Canonical Measure of Correlation (CMC) and Canonical Measure of Distance (CMD) between sets of data. Part 3. Variable selection in classification

In multivariate regression and classification issues variable selection is an important procedure used to select an optimal subset of variables with the aim of producing more parsimonious and eventually more predictive models. Variable selection is often necessary when dealing with methodologies that produce thousands of variables, such as Quantitative Structure-Activity Relationships (QSARs) and highly dimensional analytical procedures.In this paper a novel method for variable selection for classification purposes is introduced. This method exploits the recently proposed Canonical Measure of Correlation between two sets of variables (CMC index). The CMC index is in this case calculated for two specific sets of variables, the former being comprised of the independent variables and the latter of the unfolded class matrix. The CMC values, calculated by considering one variable at a time, can be sorted and a ranking of the variables on the basis of their class discrimination capabilities results. Alternatively, CMC index can be calculated for all the possible combinations of variables and the variable subset with the maximal CMC can be selected, but this procedure is computationally more demanding and classification performance of the selected subset is not always the best one.The effectiveness of the CMC index in selecting variables with discriminative ability was compared with that of other well-known strategies for variable selection, such as the Wilks’ Lambda, the VIP index based on the Partial Least Squares-Discriminant Analysis, and the selection provided by classification trees.A variable Forward Selection based on the CMC index was finally used in conjunction of Linear Discriminant Analysis. This approach was tested on several chemical data sets. Obtained results were encouraging.     

Canonical Measure of Correlation (CMC) and Canonical Measure of Distance (CMD) between sets of data: Part 2. Variable reduction

This paper proposes a new method for determining the subset of variables that reproduce as well as possible the main structural features of the complete data set. This method can be useful for pre-treatment of large data sets since it allows discarding variables that contain redundant information. Reducing the number of variables often allows one to better investigate data structure and obtain more stable results from multivariate modelling methods.The novel method is based on the recently proposed canonical measure of correlation (CMC index) between two sets of variables [R. Todeschini, V. Consonni, A. Manganaro, D. Ballabio, A. Mauri, Canonical Measure of Correlation (CMC) and Canonical Measure of Distance (CMD) between sets of data. Part 1. Theory and simple chemometric applications, Anal. Chim. Acta submitted for publication (2009)]. Following a stepwise procedure (backward elimination), each variable in turn is compared to all the other variables and the most correlated is definitively discarded. Finally, a key subset of variables being as orthogonal as possible are selected. The performance was evaluated on both simulated and real data sets. The effectiveness of the novel method is discussed by comparison with results of other well known methods for variable reduction, such as Jolliffe techniques, McCabe criteria, Krzanowski approach and its modification based on genetic algorithms, loadings of the first principal component, Key Set Factor Analysis (KSFA), Variable Inflation Factor (VIF), pairwise correlation approach, and K correlation analysis (KIF). The obtained results are consistent with those of the other considered methods; moreover, the advantage of the proposed CMC method is that calculation is very quick and can be easily implemented in any software application.     

A chemometric approach based on a novel similarity/diversity measure for the characterisation and selection of electronic nose sensors

Electronic nose sensor signals provide a digital fingerprint of the product in analysis, which can be subsequently investigated by means of chemometrics. In this paper, the fingerprint characterisation of electronic nose data has been studied by means of a novel chemometric approach based on the partial ordering technique and the Hasse matrix. This matrix can be associated to each data sequence and the similarity between two sequences can be evaluated with the definition of a distance between the corresponding Hasse matrices. Since all the signals achieved along time are intrinsically ordered, the data provided by electronic nose can be also considered as sequential data and consequently characterized by means of the proposed approach. The similarity/diversity measure has been here applied in order to characterize the class discrimination capability of each electronic nose sensor: extra virgin olive oil samples of different geographical origin have been considered and Hasse distances have been used to select the sensors which appear more able to discriminate the olive oil origins. The distance based on the Hasse matrix has showed some useful properties and proved to be able to link each electronic nose time profile to a meaningful mathematical term (the Hasse matrix), which can be consequently studied by multivariate analysis.     

