scholarly journals Depth classification based on affine-invariant, weighted and kernel-based spatial depth functions

2021 ◽  
Vol 48 (2) ◽  
Author(s):  
Olusola S. Makinde ◽  
Keyword(s):  
Affine Invariant ◽  
Classification Methods ◽  
Statistical Depth ◽  
Depth Functions ◽  
Maximal Depth ◽  
Depth Classification ◽  
Multivariate Outcomes ◽  
Statistical Depth Functions ◽  
Spatial Depth

Several multivariate depth functions have been proposed in the literature, of which some satisfy all the conditions for statistical depth functions while some do not. Spatial depth is known to be invariant to spherical and shift transformations. In this paper, the possibility of using different versions of spatial depth in classification is considered. The covariance-adjusted, weighted, and kernel-based versions of spatial depth functions are presented to classify multivariate outcomes. We extend the maximal depth classification notions for the covariance-adjusted, weighted, and kernel-based spatial depth versions. The classifiers' performance is considered and compared with some existing classification methods using simulated and real datasets.

scholarly journals Comparison-based centrality measures

2021 ◽  
Author(s):  
Luca Rendsburg ◽  
Damien Garreau
Keyword(s):  
Machine Learning ◽  
Learning Community ◽  
Outlier Detection ◽  
Centrality Measures ◽  
Human Intelligence ◽  
Ordinal Information ◽  
Statistical Depth ◽  
Depth Functions ◽  
Statistical Depth Functions ◽  
Synthetic Datasets

AbstractRecently, learning only from ordinal information of the type “item x is closer to item y than to item z” has received increasing attention in the machine learning community. Such triplet comparisons are particularly well suited for learning from crowdsourced human intelligence tasks, in which workers make statements about the relative distances in a triplet of items. In this paper, we systematically investigate comparison-based centrality measures on triplets and theoretically analyze their underlying Euclidean notion of centrality. Two such measures already appear in the literature under opposing approaches, and we propose a third measure, which is a natural compromise between these two. We further discuss their relation to statistical depth functions, which comprise desirable properties for centrality measures, and conclude with experiments on real and synthetic datasets for medoid estimation and outlier detection.

scholarly journals Robust multivariate estimation based on statistical depth filters

Test ◽  
2021 ◽  
Author(s):  
Giovanni Saraceno ◽  
Claudio Agostinelli
Keyword(s):  
Missing Values ◽  
Statistical Data ◽  
Data Depth ◽  
Data Set ◽  
Statistical Depth ◽  
Depth Functions ◽  
Gross Error ◽  
Special Cases ◽  
Model Cell ◽  
Multivariate Estimation

AbstractIn the classical contamination models, such as the gross-error (Huber and Tukey contamination model or case-wise contamination), observations are considered as the units to be identified as outliers or not. This model is very useful when the number of considered variables is moderately small. Alqallaf et al. (Ann Stat 37(1):311–331, 2009) show the limits of this approach for a larger number of variables and introduced the independent contamination model (cell-wise contamination) where now the cells are the units to be identified as outliers or not. One approach to deal, at the same time, with both type of contamination is filter out the contaminated cells from the data set and then apply a robust procedure able to handle case-wise outliers and missing values. Here, we develop a general framework to build filters in any dimension based on statistical data depth functions. We show that previous approaches, e.g., Agostinelli et al. (TEST 24(3):441–461, 2015b) and Leung et al. (Comput Stat Data Anal 111:59–76, 2017), are special cases. We illustrate our method by using the half-space depth.

scholarly journals Depth-based Classification for Multivariate Data

2017 ◽  
Vol 46 (3-4) ◽  
pp. 117-128 ◽  
Author(s):  
Ondřej Vencálek
Keyword(s):  
Multivariate Data ◽  
Data Depth ◽  
Depth Functions ◽  
Current State ◽  
Short Summary ◽  
Maximal Depth ◽  
Local Depth

Concept of data depth provides one possible approach to the analysis of multivariate data.Among other it can be also used for classification purposes. The present paper is an overview of the research in the field of depth-based classification for multivariate data.It provides a short summary of current state of knowledge in the field of depth-based classification followed by detailed discussion of four main directions in the depth-based classification, namely semiparametric depth-based classifiers, maximal depth classifier, (maximal depth) classifiers which use local depth functions and finally advanced depth-based classifiers.We do not restrict our attention only on proposed classifiers. The paper rather aims to overview the ideas connected with depth-based classification and problems that were discussed in this context.

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