Abstract

Proximity scaling methods such as multidimensional scaling represent objects in a low-dimensional configuration so that fitted object distances optimally approximate object proximities. Besides finding the optimal configuration, an additional goal may be to make statements about the cluster arrangement of objects. This fails if the configuration lacks appreciable clusteredness. We present cluster optimized proximity scaling (COPS), which attempts to find a configuration that exhibits clusteredness. In COPS, a flexible parameterized scaling loss function that may emphasize differentiation information in the proximities is augmented with an index (OPTICS Cordillera) that penalizes lack of clusteredness of the configuration. We present two variants of this, one for finding a configuration directly and one for hyperparameter selection for parametric stresses. We apply both to a functional magnetic resonance imaging dataset on neural representations of mental states in a social cognition task and show that COPS improves clusteredness of the configuration, enabling visual identification of clusters of mental states. Online supplementary materials are available including an R package and a document with additional details.

摘要

诸如多维缩放之类的接近缩放方法表示低维配置中的对象，以便拟合的对象距离最佳地近似对象接近。除了找到最佳配置外，另一个目标可能是对对象的集群排列进行陈述。如果配置缺乏明显的集群性，这将失败。我们提出了集群优化邻近度缩放 (COPS)，它试图找到一种表现出集群性的配置。在 COPS 中，一个灵活的参数化缩放损失函数可以强调邻近区域的微分信息，并增加了一个指数（OPTICS Cordillera），该指数惩罚缺乏配置的集群性。我们提出了这个的两种变体，一种用于直接查找配置，另一种用于参数应力的超参数选择。我们将两者应用于社会认知任务中精神状态神经表征的功能磁共振成像数据集，并表明 COPS 提高了配置的聚类性，从而能够对精神状态的聚类进行视觉识别。提供在线补充材料，包括 R 包和包含其他详细信息的文档。