A simple synthesis of (R)-3-aminooctanoic acid (D-BAOA) from (S)-1-octyn-3-ol

A simple substrate-controlled asymmetric synthesis of (R)-3-aminooctanoic acid (D-BAOA) is described. The present method involves the conversion of commercially available (S)-1-octyn-3-ol into the protected propargylic amine, with complete inversion of configuration, and the successive transformation of the (phenylseleno)acetylene intermediate into the Se-phenyl selenocarboxylate, which is then easily converted into the carboxylic group. The phthalimido group was eventually removed by treatment with hydrazine hydrate.     

The two-phase region in 2(ZnSe)x(CuInSe2)1−x alloys and structural relation between the tetragonal and cubic phases

The two-phase region in the system 2(ZnSe)_x(CuInSe₂)_1−x covers the chemical composition range 0.10<x?0.36, in which a tetragonal and a cubic phase are coexisting. The structural relation between both phases was determined by selected area diffraction (SAD) and transmission electron microscopy (TEM). Both crystal structures are very similar and the extremely small mismatch of the lattice constants of the tetragonal phase and the embedding cubic matrix phase allows for the grain boundaries to be virtually strain-free and, therefore, without notable dislocations. The tetragonal phase forms grains of flat discus-like shape in the ambient cubic matrix, with the short discus axis parallel to the tetragonal c-axis. TEM experiments proved that the discus-shaped tetragonal particles are collinear with the (100)_cub, (010)_cub and (001)_cub planes of the cubic phase. Cooling and annealing experiments revealed a near-equilibrium state only to be realized for small cooling rates less than 2 K/h and/or for a long-time annealing with subsequent rapid quenching. Only then there will be no cation ordering in both, the tetragonal domains and the parental cubic matrix phase. If, however, the samples are kept in a state far away from the equilibrium condition both phases reveal Stannite-type cation ordering. Within the composition range of 0?x?0.10 only tetragonal 2(ZnSe)_x(CuInSe₂)_1−x-alloys exist. At concentration rates above 36 mol% 2(ZnSe) only cubic structured solid solutions of ZnSe and CuInSe₂ are found to be stable. However, in the range 36 mol% to about 60 mol% 2(ZnSe) tiny precipitates with Stannite-like structure exist, too.     

Reductive electrochemical formation of 6H-dibenzo[b,d]pyran-6-one and 2-benzopyran-1(1H)-one

In the present Letter several carbolactones (oxidative products) are obtained under aprotic cathodic conditions in the preparative scaled electrolysis of 1,2-quinones in a divided electrochemical cell and in the presence of oxygen. When 9,10-phenanthrenequinone is reduced 6H-dibenzo[b,d]pyran-6-one and [1,1′-biphenyl]-2,2′-dicarboxylic acid are obtained as major products. In the reduction of 1,2-naphthoquinone, 2-benzopyran-1(1H)-one, and 2-(2-carboxyethenyl)-benzoic acid were formed as main products. The proposed mechanism to explain the formation of these and other products, that involves an electron-transfer reaction to the oxygen in air, is now discussed.     

A simple synthesis of B-2-(1-trimethylsilyl-1-alkyl)-1,3,2-dioxaborinanes. Isolation and selective oxidation to 1-trimethylsilyl-1-alkanols

(Z)-1-Trimethylsilyl-1-alkenes easily prepared by the hydroboration of the corresponding 1-trimethylsilyl-1-alkynes followed by protonolysis with acetic acid, readily react with dibromoborane-methyl sulfide complex in dichloromethane for 6 h. The resulting solution is then treated with 1,3-propane diol in a 1:1 mixture of dichloromethane and n-pentane at 0°C for half an hour to provide the corresponding gem-dimetalloalkanes containing boron and silicon. These alpha-trimethylsilylalkylboronate esters are purified by vacuum distillation in high yields (72-84%) and the structures of these novel intermediates are further confirmed by selective oxidation with alkaline hydrogen peroxide to provide the corresponding alcohols containing trimethylsilyl group.     

