聚类方法论可被视为“热流”。当热流的信息熵在广泛的时间范围内（无论是全局还是我们定义的局部意义下）保持稳定时，我们将这种稳定性解释为已发现数据本质特征的迹象，并据此生成簇。