Features

This page introduces the main features of AMISESCAL.

Formulation of Asymmetry

In AMISESCAL, asymmetry in data is expressed using the von Mises distribution. For example, Person i takes a liking to Person j, but Person j does not take a liking to Person i. The asymmetry of the feelings between the two persons is explained by the differences in the parameters of their von Mises distributions. The figure below represents the asymmetry of the feelings between the two persons as reflected by the difference between πij and πji. If a detailed explanation is necessary, please refer to Quick Introduction on the top page.

Basic Behavior of Model

The table on the left is the asymmetric data matrix for three persons. A state of stronger positive feeling denotes lower psychological proximity: the stronger the positive feeling, the smaller is the value expressed in the data matrix. That is, in the data, Person A likes Person B, Person B likes Person C, and Person C likes Person A. After analyzing this trianglular relationship by AMISESCAL, we obtain the result shown in the map on the right. Each person looks to the direction that he/she likes.

 

In this example, Persons A and B like each other because the values A to B and B to A are small. In addition, Both Persons A and B like Person C. However, Person C likes Person D, and Person D like Persons A and B. By analyzing the asymmetric data, the result is obtained as the map on the right. In AMISESCAL, each person looks to his/her one-sided love object(s) as well as the positions of the persons in mutual love are close to with each other.

 

The table on the left illustrates the situation where Persons B, C, and D like Person A, and Person A like no one. In addition, Person B likes Person C, Person C likes Person D, and Person D likes Person B. That is, the relationship among Persons B, C, and D is triangular. By analyzing the asymmetric matrix, the map on the right is obtained. Person A looks nowhere because he/she likes no one. Person B looks toward the midpoint between the positions of Persons A and C. In the same manner, Person C looks toward the midpoint between Persons A and D, and Person D looks toward the midpoint between Persons A and B.

 

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