Prototype generation in the string space via approximate median for data reduction in nearest neighbor classification

The k-nearest neighbor (kNN) rule is one of the best-known distance-based classifiers, and is usually associated with high performance and versatility as it requires only the definition of a dissimilarity measure. Nevertheless, kNN is also coupled with low-efficiency levels since, for each new query, the algorithm must carry out an exhaustive search of the training data, and this drawback is much more relevant when considering complex structural representations, such as graphs, trees or strings, owing to the cost of the dissimilarity metrics. This issue has generally been tackled through the use of data reduction (DR) techniques, which reduce the size of the reference set, but the complexity of structural data has historically limited their application in the aforementioned scenarios. A DR algorithm denominated as reduction through homogeneous clusters (RHC) has recently been adapted to string representations but as obtaining the exact median value of a set of string data is known to be computationally difficult, its authors resorted to computing the set-median value. Under the premise that a more exact median value may be beneficial in this context, we, therefore, present a new adaptation of the RHC algorithm for string data, in which an approximate median computation is carried out. The results obtained show significant improvements when compared to those of the set-median version of the algorithm, in terms of both classification performance and reduction rates.