The Cosine Depth Distribution Classifier for Directional Data
Directions, rotations, axes, clock, or calendar measurements can be represented as angles or equivalently as unit vectors. As points lying on the boundary of circles, spheres, or hyper-spheres, they are also referred as directional data, and they require dedicated methods to be analyzed. In the framework of supervised classification, this work introduces a directional data classifier based on a data depth function. Depth functions provide an inner–outer ordering of the data in a reference space according to some centrality measure, and have appeared as a powerful tool in many fields of multivariate statistics. The recently introduced distance-based depth functions for directional data are considered here. More specifically, this work introduces a cosine depth based distribution method which aims at assigning directional data to classes, given that a training set with class labels is already available. A simulation study evaluating the performance of the proposed method is provided.
The authors wish to thank the two anonymous referees for their precious comments on a first version of this work. Thanks are also due to Giuseppe Pandolfo and Ondrej Vencalek for their valuable support and suggestions.
- Batschelet, E. (1981). Circular statistics in biology. London: Academic.Google Scholar
- Chang, T. (1993). Spherical regression and the statistics of tectonic plate reconstructions. International Statistical Review/Revue Internationale de Statistique, 61(2), 299316.Google Scholar
- Downs, T. D., & Liebman, J. (1969). Statistical methods for vectorcardiographic directions. IEEE Transactions on Biomedical Engineering, 16(1), 8794.Google Scholar
- James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An introduction to statistical learning. New York: Springer.Google Scholar
- Mahalanobis, P. (1936). On the generalized distance in statistics. Proceedings of the National Institute of Science of India, 12, 4955.Google Scholar
- Mardia, K. V., & Jupp, P. E. (2009). Directional statistics. New York: Wiley.Google Scholar
- Rousseeuw, P. J., Ruts, I., & Tukey, J. W. (1999). The bagplot: A bivariate boxplot. The American Statistician, 53(4), 382387.Google Scholar
- Tukey, J. W. (1975). Mathematics and the picturing of data. Proceedings of the International Congress of Mathematicians, Vancouver, 1975(2), 523531.Google Scholar
- Vapnik, V. (1998). Statistical learning theory. New York: Wiley.Google Scholar
- Vencálek, O. (2017). Depth-based classification for multivariate data. Austrian Journal of Statistics, 46(34), 117128.Google Scholar