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Extreme Maximum Margin Clustering

Chen ZHANG, ShiXiong XIA, Bing LIU, Lei ZHANG
2013 IEICE transactions on information and systems  
Maximum margin clustering (MMC) is a newly proposed clustering method that extends the large-margin computation of support vector machine (SVM) to unsupervised learning.  ...  Since extreme learning machine (ELM) has achieved similar generalization performance at much faster learning speed than traditional SVM and LS-SVM, we propose an extreme maximum margin clustering (EMMC  ...  In this paper, we propose an extreme maximum margin clustering (EMMC) method based on ELM.  ... 
doi:10.1587/transinf.e96.d.1745 fatcat:fie5sykj4bg7bp3p3tllpgkv4i

Explicit agreement extremes for a 2×2 table with given marginals [article]

José E. Chacón
2020 arXiv   pre-print
The problem of maximizing (or minimizing) the agreement between clusterings, subject to given marginals, can be formally posed under a common framework for several agreement measures.  ...  Here, an explicit solution is shown for the case where the two clusterings have two clusters each.  ...  However, Hubert and Arabie (1985) also noted that another (perhaps more adequate) bound that could be used is the maximum of the index given the fixed marginals (i.e., the cluster sizes of each of the  ... 
arXiv:2001.07415v1 fatcat:kublxryfbzdunjdpgl77363zla

Modelling heatwaves in central France: a case-study in extremal dependence

Hugo C. Winter, Jonathan A. Tawn
2015 Journal of the Royal Statistical Society, Series C: Applied Statistics  
Extreme value theory is a general framework from which inference can be drawn from extreme events.  ...  Heatwaves are a type of extreme event which are by definition rare and as such there exists little data in the historical record to help planners.  ...  Marginal parameters are estimated using a censored likelihood approach. For modelling extremal dependence we need to select an appropriate margin to transform onto.  ... 
doi:10.1111/rssc.12121 fatcat:2nopfc6qqrbdvfg6c63q3ccf4i

PARTITION METHOD IN COPULA BASED HIERARCHICAL BAYESIAN SPATIO-TEMPORAL MODEL(Session 5C(IASC-ARS))

Amran, Iriawan N, Subiono, Irhamah
2012 Proceedings of the Symposium of Japanese Society of Computational Statistics  
In this paper, we propose partition method to make homogeneity clusters in order to apply Copula Based Hierarchical Bayesian Spatio-Temporal Model at non-homogeneity extreme rainfa11s observation.  ...  There are three difllerent characteristics of extreme rainfa11s were fbund by this method.  ...  extreme observation into different clusters.  ... 
doi:10.20551/jscssymo.26.0_181 fatcat:n5aiiklj4vagll75sbdshm53ni

kth-order Markov extremal models for assessing heatwave risks

Hugo C. Winter, Jonathan A. Tawn
2016 Extremes  
Under this new framework, the observed daily maximum temperatures at Orleans, in central France, are found to be well modelled by an asymptotically independent third-order extremal Markov model.  ...  Previous studies of temporal dependence of extremes have assumed either a first-order Markov model or a particularly strong form of extremal dependence, known as asymptotic dependence.  ...  As in , daily maximum temperatures have been analysed instead of looking at the joint distribution of daily maximum and minimum temperatures.  ... 
doi:10.1007/s10687-016-0275-z fatcat:3qijdro2ibhnzezrhh7lhmgvja

Characterising the changing behaviour of heatwaves with climate change

Hugo C. Winter, Simon J. Brown, Jonathan A. Tawn
2017 Dynamics and Statistics of the Climate System  
Acknowledgements We also thank Met Office for data, Pete Falloon for literature and background on how climate change affects food security, and the referees for extremely helpful comments that have improved  ...  Firstly, the extremal index to give an estimate of the average length of a cluster.  ...  Marginal modelling Modelling strategy Daily maximum temperatures at a site are related to a covariate g t .  ... 
doi:10.1093/climsys/dzw006 fatcat:3e3vd6ovmvhnnhhtu5mzfgnosq

Bayesian comparison of different rainfall depth–duration–frequency relationships

Aurélie Muller, Jean-Noël Bacro, Michel Lang
2007 Stochastic environmental research and risk assessment (Print)  
An empirical model based on the Generalized Extreme Value Distribution is presented for hourly maximum rainfall, and improved by the inclusion of daily maximum rainfall, through the extremal indexes of  ...  Dependence is modelled using the bivariate extreme logistic distribution. The results are calculated in a Bayesian framework with a Markov Chain Monte Carlo algorithm.  ...  the size of clusters of extreme values.  ... 
doi:10.1007/s00477-006-0095-9 fatcat:i3cx7fzwofcxtkslhps7ylvxgq

Clustering by the Probability Distributions from Extreme Value Theory [article]

