Depth-based classification for functional data

Abstract

Classification is an important task when data are curves. Recently, the notion of statistical depth has been extended to deal with functional observations. In this paper, we propose robust procedures based on the concept of depth to classify curves. These techniques are applied to a real data example. An extensive simulation study with contaminated models illustrates the good robustness properties of these depth-based classification methods. Madrid, e-mail: juan.romo@uc3m.es. DIMACS Series in Discrete Mathematics and Theoretical Computer ScienceDepth-based classification for functional data Sara López-Pintado and Juan RomoAbstract. Classification is an important task when data are curves. Recently, the notion of statistical depth has been extended to deal with functional observations. In this paper, we propose robust procedures based on the concept of depth to classify curves. These techniques are applied to a real data example. An extensive simulation study with contaminated models illustrates the good robustness properties of these depth-based classification methods.

Consistency of non-integrated depths for functional data

“…See also López-Pintado and Romo (2006a) and López-Pintado and Romo (2007). These band depths have been generalized to the setup of vector-valued functions (Ieva and Paganoni, 2013;López-Pintado et al, 2014) and sparsely observed functional data (López-Pintado and Wei, 2011).…”

On local times, density estimation and supervised classification from functional data

“…This has been pointed out by Cèrou and Guyader [9] who have studied the consistency of the k-NN classifier when E is a metric space. Some recent results regarding supervised classification methods for functional data can be found in [11,12,9,13,14,19,23,28,30,33,38,7,10].…”

Resampling-based Classification Using Depth for Functional Curves

“…Fraiman and Muniz's depth (FM depth) (9) is defined as an integrated value of simplicial depths (12; 13) which are calculated with the values of a function over the whole interval (9). Since FM depth, some functional depths have been proposed, such as h-mode depth (3), Graphical Band based Depth (GBD) (14) and Kernelized Functional Spatial Depth (KFSD) (23). In addition to these, there is also a random projection type.…”

“…The respective depths between different classes were compared to assign an object to one of given classes (3). The distance from an object to a class was introduced for functional classification with two different methods (14). One is Distance from Trimmed Mean (DTM), and the other is Weighted Average Distance from Trimmed Mean (WAD).…”