Scalable approximate FRNN-OWA classification

Fuzzy Rough Nearest Neighbour classification with Ordered Weighted Averaging operators (FRNN-OWA) is an algorithm that classifies unseen instances according to their membership in the fuzzy upper and lower approximations of the decision classes. Previous research has shown that the use of OWA operators increases the robustness of this model. However, calculating membership in an approximation requires a nearest neighbour search. In practice, the query time complexity of exact nearest neighbour search algorithms in more than a handful of dimensions is near-linear, which limits the scalability of FRNN-OWA. Therefore, we propose approximate FRNN-OWA, a modified model that calculates upper and lower approximations of decision classes using the approximate nearest neighbours returned by Hierarchical Navigable Small Worlds (HNSW), a recent approximative nearest neighbour search algorithm with logarithmic query time complexity at constant near-100% accuracy. We demonstrate that approximate FRNN-OWA is sufficiently robust to match the classification accuracy of exact FRNN-OWA while scaling much more efficiently. We test four parameter configurations of HNSW, and evaluate their performance by measuring classification accuracy and construction and query times for samples of various sizes from three large datasets. We find that with two of the parameter configurations, approximate FRNN-OWA achieves near-identical accuracy to exact FRNN-OWA for most sample sizes within query times that are up to several orders of magnitude faster

Comparing Rough Set Theory with Multiple Regression Analysis as Automated Valuation Methodologies

This paper focuses on the problem of applying rough set theory to mass appraisal. This methodology was first introduced by a Polish mathematician, and has been applied recently as an automated valuation methodology by the author. The method allows the appraiser to estimate a property without defining econometric modeling, although it does not give any quantitative estimation of marginal prices. In a previous paper by the author, data were organized into classes prior to the valuation process, allowing for the if-then, or right “rule” for each property class to be defined. In that work, the relationship between property and class of valued was said to be dichotomic.mass appraisal; property valuation; rough set theory; valued tolerance relation

Fuzzy-Rough Nearest Neighbour Classification and Prediction

AbstractNearest neighbour (NN) approaches are inspired by the way humans make decisions, comparing a test object to previously encountered samples. In this paper, we propose an NN algorithm that uses the lower and upper approximations from fuzzy-rough set theory in order to classify test objects, or predict their decision value. It is shown experimentally that our method outperforms other NN approaches (classical, fuzzy and fuzzy-rough ones) and that it is competitive with leading classification and prediction methods. Moreover, we show that the robustness of our methods against noise can be enhanced effectively by invoking the approximations of the Vaguely Quantified Rough Set (VQRS) model, which emulates the linguistic quantifiers “some” and “most” from natural language