Evaluation of index performance Sample Clauses

Evaluation of index performance. Following the procedure used be earlier studies of this type, we considered the maximum and minimum of the following three statistics as possible usages of each index: 1. The index value for partition Uk, Ik. 2. The difference to the left: Ik − Ik−1. 3. The difference to the right: Ik+1 − Ik. 4. The “second difference,” or the elbow sharpness: (Ik − Ik+1) − (Ik − Ik−1). We calculated these statistics for each partition of the data from K = 2 through Kmax, then identified cases for which the minimum or maximum of each statistic occurred at K of the best partition. In addition to these statistics, we also determined if the best K occurred at a local minimum or maximum of the index. Indices with one or more usages making a correct choice for more than 25% of partitions were selected for further evaluation. In contrast to earlier studies, we considered that there might be multiple “best usages” of an index. For example, it is possible that a local minimum of an index indicates the best partition in some cases, and the sharpest “elbow” indicates the best partition in other cases (possibly when there is no local minimum). To characterize index performance further, we calculated the average ARI of partitions chosen by each best usage. We used logistic regression with “correct choice” as the outcome to assess the impact of data set design factors and clustering algorithm used to create the best partition on index performance. K-means and K-modes were performed on the data set for K = 2, . . . , 9 (for three-subtype data) or K = 2, . . . , 11 (for six-subtype data), using the combined batch and individual reassignment K-means algorithm (Spa¨th, 1985). To reduce the chances of finding local rather than global minima, each algorithm (i.e. K-means and K-modes) was performed 10,000 times for each level of K, with the K-th partition taken to be the partition with the lowest SSW or SAD. All computations were performed in MATLAB v2008a. The MATLAB statistics toolbox kmeans.m function was used for K-means and K-modes. Indices were calculated by MATLAB routines written by the author.
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