Kmedians - K-Medians
Online, Semi-online, and Offline K-medians algorithms are
given. For both methods, the algorithms can be initialized
randomly or with the help of a robust hierarchical clustering.
The number of clusters can be selected with the help of a
penalized criterion. We provide functions to provide robust
clustering. Function gen_K() enables to generate a sample of
data following a contaminated Gaussian mixture. Functions
Kmedians() and Kmeans() consists in a K-median and a K-means
algorithms while Kplot() enables to produce graph for both
methods. Cardot, H., Cenac, P. and Zitt, P-A. (2013).
"Efficient and fast estimation of the geometric median in
Hilbert spaces with an averaged stochastic gradient algorithm".
Bernoulli, 19, 18-43. <doi:10.3150/11-BEJ390>. Cardot, H. and
Godichon-Baggioni, A. (2017). "Fast Estimation of the Median
Covariation Matrix with Application to Online Robust Principal
Components Analysis". Test, 26(3), 461-480
<doi:10.1007/s11749-016-0519-x>. Godichon-Baggioni, A. and
Surendran, S. "A penalized criterion for selecting the number
of clusters for K-medians" <arXiv:2209.03597> Vardi, Y. and
Zhang, C.-H. (2000). "The multivariate L1-median and associated
data depth". Proc. Natl. Acad. Sci. USA, 97(4):1423-1426.
<doi:10.1073/pnas.97.4.1423>.
