Special issue on “Advances on model-based clustering and classification”

Advances in Data Analysis and Classification -     

Synthesis of the first stable phosphonamide transition state analogue

Three methods were selected for the one-pot synthesis of the fully protected beta-fluoroaminophosphonic acids, using the readily accessible N-protected beta-fluoroaminals. These were activated by acylation leading, by beta-elimination, to a transient N-acylimine immediately trapped by reactive forms of dialkyl phosphites. Avoiding basic conditions, the complete or partial deprotection of these N-protected beta-fluoroaminophosphonic esters allowed the synthesis of the free amino acids, their esters, and a racemic beta-trifluorophosphonamidic acid. The latter, which represents a transition state analogue formed by the bacterial transpeptidase, is perfectly stable at pH 4.7, contrary to the nonfluorinated compounds.     

An Improved Model for Predicting Proton NMR Shielding by Alkenes Based on Ab Initio GIAO Calculations

In a strong magnetic field, nuclei located over a carbon-carbon double bond experience NMR shielding effects that are the net result of the magnetic anisotropy of the nearby double bond and various other intramolecular shielding effects. We have used GIAO, a subroutine in Gaussian 4, to calculate isotropic shielding values and to predict the proton NMR shielding increment for a simple model system: methane held in various orientations and positions over ethene. The average proton NMR shielding increments of several orientations of methane have been plotted versus the Cartesian coordinates of the methane protons relative to the center of ethene. A single empirical equation for predicting the NMR shielding experienced by protons over a carbon-carbon double bond has been developed from these data. The predictive capability of this equation has been validated by comparing the shielding increments for several alkenes calculated using our equation to the experimentally observed shielding increments. This equation predicts the NMR shielding effects more accurately than a previous model that was based on only one orientation of methane over ethene. Deshielding is predicted by this equation for protons over the center and within about 3 Å of a carbon-carbon double bond. This result is in contrast to predictions made by the long-held shielding cone model based on the McConnell equation found in nearly every textbook on NMR, but is consistent with experimental observations.     

Clustering bivariate mixed-type data via the cluster-weighted model

The cluster-weighted model (CWM) is a mixture model with random covariates that allows for flexible clustering/classification and distribution estimation of a random vector composed of a response variable and a set of covariates. Within this class of models, the generalized linear exponential CWM is here introduced especially for modeling bivariate data of mixed-type. Its natural counterpart in the family of latent class models is also defined. Maximum likelihood parameter estimates are derived using the expectation-maximization algorithm and some computational issues are detailed. Through Monte Carlo experiments, the classification performance of the proposed model is compared with other mixture-based approaches, consistency of the estimators of the regression coefficients is evaluated, and several likelihood-based information criteria are compared for selecting the number of mixture components. An application to real data is also finally considered.     

Special issue on “Innovations on model based clustering and classification”

Advances in Data Analysis and Classification -     

Special issue on “Models and learning for clustering and Classification”

Advances in Data Analysis and Classification -     

An Empirical Proton NMR Shielding Equation for Alkenes Based on Ab Initio Calculations

Nuclei of hydrogen atoms located over a carbon-carbon double bond in the presence of a strong magnetic field experience a perturbed magnetic field caused primarily by the magnetic anisotropy of the bond. However, the commonly used theoretical model for predicting the shielding effect of an alkene double bond on hydrogen nuclei is sometimes inconsistent with the observed proton NMR chemical shifts in structures that have covalently bonded hydrogens located over a carbon-carbon double bond. We have used the ab initio gauge including atomic orbital (GIAO) method to calculate isotropic shielding values and to determine the proton NMR shielding increments for a simple model system: methane held at various positions over ethene. These shielding increments calculated for one proton of methane have been mapped as a function of their position in Cartesian coordinates relative to the center of ethene. A mathematical function has been fit to this three-dimensional shielding increment surface at each of four distances from the face of the ethene molecule. Additionally, a single mathematical equation has been developed for predicting the shielding caused by the carbon-carbon double bond in ethene. In contrast to the traditionally employed shielding model, our results predict deshielding for protons within 3 Å above the center of a carbon-carbon double bond, consistent with experimental observations in several molecular systems. The NMR shielding increments predicted by this equation are compared to observed shielding increments in some test alkenes.     

Eigenvalues and constraints in mixture modeling: geometric and computational issues

This paper presents a review about the usage of eigenvalues restrictions for constrained parameter estimation in mixtures of elliptical distributions according to the likelihood approach. The restrictions serve a twofold purpose: to avoid convergence to degenerate solutions and to reduce the onset of non interesting (spurious) local maximizers, related to complex likelihood surfaces. The paper shows how the constraints may play a key role in the theory of Euclidean data clustering. The aim here is to provide a reasoned survey of the constraints and their applications, considering the contributions of many authors and spanning the literature of the last 30 years.     

Mixture decomposition via the simulated annealing algorithm

This paper presents the problem of the evaluation of the maximum likelihood estimator, when the likelihood function has multiple maxima, using the stochastic algorithm called ‘simulated annealing’. Analysis of the particular case of the decomposition of a mixture of five univariate normal distributions shows the properties of this methodology with respect to the E—M algorithm. The results are compared considering some distance measures between the estimated distribution functions and the true one.