Sixiao Zheng, Ke Fan, Yanxi Hou, Jianfeng Feng, Yanwei Fu
2022 arXiv   pre-print
Notably, we propose the concept of centroid margin distance, use GPD to establish a probability model for each cluster, and perform a clustering algorithm based on the covering probability function derived  ...  Our novel clustering algorithm thus models the distributions of distances to centroids over a threshold by Generalized Pareto Distribution (GPD) in Extreme Value Theory (EVT).  ...  We propose the concept of centroid margin distance, and use GPD to establish a probability model for each cluster, and perform clustering based on covering probability function derived from GPD.  ... 
arXiv:2202.09784v1 fatcat:vf7e35hwqfbw3efmzzxt5hnvmi

Extremes of Stationary Time Series [chapter]

2005 Statistics of Extremes  
The Sample Maximum Let X 1 , X 2 , . . . be a (strictly) stationary sequence of random variables with marginal distribution function F .  ...  The distinction is due to the extremal index, introduced in section 10.2.3, which measures the tendency of extreme values to occur in clusters.  ...  cluster maximum, cluster size and cluster excess.  ... 
doi:10.1002/0470012382.ch10 fatcat:ef7vabpzhnfcfc2dsp2vpvrzcm

Inference for clusters of extreme values

Christopher A. T. Ferro, Johan Segers
2003 Journal of The Royal Statistical Society Series B-statistical Methodology  
Recall that a string characterises the position of cluster points relative to the cluster maximum. In order to compute strings, the marginal distribution of the exceedances must be specified.  ...  Processes 2 and 3 have two points per cluster, each of which contributes a coordinate to the cluster maximum. The distance between the cluster points and the cluster maximum is greater in process 3.  ... 
doi:10.1111/1467-9868.00401 fatcat:enuipfdmwzbdllti6xko6wcbjq

Modelling extremes of time-dependent data by Markov-switching structures

Péter Elek, András Zempléni
2009 Journal of Statistical Planning and Inference  
We investigate the extremal clustering behaviour of stationary time series that possess two regimes, where the switch is governed by a hidden two-state Markov chain.  ...  Based on this observation, we propose an estimation and simulation scheme to analyse the extremal dependence structure of such models, taking into account only observations above high thresholds.  ...  Making inference on the distribution of cluster functionals such as the cluster maximum, the duration of an extremal cluster or the aggregate excess within the cluster is important both from a theoretical  ... 
doi:10.1016/j.jspi.2008.08.022 fatcat:72dhenxm7bc7lgx72t7jdiek3e

Minimum adjusted Rand index for two clusterings of a given size [article]

José E. Chacón, Ana I. Rastrojo
2020 arXiv   pre-print
Here, an explicit formula for the lowest possible value of the ARI for two clusterings of given sizes is shown, and moreover a specific pair of clusterings achieving such a bound is provided.  ...  Since its introduction, exploring the situations of extreme agreement and disagreement under different circumstances has been a subject of interest, in order to achieve a better understanding of this index  ...  are commonly referred to as the marginals, or marginal clustering distributions.  ... 
arXiv:2002.03677v3 fatcat:cfwor35o65gujdtbnbtrbwnyae

JointMMCC: Joint Maximum-Margin Classification and Clustering of Imaging Data

Roman Filipovych, Susan M. Resnick, Christos Davatzikos
2012 IEEE Transactions on Medical Imaging  
We describe a Joint Maximum-Margin Classification and Clustering (JointMMCC) approach that jointly detects the pathologic population via semi-supervised classification, as well as disentangles heterogeneity  ...  of the pathological cohort by solving a clustering subproblem.  ...  Joint maximum-margin classification and clustering A.  ... 
doi:10.1109/tmi.2012.2186977 pmid:22328179 pmcid:PMC3386308 fatcat:nxmow5rjgvbofakpruztb5vy7m

Bivariate Analysis of Extreme Wave and Storm Surge Events. Determining the Failure Area of Structures

Panagiota Galiatsatou
2011 The Open Ocean Engineering Journal  
The parameters of the margins of the bivariate distribution are defined by three different methods of estimation: a) the Maximum Likelihood Estimation (MLE) approach, b) a Bayesian procedure with flat  ...  An approach to estimate the failure area of a particular structure under extreme sea conditions is presented, using the margins resulting from the three different estimation methods.  ...  In the present paper, an attempt to "de-cluster" extreme wave height and storm surge events similar to the most commonly used approach of explicitly identifying clusters of storm events (a cluster of storm  ... 
doi:10.2174/1874835x01104010003 fatcat:stcgt6srwfa7ldnf4ndzdpyjby

Likelihood estimation of the extremal index

Mária Süveges
2007 Extremes  
Two estimators are discussed: a maximum likelihood estimator and an iterative least squares estimator based on the normalized gaps between clusters.  ...  B 65:545, 2003) to the estimation of the extremal index, and proposes the use of a new variable decreasing the bias of the likelihood based on the point process character of the exceedances.  ...  θ , which governs the clustering of the extremes of a univariate observational series.  ... 
doi:10.1007/s10687-007-0034-2 fatcat:agiogosqcbfbzefwwcdfal2a54
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