Evaluation of the trade-off curve in the bump hunting using the tree genetic algorithm


H. Hirose


"1st IMS Asia Pacific Rim Meetings", Abstract 166, June 28-July 1, 2009 at Soeul National University, Korea.


Suppose that we are interested in classifying $n$ points in a $z$-dimensional space into two groups having response 1 and response 0 as the target variable. In some real data cases in customer classification, it is difficult to discriminate the favorable customers showing response 1 from others because many response 1 points and 0 points are closely located. In such a case, to find the denser regions to the favorable customers is considered to be an alternative. Such regions are called the bumps, and finding them is called the bump hunting.
By pre-specifying a pureness rate $p$ in advance a maximum capture rate $c$ could be obtained; the pureness rate is the ratio of the number of response 1 points to the total number of points in the target region; the capture rate is the ratio of the number of response 1 points to the total number of points in the total regions. Then a trade-off curve between $p$ and $c$ can be constructed. Thus, to find the bump regions is equivalent to construct the trade-off curve.
In order to make future actions easier, we adopt simpler boundary shapes for the bumps such as the union of $z$-dimensional boxes located parallel to some explanation variable axes; this means that we adopt the binary decision tree. Since the conventional binary decision tree will not provide the maximum capture rates because of its local optimizer property, some probabilistic methods would be required. Here, we use the genetic algorithm (GA) specified to the tree structure to accomplish this; we call this the tree GA. Using the property that the tree GA has a tendency to provide many local maxima of the capture rates, we can estimate the upper bound curve for the trade-off curve by using the extreme-value statistics.
However, the bump regions obtained by using the tree GA are conservative comparing to the optimal regions because the tree GA finds the shrunk regions. Therefore, we should know how accurate the trade-off curve using the tree GA. In this paper, we have assessed the accuracy for the trade-off curve in typical fundamental cases that may be observed in real customer data cases. We have found that the proposed tree GA can construct the trade-off curve which is close to the optimal one.


Key Words
Data Mining, Genetic Algorithm, Bump Hunting, Extreme-Value Statistics, Trade-off curve, Evaluation.



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