Classification with the pot–pot plot

Pokotylo, Oleksii; Mosler, Karl

doi:10.1007/s00362-016-0854-8

Cited by 4 publications

(3 citation statements)

References 23 publications

(43 reference statements)

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“…An alternative to calculating a local depth at a given point is estimating its density value through a proper kernel estimate; this proves useful in DD-plot-like classification (Pokotylo and Mosler, 2019).…”

Section: Local Depthsmentioning

confidence: 99%

Choosing among notions of multivariate depth statistics

Mosler¹,

Mozharovskyi²

2020

Preprint

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Classical multivariate statistics measures the outlyingness of a point by its Mahalanobis distance from the mean, which is based on the mean and the covariance matrix of the data. A depth function is a function which, given a point and a distribution in d-space, measures centrality by a number between 0 and 1, while satisfying certain postulates regarding invariance, monotonicity, convexity and continuity. Accordingly, numerous notions of multivariate depth have been proposed in the literature, some of which are also robust against extremely outlying data. The departure from classical Mahalanobis distance does not come without cost. There is a trade-off between invariance, robustness and computational feasibility. In the last few years, efficient exact algorithms as well as approximate ones have been constructed and made available in R-packages. Consequently, in practical applications the choice of a depth statistic is no more restricted to one or two notions due to computational limits; rather often more notions are feasible, among which the researcher has to decide. We discuss the theoretical and practical aspects of this choice, including invariance and uniqueness, robustness and computational feasibility. Complexity and speed of exact algorithms are compared and the use of different depths in classification problems. The accuracy of approximate approaches like the random Tukey depth is discussed as well as the application to large and high-dimensional data. Also, local and functional depths are shortly addressed.

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Section: Local Depthsmentioning

confidence: 99%

Choosing among notions of multivariate depth statistics

Mosler¹,

Mozharovskyi²

2020

Preprint

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“…• A classifier which uses a specific local depth was suggested by Pokotylo and Mosler (2016). Instead of term "DD-plot" used by Li et al (2012) they use term "pot-pot plot", where pot-pot is a shortcut for potential versus potential.…”

Section: Advanced Depth-based Classifiersmentioning

confidence: 99%

Depth-based Classification for Multivariate Data

Vencálek

2017

AJS

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Concept of data depth provides one possible approach to the analysis of multivariate data.<br />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.<br />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.<br />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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“…The sample h-depth (2) is fast to compute and easily interpretable. Even though in X = R d the concept does not fit directly into the framework of (global) statistical depths [100,84] but rather to their localised counterparts [76], in function spaces it proved to be highly competitive [16,17,24,25,8,75,78]. The h-depth is frequently used as a well performing benchmark method in nonparametric FDA [33,54,14], and is available in standard FDA software packages [26,79].…”

Section: Introduction: Statistical Depth For Functional Datamentioning

confidence: 99%

Statistical Depth Meets Machine Learning: Kernel Mean Embeddings and Depth in Functional Data Analysis

Wynne,

Nagy

2021

Preprint

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Statistical depth is the act of gauging how representative a point is compared to a reference probability measure. The depth allows introducing rankings and orderings to data living in multivariate, or function spaces. Though widely applied and with much experimental success, little theoretical progress has been made in analysing functional depths. This article highlights how the common h-depth and related statistical depths for functional data can be viewed as a kernel mean embedding, a technique used widely in statistical machine learning. This connection facilitates answers to open questions regarding statistical properties of functional depths, as well as it provides a link between the depth and empirical characteristic function based procedures for functional data.

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Classification with the pot–pot plot

Cited by 4 publications

References 23 publications

Choosing among notions of multivariate depth statistics

Choosing among notions of multivariate depth statistics

Depth-based Classification for Multivariate Data

Statistical Depth Meets Machine Learning: Kernel Mean Embeddings and Depth in Functional Data Analysis

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