Increasing index specificity Sample Clauses

Increasing index specificity. There is an important drawback of evaluating index performance by determining the percent of best partitions identified by index/statistic combinations. Because there is always a global minimum or maximum of these statistics, index/statistic combinations have no specificity. We explored two types of specificity for selected index/global statistic optima pairings. First, we evaluated the ability of a local shape occurring at a statistic’s global optimum to identify cases in which the global optimum correctly chose the best partition. Second, we evaluated the ability of the joint occurrence of two statistics’ global optima to identify cases in which the global optima chose correctly. Local shapes Figure 4.1 gives examples of local shapes that can be found in the plot of an index for a range of partitions: a local minimum, a local maximum, an upward-concave elbow with an overall decrease in index value, a downward-concave elbow with an overall decrease in index value, an upward-concave elbow with an overall increase in index value, a downward-concave elbow with an overall increase in index value. In Figure 4.2, the contingency table on the left shows how local shapes can be used to create specific index usages. In this table, the “test” is that a certain local shape occurs at the same K as a certain statistic’s global optimum of choice. The table on the left depicts the general contingency table for using local shapes to increase specificity, where the global optimum of statistic A is at KA. The table on the right depicts use of local minima to identify cases in which global minima of the Xxxxxx-Xxxxxxx index have chosen correctly. Intersection of global optima In Figure 4.3, the table on the left depicts the general contingency table for using the co-occurrence of two statistics’ global optima to increase specificity, where the global optimum of statistic A is at KA and the global optimum of statistic B is at KB. The table on the right depicts use of joint occurrence of the maximum difference to the left and minimum different to the right to identify cases in which global minima of these statistics for the Calinski-Harabasz index have chosen correctly.