Question about a particular paper on categorical data

[ZPlayer]

I am not sure this is the right forum for this -- I have a question about a particular paper:

http://www-users.cs.umn.edu/~sboriah/PDFs/ChandolaCBK2009.pdf

The authors describe 4 heuristics that can be derived from categorical data -- this is in order to map categorical data to numerical. These heuristics are d_m, f_m, n_x, f_x. They also provide two examples y and z and the values of the quantities above computed with respect to dataset in table 3. I am able to lock into their values exactly for d_m and f_m but I cannot reproduce n_x and f_x.

Could someone read this paper and try to derive these values? I basically take it their equation (3.3) shows summation of reciprocals of arity for A_x set (i.e. the set of mismatching attributes) -- I can't reproduce -5.45 and -7.90.

Please note I already contacted the authors -- one responded that Dr. Boriah is the person responsible for these calculations but he is apparently not reachable.

 

[Stephen Tashi]

I am not sure this is the right forum for this -- I have a question about a particular paper:

http://www-users.cs.umn.edu/~sboriah/PDFs/ChandolaCBK2009.pdf

What that paper proposes to do is very interesting, but will understanding it be worth dealing with its problems !

I cannot reproduce n_x and f_x.

I can't either.

It's interesting that $z = (a_3,b_2,c_{10},d_5)$ has attribute $a_3$ that does not occur in the "reference" data set. I wonder if that example is supposed to emphasize that you can compute the statistics when such a situation comes up.

The formula (3.3) $n_x = -\sum_{i \in A_x} \frac{1}{n_i}\$ is not consistent with the passage in the article that says:

The statistic $n_x$ is a function of the arity of the mismatching attributes between an instance and a reference data set. In particular, the value of the statistic is higher when the mismatching attributes have lower arity, i.e. they take fewer values.

In the formula, lower airty would produce a "more negative" contribution and the statistic would be lower instead of higher.

The notation in formula (3.4) $\ f_x = -\sum_{i \in A_x} ( \frac{1}{z_i} + \frac{1}{y_i}) \$ doesn't make sense to me because $z_i$ and $y_i$ are values of categories ( like "smooth" and "urban") , not numbers.