Journal ArticleDOI
Minimum covariance determinant
Mia Hubert,Michiel Debruyne +1 more
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The minimum covariance determinant (MCD) estimator is a highly robust estimator of multivariate location and scatter and can be computed efficiently with the FAST‐MCD algorithm of Rousseeuw and Van Driessen.Abstract:
The minimum covariance determinant (MCD) estimator is a highly robust estimator of multivariate location and scatter. It can be computed efficiently with the FAST-MCD algorithm of Rousseeuw and Van Driessen. Since estimating the covariance matrix is the cornerstone of many multivariate statistical methods, the MCD has also been used to develop robust and computationally efficient multivariate techniques.
In this paper, we review the MCD estimator, along with its main properties such as affine equivariance, breakdown value, and influence function. We discuss its computation, and list applications and extensions of the MCD in theoretical and applied multivariate statistics. Copyright © 2009 John Wiley & Sons, Inc.
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Citations
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Journal ArticleDOI
SC3: consensus clustering of single-cell RNA-seq data
Vladimir Yu. Kiselev,Kristina Kirschner,Michael T. Schaub,Michael T. Schaub,Tallulah S. Andrews,Andrew Yiu,Tamir Chandra,Tamir Chandra,Kedar Nath Natarajan,Kedar Nath Natarajan,Wolf Reik,Wolf Reik,Wolf Reik,Mauricio Barahona,Anthony R. Green,Martin Hemberg +15 more
TL;DR: It is demonstrated that SC3 is capable of identifying subclones from the transcriptomes of neoplastic cells collected from patients and achieves high accuracy and robustness by combining multiple clustering solutions through a consensus approach.
Journal ArticleDOI
Robust statistics for outlier detection
Peter J. Rousseeuw,Mia Hubert +1 more
TL;DR: An overview of several robust methods and outlier detection tools for univariate, low‐dimensional, and high‐dimensional data such as estimation of location and scatter, linear regression, principal component analysis, and classification are presented.
Posted ContentDOI
SC3 consensus clustering of singlecell RNASeq data
Vladimir Yu. Kiselev,Kristina Kirschner,Michael T. Schaub,Tallulah S. Andrews,Tamir Chandra,Kedar Nath Natarajan,Wolf Reik,Mauricio Barahona,Anthony R. Green,Martin Hemberg +9 more
TL;DR: Single-Cell Consensus Clustering (SC3), a tool for unsupervised clustering of scRNA-seq data, achieves high accuracy and robustness by consistently integrating different clustering solutions through a consensus approach.
Posted Content
Influence Function and Efficiency of the Minimum Covariance Determinant Scatter MAtrix Estimator
TL;DR: In this paper, the influence function of the MCD scatter estimator is derived and the asymptotic variances of its elements are compared with the one step reweighted MCD and with S-estimators.
Journal ArticleDOI
Review and big data perspectives on robust data mining approaches for industrial process modeling with outliers and missing data
TL;DR: A systematic review of various state-of-the-art data preprocessing tricks as well as robust principal component analysis methods for process understanding and monitoring applications and big data perspectives on potential challenges and opportunities have been highlighted.
References
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Robust statistics: the approach based on influence functions
TL;DR: This paper presents a meta-modelling framework for estimating the values of Covariance Matrices and Multivariate Location using one-Dimensional and Multidimensional Estimators.
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Least Median of Squares Regression
TL;DR: In this paper, the median of the squared residuals is used to resist the effect of nearly 50% of contamination in the data in the special case of simple least square regression, which corresponds to finding the narrowest strip covering half of the observations.
Journal ArticleDOI
A fast algorithm for the minimum covariance determinant estimator
TL;DR: For small datasets, FAST-MCD typically finds the exact MCD, whereas for larger datasets it gives more accurate results than existing algorithms and is faster by orders.