[SOUND] Now we examine distance between categorical attributes, ordinal attributes, and mixed types. What are categorical attributes? Categorical attributes, also called nominal attributes because their value references by names. Take color as a example, we may have yellow, red, orange, blue, green. If we get their positions in color spectrum in physics, they are not ordered. In the sense either the two values are the same or they are different. The same as profession and many other things. Then how to calculate their distance. We can use simple matching method. For example, suppose there are total p variables, and their m matches. Then the number of mismatch is p minus m. So their distance between i and j will be the number of mismatches versus the total number of variables. Another measure is we can mapthem into binary variables. That means each value like red if they are existing as a red we write down as one. If they are not red, we write down as zero. Then we can change the categorical attributes into a set of binary variables. Then we can use the previous binary attribute evaluation function to evaluate them. Another kind of variable called ordinal variables. Ordinal variable means they do have order. They can be discrete like a rank, like a military rank, or even the rank for undergraduate students in the university, okay. Or they could be continuous, like time, okay? Then order becomes important. For example, in the University, a freshman is a first year, a senior is a fourth year student. In that sense, we can replace ordinal variable value by its rank. Then we can map any particular variable using this formula map onto this either 0 or 1, okay. Just give you an example. For example, we can map freshman into 0 because their position is 1- 1 0. And the same for senior it is four so by the total range is four. That's why they map into one. Then the distance for example between freshman and senior would be one minus zero, their distance is one. But between junior and senior their distance is only one third because with this one, now we can compute the other dissimilarity using the interval scale variables. What about we get a dataset may contain all attribute types, nominal symmetric binary, asymmetric binary, numerical or ordinal. No one can use a weighted formula to combine the facts. Then, if they are numerical data, we can use normalize the distance, like [INAUDIBLE]. If they are binary, or nominal data, we can use this formula as we just discussed. If they are ordinal data we can compute their distance using this formula. Then we can combine all their effects to compute their overall distance. [MUSIC]
