Question

[1+2] Attribute5 Attribute4 a) Given the following three objects with five binary attributes. Attributel Attribute2 Attribute3 Object11 Object20 0 1 Object3 0 Among the three objects, find the most similar pair of objects assuming attributes are symmetric binary variables? Which pair would be most similar if attributes are asymmetric binary variables?

please provide detailed concept andother combinations also. So thatI can answer any type questions on this concept.

Please provide clear view, i am struggling a lot here.

Answer 1

Since you are asking for the concept in clear, I am explaining you it in detail. So it was a bit long answer. Please be patient enough and try to understand it.

The question comes under the similarity and distance measures.The data provided by you is the binary data. So here is the metrics used for the calculation of similarity between the objects when the data is binary.

Proximity Measure for Binary Attributes Object j 10 · A contingency table for binary data Object in sum q+r 8+t p § Distance measure for symmetric binary S t sum 9+8 rtt rts d(i, j) = - q+r+s+t variables: • Distance measure for asymmetric binary variables: rts dai, j) = - q+r+s Jaccard coefficient (similarity measure for asymmetric binary variables): sim Jaccard(i, j) = -1 q+rts

So using the above formula, we compute the distances between all the combinations and the combinations for which the distance measure is minimum, the objects in that combination are more similar

Assuming the attributes are symmetric :

Considering the objects (1,2)

From contingency matrix,

q=2, r= 2, s= 0, t=1

d(i,j) =(r+s)/(q+r+s+t) = (2+0)/(2+2+0+1) = 2/5

Considering the objects (2,3)

From contingency matrix,

q=1, r= 1, s= 1, t=2

d(i,j) =(r+s)/(q+r+s+t) = (1+1)/(1+1+1+2) = 2/5

Considering the objects (1,3)

From contingency matrix,

q=1, r= 2, s= 1, t=1

d(i,j) =(r+s)/(q+r+s+t) = (2+1)/(1+2+1+1) = 3/5

So among all the three combinations, (1,3) are more dissimilar.Therefore, those two objects(1,3) are less Similar.

The combinations of (1,2) and (2,3) are equally less dissimilar. So those two combinations are equally more similar.

Assuming the attributes are asymmetric :

Considering the objects (1,2)

From contingency matrix,

q=2, r= 2, s= 0, t=1

d(i,j) =(r+s)/(q+r+s) = (2+0)/(2+2+0) = 2/4=0.5

Considering the objects (2,3)

From contingency matrix,

q=1, r= 1, s= 1, t=2

d(i,j) =(r+s)/(q+r+s) = (1+1)/(1+1+1) = 2/3=0.66

Considering the objects (1,3)

From contingency matrix,

q=1, r= 2, s= 1, t=1

d(i,j) =(r+s)/(q+r+s) = (2+1)/(1+2+1) = 3/4=0.75

Among all the combinations, the combinations of objects (1,2) are less dissimilar i.e, they are more similar.

Summary

Attributes are symmetric : objects (1,2) and objects(2,3) are equally similar.

Attributes are asymmetric : objects (1,2) are more similar than other combinations.

So I feel that I have provided you the complete concept on this topic and answered your question also.Now using this, you can solve any question of this kind.

If you have any further doubts, feel free to ask in the comment section.

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