Cluster Optimized Proximity Scaling

Proximity scaling methods such as Multidimensional Scaling (MDS) 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 parametrized 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 (fMRI) data set 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 material is available including an R package and a document with additional details.