[MUSIC] In this session, we are going to discus proximity measure for symmetric vs asymmetric binary variables. For binary variables, we usually report their occurrences using contingency tables. Okay, suppose we have two objects, i and j. The number of times they both appear could be q, they both missing could be t cases. I appears and j does not, there are r cases. And i does not appear, and j appears s times, then for symmetric binary variables that means the chance they appear or they not appear actually have equivalent chances, or approximately same chances w call this as symmetric binary variables. In our case they are distance, like r and s. These two cases, they are different, so their distance measure is r+s divided by all the cases. For asymmetric binary variables, usually we assume they both appear, the case is much rarer than they both not appearing, okay. So for these asymmetric variables, they are different as r + s, but they both not appearing. In that case, actually is t is not so important. The reason For example has only the parts of y where attract attention. Then for that distance measure it we look at r + s divide by q + r + s. That means all the cases with t cases removed, okay. Then for their similarity measure, that means, how many times they are the same? Actually it's a q cases. For the q cases, we probably can't see that's a same denominator. Actually, Jaccard coefficient was somehow rediscovered in the Pattern Discovery here, they call this one coherence. And here, this coherence definition, if you really map them into this contingence table, they have the same definition as Jaccard coefficient. So then we look at the real cases, suppose we have some medical tests. Then we have Jack, Mary, and Jim, three cases, three people. Their tests actually is represented in this table. We can map them into table, since gender, the chance to be male or female are roughly equivalent, so this is a symmetric cases, so for us we are only interested in asymmetric cases, that is the remaining attributes becomes more important. Then we try to examine how they are different. Suppose we say Y and P, is positive case, and the value N, no, are not the case, will be 0, okay. In our case, we look at our distance special for asymmetric attributes, we can work out these [INAUDIBLE] for example, if a Jack and Mary, would proceed, Jack and Mary, they are the same parts of the case, like those have fever.both the test one actually is positive. There are two such cases. They are both negative, like a cough. Test two and test four, actually there are three cases they are both negative. But they do have one case they are different. Similarly, we can work the table for Jack and Jim, Jim and Mary. In this case we can calculate their difference. Probably we can easily see Jack and Mary actually are most similar, Jim and Mary are most different. We may conclude that Jack and Mary may have similar a disease in this case. [MUSIC]
