173,758 research outputs found
What are the true clusters?
No full textConstructivist philosophy and Hasok Chang's active scientific realism are used to argue that the idea of ``truth'' in cluster analysis depends on the context and the clustering aims. Different characteristics of clusterings are required in different situations. Researchers should be explicit about on what requirements and what idea of ``true clusters'' their research is based, because clustering becomes scientific not through uniqueness but through transparent and open communication. The idea of ``natural kinds'' is a human construct, but it highlights the human experience that the reality outside the observer's control seems to make certain distinctions between categories inevitable. Various desirable characteristics of clusterings and various approaches to define a context-dependent truth are listed, and I discuss what impact these ideas can have on the comparison of clustering methods, and the choice of a clustering methods and related decisions in practice
An adequacy approach for deciding the number of clusters for OTRIMLE robust Gaussian mixture-based clustering
No full textWe introduce a new approach to deciding the number of clusters. The approach is applied to Optimally Tuned Robust Improper Maximum Likelihood Estimation (OTRIMLE; Coretto & Hennig, Journal of the American Statistical Association111, 1648–1659) of a Gaussian mixture model allowing for observations to be classified as ‘noise’, but it can be applied to other clustering methods as well. The quality of a clustering is assessed by a statistic Q that measures how close the within-cluster distributions are to elliptical unimodal distributions that have the only mode in the mean. This non-parametric measure allows for non-Gaussian clusters as long as they have a good quality according to Q. The simplicity of a model is assessed by a measure S that prefers a smaller number of clusters unless additional clusters can reduce the estimated noise proportion substantially. The simplest model is then chosen that is adequate for the data in the sense that its observed value of Q is not significantly larger than what is expected for data truly generated from the fitted model, as can be assessed by parametric bootstrap. The approach is compared with model-based clustering using the Bayesian information criterion (BIC) and the integrated complete likelihood (ICL) in a simulation study and on real two data sets
On the neural encoding of object information : a model simulation study of the fly lobula plate network
No full textHennig P. On the neural encoding of object information : a model simulation study of the fly lobula plate network. Bielefeld: Universität; 2011
An adequacy approach for deciding the number of clusters for OTRIMLE robust Gaussian mixture‐based clustering
No full textWe introduce a new approach to deciding the number of clusters. The approach is applied to Optimally Tuned Robust Improper Maximum Likelihood Estimation (OTRIMLE; Coretto & Hennig, Journal of the American Statistical Association111, 1648-1659) of a Gaussian mixture model allowing for observations to be classified as 'noise', but it can be applied to other clustering methods as well. The quality of a clustering is assessed by a statistic Q that measures how close the within-cluster distributions are to elliptical unimodal distributions that have the only mode in the mean. This non-parametric measure allows for non-Gaussian clusters as long as they have a good quality according to Q. The simplicity of a model is assessed by a measure S that prefers a smaller number of clusters unless additional clusters can reduce the estimated noise proportion substantially. The simplest model is then chosen that is adequate for the data in the sense that its observed value of Q is not significantly larger than what is expected for data truly generated from the fitted model, as can be assessed by parametric bootstrap. The approach is compared with model-based clustering using the Bayesian information criterion (BIC) and the integrated complete likelihood (ICL) in a simulation study and on real two data sets
C. Hennig's compendiöse Menagerie der vorzüglichsten Säugethiere und Vögel; Ein unterhaltendes und lehrreiches Lese- und Schaubuch für die Jugend zur ersten Begründung naturwissenschaftlicher Kenntnisse
No full textFour-dimensional quantum study on exothermic complex-forming reactions: Cl−+CH3Br→ClCH3+Br−
No full textThe exothermic gas-phase bimolecular nucleophilic substitution (S(N)2) reaction Cl-+CH3Br (upsilon(1)('),upsilon(2)('),upsilon(3)('))-> ClCH3 (upsilon(1),upsilon(2),upsilon(3))+Br- and the corresponding endothermic reverse reaction have been studied by time-independent quantum scattering calculations in hyperspherical coordinates on a coupled-cluster potential-energy surface. The dimensionality-reduced model takes four degrees of freedom into account [Cl-C and C-Br stretching modes (quantum numbers upsilon(3)(') and upsilon(3)); totally symmetric modes of the methyl group, i.e., C-H stretching (upsilon(1)(') and upsilon(1)) and umbrella bending vibrations (upsilon(2)(') and upsilon(2))]. Diagonalization of the Hamiltonian was performed employing the Lanczos algorithm with a variation of partial reorthogonalization. A narrow grid in the total energy was employed so that long-living resonance states could be resolved and extracted. While excitation of the reactant umbrella bending mode already leads to a considerable enhancement of