# Why does measuring for Asymmetric Binary Attributes exclude t (Values which are 0 for both)?

I'm teaching myself Data mining and now struggling from this problem.

According to this table(http://slidewiki.org/slide/22352), if the attributes are Asymmetric, dissimilarity is calculated without t (Values which are 0 for both)

Let me give an example.

There are 2 objects, called Products.

They have 2 attributes, COLOR and SIZE.

• COLOR is either RED(1) and BLUE(0) (They are binary).
• SIZE is either BIG(1) or SMALL(0) (They are binary too).

When there are RED-BIG(1-1) & RED-SMALL(1-0) objects, d is 1/2, regardless of if the attributes are symmetric or asymmetric.

However, if they are BLUE-SMALL(0-0) and BLUE/BIG(0-1), d is 1/2 for symmetric BUT 1/1 for asymmetric.

How does the difference come from? In both cases, there is only one difference, BUT dissimilarity isn't the same.

## 1 Answer

I know it is the old post, but I also search for the answer to this question. and here what I got:

first of all, binary asymmetric attributes only care the 1 values. for example in measuring the distance of the patient based on their symptom, 1 means the symptom exists and 0 mean it does not exist. Or another example in measuring the distance between 2 documents based on the occurrence of words/term (most of these cases not using binary, but still asymmetric), 0 means the term does not exist in the document.

in those 2 cases, the number of symptom or term can be very huge and may cause a lot of 0 values appear in 1 records. This is because one disease may only have a small number of symptoms or one document may only contain a small number of words/term. If all of these 0 values are used to calculate the distance between two records, the similarity can be huge. example

record 1 : 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

record 2 : 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

assymetric: d(1,2) = 3/4 --> similarity(1,2) = 1-3/4 = 1/4

IF we consider it as symmertic: d(1,2) = 3/20 --> similarity(1,2) = 1-3/20 = 17/20 (large similarity)

that is why the attributes with the same 0 values between two records are not included in the distance calculation.