Robust estimation and classification for functional data via projection-based depth notions
Computational Statistics
The Tukey and the random Tukey depths characterize discrete distributions
Journal of Multivariate Analysis
Geometric median-shift over Riemannian manifolds
PRICAI'10 Proceedings of the 11th Pacific Rim international conference on Trends in artificial intelligence
A half-region depth for functional data
Computational Statistics & Data Analysis
Mathematical morphology for vector images using statistical depth
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
A multivariate control quantile test using data depth
Computational Statistics & Data Analysis
Interpretable dimension reduction for classifying functional data
Computational Statistics & Data Analysis
Clustering via geometric median shift over Riemannian manifolds
Information Sciences: an International Journal
Absolute approximation of Tukey depth: Theory and experiments
Computational Geometry: Theory and Applications
A method to form learners groups in computer-supported collaborative learning systems
Proceedings of the First International Conference on Technological Ecosystem for Enhancing Multiculturality
Local Mutual Information for Dissimilarity-Based Image Segmentation
Journal of Mathematical Imaging and Vision
A random-projection based test of Gaussianity for stationary processes
Computational Statistics & Data Analysis
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The computation of the Tukey depth, also called halfspace depth, is very demanding, even in low dimensional spaces, because it requires that all possible one-dimensional projections be considered. A random depth which approximates the Tukey depth is proposed. It only takes into account a finite number of one-dimensional projections which are chosen at random. Thus, this random depth requires a reasonable computation time even in high dimensional spaces. Moreover, it is easily extended to cover the functional framework. Some simulations indicating how many projections should be considered depending on the kind of problem, sample size and dimension of the sample space among others are presented. It is noteworthy that the random depth, based on a very low number of projections, obtains results very similar to those obtained with the Tukey depth.