I am perplexed by an example given in an article about asymmetry in MDS (multi-dimensional scaling). You don't need to know anything about this to answer my question. It's all very intuitive.(adsbygoogle = window.adsbygoogle || []).push({});

There are six people. They have various likes and dislikes for each other, which are asymmetric (as one would expect). Here is the table:

http://tinyurl.com/oshtv7p [Broken]

MDS tries to give a graphical representation of the relationships. In the paper

Chino, N. (1978). A graphical technique for representing the asymmetric relationships between N objects. Behaviormetrika, 5, 23-40.

Chino presents a model and then uses this example to provide the following graph:

http://tinyurl.com/oefndcs [Broken]

Chino explains these relationships as follows:

(1) For example, the skewness between persons 1 and 4 is the greatest of all, as the angle between the lines P0P1 and P0P4 is pi/2. Further, we find it easy to see that person 4 likes person 1 very much, though person 1 doesn't like person 4 at all. It should be noted that the co-ordinate system is assumed to be right-handed.

(2) Persons 1 and 6 like each other, as the angle between the lines P0P1 and P0P6 is 0.

(3) For example, persons 1 and 3 hate each other, as the angle between the lines POP1 and P0P3 is pi.

(4) For example, person 4 likes person 5 very much, but person 5 neither likes nor dislikes him, as the angle between the lines P0P4 and P0P5 is pi/4. Such a relationship might be called "unilateral love". On the other hand, person 5 neither likes nor dislikes person 2, but person 2 hates him very much, as the angle between the lines P0P5 and P0P2 is 3pi/4. Such a relation ship might be interesting in contrast to that of "unilateral love".

I have tried to think about this and interpret what the angles and the distances in the diagram mean, but I can't wrap my head around it. Why, just looking at the graph, does P1 not like P4 at all, but P5 is indifferent towards P4???

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Asymmetry question

**Physics Forums | Science Articles, Homework Help, Discussion**