Domain-guided novelty detection for autonomous exploration
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Soft fuzzy rough sets for robust feature evaluation and selection
Information Sciences: an International Journal
A robust fuzzy rough set model based on minimum enclosing ball
RSKT'10 Proceedings of the 5th international conference on Rough set and knowledge technology
Robust fuzzy rough classifiers
Fuzzy Sets and Systems
Soft Minimum-Enclosing-Ball Based Robust Fuzzy Rough Sets
Fundamenta Informaticae - Rough Sets and Knowledge Technology (RSKT 2010)
Robust kernel density estimation
The Journal of Machine Learning Research
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Statistical depth functions provide from the âdeepestâ point a âcenter-outward orderingâ of multidimensional data. In this sense, depth functions can measure the âextremenessâ or âoutlyingnessâ of a data point with respect to a given data set. Hence, they can detect outliersâobservations that appear extreme relative to the rest of the observations. Of the various statistical depths, the spatial depth is especially appealing because of its computational efficiency and mathematical tractability. In this article, we propose a novel statistical depth, the kernelized spatial depth (KSD), which generalizes the spatial depth via positive definite kernels. By choosing a proper kernel, the KSD can capture the local structure of a data set while the spatial depth fails. We demonstrate this by the half-moon data and the ring-shaped data. Based on the KSD, we propose a novel outlier detection algorithm, by which an observation with a depth value less than a threshold is declared as an outlier. The proposed algorithm is simple in structure: the threshold is the only one parameter for a given kernel. It applies to a one-class learning setting, in which ânormalâ observations are given as the training data, as well as to a missing label scenario, where the training set consists of a mixture of normal observations and outliers with unknown labels. We give upper bounds on the false alarm probability of a depth-based detector. These upper bounds can be used to determine the threshold. We perform extensive experiments on synthetic data and data sets from real applications. The proposed outlier detector is compared with existing methods. The KSD outlier detector demonstrates a competitive performance.