Fast nonparametric classification based on data depth
This work addresses classification tasks in statistics and machine learning, offering a faster alternative to existing methods, though it appears incremental as it builds on depth-based approaches.
The authors tackled the problem of classifying multi-dimensional objects into multiple classes by developing a nonparametric procedure called DDa-classifier, which uses depth plots and an efficient algorithm, resulting in comparable error rates but significantly faster performance than other methods like SVM.
A new procedure, called DDa-procedure, is developed to solve the problem of classifying d-dimensional objects into q >= 2 classes. The procedure is completely nonparametric; it uses q-dimensional depth plots and a very efficient algorithm for discrimination analysis in the depth space [0,1]^q. Specifically, the depth is the zonoid depth, and the algorithm is the alpha-procedure. In case of more than two classes several binary classifications are performed and a majority rule is applied. Special treatments are discussed for 'outsiders', that is, data having zero depth vector. The DDa-classifier is applied to simulated as well as real data, and the results are compared with those of similar procedures that have been recently proposed. In most cases the new procedure has comparable error rates, but is much faster than other classification approaches, including the SVM.