The Rectified Nearest Feature Line Segment (RN-FLS) classifier is an improved version of the Nearest Feature Line (NFL) classification rule. RNFLS corrects two drawbacks of NFL, namely the interpolation and extrapolation inaccuracies, by applying two consecutive processes - segmentation and rectification - to the initial set of feature lines. The main drawbacks of this technique, occurring in both training and test phases, are the high computational cost of the rectification procedure and the exponential explosion of the number of lines. We propose a cheaper version of RNFLS, based on a characterization of the points that should form good lines. The characterization relies on a recent neighborhood-based principle that categorizes objects into four types: safe, borderline, rare and outliers, depending on the position of each point with respect to the other classes. The proposed approach represents a variant of RNFLS in the sense that it only considers lines between safe points. This allows a drastic reduction in the computational burden imposed by RNFLS. We carried out an empirical and thorough analysis based on different public data sets, showing that our proposed approach, in general, is not significantly different from RNFLS, but cheaper since the consideration of likely irrelevant feature line segments is avoided.

In this paper we investigate the exploitation of non linear scaling of distances for advanced nearest neighbor classification. Starting from the recently found relation between the Hypersphere Classifier (HC) and the Adaptive Nearest Neighbor rule (ANN), here we propose PowerHC, an improved version of HC in which distances are normalized using a non linear mapping; non linear scaling of data, whose usefulness for feature spaces has been already assessed, has been hardly investigated for distances. A thorough experimental evaluation, involving 24 datasets and a challenging real world scenario of seismic signal classification, confirms the suitability of the proposed approach.