A fuzzy vector valued KNN-algorithm for automatic outlier detection

The K nearest neighbors approach is a viable technique in time series analysis when dealing with ill-conditioned and possibly chaotic processes. Such problems are frequently encountered in, e.g., finance and production economics. More often than not, the observed processes are distorted by nonnormal disturbances, incomplete measurements, etc. that undermine the identification, estimation and performance of multivariate techniques. If outliers can be duly recognized, many crisp statistical techniques may perform adequately as such. Geno-mathematical programming provides a connection between statistical time series theory and fuzzy regression models that may be utilized e.g., in the detection of outliers. In this paper we propose a fuzzy distance measure for detecting outliers via geno-mathematical parametrization. Fuzzy KNN is connected as a linkable library to the genetic hybrid algorithm (GHA) of the author, in order to facilitate the determination of the LR-type fuzzy number for automatic outlier detection in time series data. We demonstrate that GHA[Fuzzy KNN] provides a platform for automatically detecting outliers in both simulated and real world data.