On robust classification using projection depth

Dutta, Subhajit; Ghosh, Anil K.

doi:10.1007/s10463-011-0324-y

Cited by 44 publications

(22 citation statements)

References 38 publications

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“…To describe multimodal densities, Paindaveine and van Bever (2013) and Agostinelli and Romanazzi (2011) proposed local versions of depth and Lok and Lee (2011) introduced a depth function based on interpoint distances. Depth is also applied to analyze distributions as shown by Kong and Zuo (2010), Mizera and Müller (2004) and Rousseeuw and Ruts (1999) or for classification as presented by Dutta and Ghosh (2012) and Li et al (2012). See also the book of Mosler (2002) and the general approaches of Zuo and Serfling (2000a,b) or Mizera (2002).…”

Section: Introductionmentioning

confidence: 99%

Simplified simplicial depth for regression and autoregressive growth processes

Kustosz

Müller

Wendler

2016

Journal of Statistical Planning and Inference

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We simplify simplicial depth for regression and autoregressive growth processes in two directions. At first we show that often simplicial depth reduces to counting the subsets with alternating signs of the residuals. The second simplification is given by not regarding all subsets of residuals. By consideration of only special subsets of residuals, the asymptotic distributions of the simplified simplicial depth notions are normal distributions so that tests and confidence intervals can be derived easily. We propose two simplifications for the general case and a third simplification for the special case where two parameters are unknown. Additionally, we derive conditions for the consistency of the tests. We show that the simplified depth notions can be used for polynomial regression, for several nonlinear regression models, and for several autoregressive growth processes. We compare the efficiency and robustness of the different simplified versions by a simulation study concerning the Michaelis-Menten model and a nonlinear autoregressive process of order one.

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Section: Introductionmentioning

confidence: 99%

Simplified simplicial depth for regression and autoregressive growth processes

Kustosz

Müller

Wendler

2016

Journal of Statistical Planning and Inference

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“…On the other hand it often yields ties when the depth function is identically zero on large domains, as is the case with halfspace depth and simplicial depth. Dutta and Ghosh (2011) avoided this problem by using projection depth instead, whereas Hubert and Van der Veeken (2010) employed the skew-adjusted projection depth.…”

Section: Multivariate Classifiers 41 Existing Methodsmentioning

confidence: 99%

Multivariate and functional classification using depth and distance

Hubert

Rousseeuw

Segaert

2016

Adv Data Anal Classif

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We construct classifiers for multivariate and functional data. Our approach is based on a kind of distance between data points and classes. The distance measure needs to be robust to outliers and invariant to linear transformations of the data. For this purpose we can use the bagdistance which is based on halfspace depth. It satisfies most of the properties of a norm but is able to reflect asymmetry when the class is skewed. Alternatively we can compute a measure of outlyingness based on the skew-adjusted projection depth. In either case we propose the DistSpace transform which maps each data point to the vector of its distances to all classes, followed by k-nearest neighbor (kNN) classification of the transformed data points. This combines invariance and robustness with the simplicity and wide applicability of kNN. The proposal is compared with other methods in experiments with real and simulated data. arXiv:1504.01128v3 [stat.ME] 7 Jul 2016 z := λx + (1 − λ)y. We can verify that z := (λg(x) + (1 − λ)g(y)) −1 z is a convex combination of c x and c y . By compactness of B we know that c x , c y ∈ B, and from convexity of B it then follows that z ∈ B. Therefore c z = c z z so that finally g(z) = z c z z z = λg(x) + (1 − λ)g(y) .

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“…The data depth function is a robust tool to rank multivariate datasets (Dutta and Ghosh 2012). We use Depth-Depth plots (DD-plots; described in Section 2.2) to define catchment similarity based on catchment response behaviour.…”

Section: Contribution Of This Papermentioning

confidence: 99%

Nonparametric catchment clustering using the data depth function

Singh

McMillan

Bàrdossy

et al. 2016

Hydrological Sciences Journal

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The clustering of catchments has been important for prediction in ungauged basins, model parameterization and watershed development and management. The aim of this study is to explore a new measure of similarity among catchments, using a data depth function and comparing it with catchment clustering indices based on flow and physical characteristics. A cluster analysis was performed for each similarity measure using the affinity propagation clustering algorithm. We evaluated the similarity measure based on depth-depth plots (DDplots) as a basis for transferring parameter sets of a hydrological model between catchments.A case study was developed with 21 catchments in a diverse New Zealand region. Results show that clustering based on the depth-depth measure is dissimilar to clustering on catchment characteristics, flow, or flow indices. A hydrological model was calibrated for 21 catchments and the transferability of model parameters among similar catchments was tested within and between clusters defined by each clustering method. The mean model performance for parameters transferred within group always outperformed those from outside the group. The DD-plot based method was found to produce the best in-group performance and second-highest difference between in-group and out-group performance.

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On robust classification using projection depth

Cited by 44 publications

References 38 publications

Simplified simplicial depth for regression and autoregressive growth processes

Simplified simplicial depth for regression and autoregressive growth processes

Multivariate and functional classification using depth and distance

Nonparametric catchment clustering using the data depth function

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