Boundary Methods for Distribution Analysis

Multiresolution estimates of classification complexity

“…Bayes error-based parametric and nonparametric approaches [15] (use of probability distance measure bounds [7], [45], entropy measures [4], [47], nonparametric estimation including k nearest neighbor [6], [10], [25], [46], and Parzen estimation [28], interclass distance measures [9], [13], [41], [47], probability distances such as Bhattacharya [2], Chernoff [5], etc., for multiclass problems [1], [14]). See [13], [43] for a criticism of such approaches; 2. scatter matrices [7], [13]; 3. information-theory-based approaches [26], [44]; 4. boundary methods [30], [31], [32], [35], [36]; 5. correlation-based approaches [33]; 6. nonparametric methods [17], [20]; and 7. feature space partitioning methods [24]. The above approaches to estimating class separability are very different to each other in terms of their methodology, assumptions, and computational complexities.…”