Two-Mode Three-Way Dominance Points Model for Periodic Dissimilarity

Asymmetric multidimensional scaling (AMDS) is important for visualizing asymmetric relationships between objects. The dominance point model involves AMDS and represents asymmetry between objects through the difference in the distances between the dominance point and objects. The advantage of this model is that the dominance point and points of objects are represented in the same space. However, there is a problem when applying the dominance point to a two-mode three-way distance model (object X object X condition). The dominance point model ignores the order of condition; that is, the estimator of the model is not changed although the order of condition is changed. To overcome this problem, we propose a two-mode three-way dominance point model using a hypersphere. Constraining the coordinate vector of objects on the hypersphere, the proposed model considers the order of condition. Moreover, the coordinate vector of objects has a periodic property. We introduce the majorizing function of the objective function of our model and obtain the estimator using the majorization-minimization algorithm