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- W2019356048 abstract "The center µ of a multivariate data set {x1,…,xn} can be defined as minimizer of the norm of a vector of distances. In this paper, we consider a vector of L 1-distances y′1= (‖x1 − µ‖1 …, ‖xn −µ‖1) and a vector of L 2-distances y’2 = (‖x1 −µ‖2, …, ‖xn-µ‖2). We define the L 1-median and the L 1-mean as the minimizers of respectively the L 1- and the L 2-norm of yi; and then the L 2-median and the L 2-mean as the minimizers of respectively the L 1- and the L 2-norm of y2. In doing so, we obtain four alternatives to describe the center of a multivariate data set. While three of them have been already investigated in the statistical literature, the L 1-mean appears to be a new concept. Contrary to the L 1-median, the L 1-mean is proved to be unique in almost all situations." @default.
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- W2019356048 date "1998-01-01" @default.
- W2019356048 modified "2023-09-27" @default.
- W2019356048 title "Multivariate L 1 Mean" @default.
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- W2019356048 doi "https://doi.org/10.1007/978-3-642-72253-0_73" @default.
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