the reaction probability, its combination with vibrational excitation of the broken C-Br bond, (0, 1, 1), results in a strong synergic effect that can be rationalized by the similarity with the classical transitional normal mode. Exciting the C-H stretch has a non-negligible effect on the reaction probability, while for larger translational energies this mode follows the expected spectatorlike behavior. Combination of C-Br stretch and symmetric C-H, (1,0,1), stretch does not show a cooperative effect. Contrary to the spectator mode concept, energy originally stored in the C-H stretching mode is by no means conserved, but almost completely released in other modes of the reaction products. Products are most likely formed in states with a high degree of excitation in the new C-Cl bond, while the internal modes of the methyl group are less important. Reactants with combined umbrella/C-Br stretch excitation, (0, 1, 1), may yield products with two quanta in the umbrella mode. (C) 2005 American Institute of Physics
Breakdown points for maximum likelihood estimators of location-scale mixtures
No full textML-estimation based on mixtures of Normal distributions is a widely used tool for cluster analysis. However, a single outlier can make the parameter estimation of at least one of the mixture components break down. Among others, the estimation of mixtures of t-distributions by McLachlan and Peel [Finite Mixture Models (2000) Wiley, New York] and the addition of a further mixture component accounting for ?noise? by Fraley and Raftery [The Computer J. 41 (1998) 578?588] were suggested as more robust alternatives. In this paper, the definition of an adequate robustness measure for cluster analysis is discussed and bounds for the breakdown points of the mentioned methods are given. It turns out that the two alternatives, while adding stability in the presence of outliers of moderate size, do not possess a substantially better breakdown behavior than estimation based on Normal mixtures. If the number of clusters s is treated as fixed, r additional points suffice for all three methods to let the parameters of r clusters explode. Only in the case of r=s is this not possible for t-mixtures. The ability to estimate the number of mixture components, for example, by use of the Bayesian information criterion of Schwarz [Ann. Statist. 6 (1978) 461?464], and to isolate gross outliers as clusters of one point, is crucial for an improved breakdown behavior of all three techniques. Furthermore, a mixture of Normals with an improper uniform distribution is proposed to achieve more robustness in the case of a fixed number of components
Reduced-dimensionality calculation of reaction cross sections and rate constant for the complex-forming gas-phase S(N)2 reaction Cl-+CH3Cl ' -> ClCH3+Cl '(-)
No full textEmploying a 4D CCSD(T) potential energy surface, initial-state selected reaction cross sections for the complex-forming gas-phase identity S(N)2 reaction Cl- + CH3Cl' (upsilon(1), upsilon(2), upsilon(3)) --> ClCH3 (upsilon(1)', upsilon(2)', upsilon(3)') + Cl'(-) have been calculated by means of time-independent quantum scattering theory in hyperspherical coordinates. The totally symmetric internal modes of the methyl group (C-H stretching vibration, quantum numbers upsilon(1) and upsilon(1)', and umbrella bending vibration, upsilon(2) and upsilon(2)') and the two C-Cl stretching modes (upsilon(3) and upsilon(3)') are included. The results for pure C-Cl stretching excitation in the reactants are similar to those obtained in earlier 2D calculations. The cooperative effect of C-Cl stretching and umbrella bending modes is even more pronounced for cross sections than for reaction probabilities. The same holds for excitations of the pure internal CH3 modes; in particular, the ratio of cross sections for reaction with the C-H stretch excited to reaction out of the vibrational ground state is five orders of magnitude larger than the ratio of the corresponding probabilities. This questions the concept of "spectator' modes in reaction dynamics which is valid only for thermal rate constants where the "spectator' modes play a negligible role due to their low population. Transition state theory rate constants fortuitously show good agreement with experiment while the reduced-dimensionality quantum calculations show larger deviations. Possible sources of this discrepancy are discussed in detail. Neglect of reactant CH3Cl rotation and the related modes in the transition state (doubly degenerate Cl center dot center dot center dot CH(3)center dot center dot center dot Cl' bend and K rotation) yields very good agreement with experiment
How many bee species? a case study in determining the number of clusters
No full textIt is argued that the determination of the best number of clusters k
is crucially dependent on the aim of clustering. Existing supposedly
“objective” methods of estimating k ignore this. k can be determined
by listing a number of requirements for a good clustering in the given
application and finding a k that fulfils them all. The approach is illustrated
by application to the problem of finding the number of species in a data
set of Australasian tetragonula bees. Requirements here include two new
statistics formalising the largest within-cluster gap and cluster separation.
Due to the typical nature of expert knowledge, it is difficult to make
requirements precise, and a number of subjective decisions is involved
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