Some Spatial depth Classifiers
Keywords:classifiers, data depth, spatial depth, kernel, weight
Several multivariate depth functions have been proposed in literature of which some satisfy all the conditions for statistical depth functions while some do not. Spatial depth is known to be invariant only to spherical and shift transformations. In this paper, the possibility of using different versions of spatial depth in classification is considered. We extend the notions of maximal depth classifiers for covariance-adjusted, weighted and kernel-based versions of spatial depth. The performance of the classifiers is considered and compared with some existing classification methods using simulated and real datasets.
Chen~Y, Dang~X, Peng~H & Bart~HL (2009). Outlier detection with the kernelized spatial depth function. IEEE Transactions on Pattern Analysis and Machine Intelligence. 31:288-305.
Donoho~DL & Gasko~M (1992). Breakdown properties of multivariate location parameters and dispersion matrices, Ann. Statist., 20:1803-1827.
Gao~Y (2003). Data depth based on spatial rank. Statistics & Probability Letters, 65:217-225.
Ghosh~AK & Chaudhuri~P (2005). On maximum depth and related classifiers. Scandinavian Journal of Statistics, 32:327-350.
Hubert~M & Van Driessen~K (2004). Fast and robust discriminant analysis. Computational Statistics and Data Analysis, 45(2):301-320.
Jornsten~R (2004) Clustering and classification based on the L_1 data depth. Journal of Multivariate Analysis, 90:67-89.
Li~J., Cuesta-Albertos~JA & Liu~RY (2012) DD-classifier: nonparametric classification procedure based on DD-plot. Journal of American Statistical Association, 107:737-753.
Liu~RY (1990). On a notion of data depth based on random simplices. The Annals of Statistics, 18:405-414.
Liu~RY, Parelius~JM & Singh~K (1999). Multivariate analysis by data depth: Descriptive statistics, graphics and inference. The Annals of Statistics, 27:783-858.
Makinde~OS & Chakraborty~B (2015). On some nonparametric classifiers based on distribution functions of multivariate ranks. In Nordhausen, K and Taskinen, S.(eds): Modern Nonparametric, Robust and Multivariate Methods, Festschrift in Honour of Hannu Oja. Springer, Switzerland, 249-264
Makinde~OS & Chakraborty~B (2019) On some classifiers based on multivariate ranks. Communication in Statistics - Theory and Methods. DOI:10.1080/03610926.2017.1366520
Tukey~J (1975) Mathematics and picturing data. Proceedings of the 1975 International Congress of Mathematics, 2:523-531.
Vapnik~VN (1998). Statistical Learning Theory. John Wiley and Sons, New York.
Zuo~Y & Serfling~R (2000) General notions of statistical depth function. The Annals of Statistics, 28(2):461-482.