论文信息 - A GRAPHICAL TECHNIQUE FOR REPRESENTING THE ASYMMETRIC RELATIONSHIPS BETWEEN N OBJECTS

A GRAPHICAL TECHNIQUE FOR REPRESENTING THE ASYMMETRIC RELATIONSHIPS BETWEEN N OBJECTS

A new procedure is discussed which represents the asymmetric relationships between N objects. These relationships must be defined at the interval levels of measurement in Steven’s terminology. This method not only reveals the clustering of the objects but also enables us to give information about both the magnitude and the orientation of the “skewness” between objects in “a” configuration. The procedure optimizes the fit of the model directly to the data by an alternating least squares procedure. It is found to be robust, as the Hessian Matrix of the loss function is positive definite at least in two dimensional case, except for a special case. The method is illustrated with an artificial data and three empirical data.

Naohito Chino | N. Chino

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