Halodemetallation of (Z)-1-[2-(Triarylstannyl)vinyl]-cyclooctanol and Correlation of Proton Chemical Shift with Electronegativity

IntroductionOrganotin compounds have attracted attentionas an optimal model for antitumour agents due tothe function of the interesting intramolecularO→Sn coordination[1,2 ] . Our recent concern hasbeen focused on the preparation of ( Z) - 1 - [2 -( triarylstannyl) vinyl]- cyclooctanol[3 ] .In order tofind more appropriate compounds used asanticancer agents and explore the effect of thecoordinate O→ Sn interaction to the antitumoractivity,the new compounds werehalodemetallated and characte…     

Correlation between excess adsorption data measured for solvent mixture/adsorbent systems and RM values obtained for different solutes chromatographed in binary mobile phases

This paper concerns the application of excess adsorption isotherms, measured for solvent mixture/adsorbent systems, to the characterization of TLC data. For this purpose the excess adsorption isotherms for three liquid mixtures: cyclohexane/ benzene, benzene/acetone, and carbon tetrachloride/ethyl acetate on silica gel at 20°C have been measured. These mixtures have been used as binary mobile phases in TLC measurements. It has been shown for a given solute in binary mobile phase that the quantity R_M is a simple function of the excess adsorption. Parameters of this function have been used to characterize chromatographic systems with binary mobile phases.     

A short, simple and general approach for the synthesis of (3S,4S)-3-methoxy-4-methylamino pyrrolidine and (3S,4R)-3-methoxy-4-methylamino pyrrolidine

A general and efficient stereoselective approach for the synthesis of (3S,4S) and (3S,4R)-3-methoxy-4-methylamino pyrrolidines, a part of the structure of AG-7352, a naphthyridine antitumor agent and quinoline antibacterial compounds has been described.     

Experimental and theoretical studies on inversion dynamics of dichloro(l-difluoromethionine-N,S)platinum(II) and dichloro(l-trifluoromethionine-N,S)platinum(II) complexes

Fluorinated analogues of methionine such as l-S-(difluoromethyl)homocysteine (l-difluoromethionine; DFM) and l-S-(trifluoromethyl)homocysteine (l-trifluoromethionine; TFM) have been demonstrated to be interesting analogues for incorporation into peptides and proteins. The presence of the fluorine nucleus adjacent to the sulfur atom in the side chain not only serves to alter the nucleophilicity and electron density of the sulfur atom but it can function as an important NMR spectroscopic (¹⁹F) probe. Additional information on the properties of these fluorinated amino acid analogues was obtained by studying their interactions with dipotassium tetrachloroplatinate (K₂PtCl₄). The resulting complexes, dichloro(l-difluoromethionine-N,S)platinum(II) and dichloro(l-trifluoromethionine-N,S)platinum(II) were investigated with respect to their sulfur inversion rates utilizing dynamic NMR methods. Inversion barriers for the DFM- and TFM-platinum complexes were experimentally determined to be 16.4 ± 0.2 and 18 ± 1 kcal/mol, respectively. Density functional calculations at the B3LYP/SDD level were also performed to model the structures and energies of the ground and transition states for these complexes.     

Stereospecific preparation of symmetrical (1Z, 3Z)- and (1E, 3E)-2,3-difluoro-1,4-disubstituted-buta-1,3-dienes from 1-bromo-1-fluoroalkenes

A straightforward method to prepare symmetrical (1Z, 3Z)- and (1E, 3E)-2,3-difluoro-1,4-disubstituted-buta-1,3-dienes is described. High E/Z ratio 1-bromo-1-fluoroalkenes, prepared by isomerization from the E/Z ≈ 1:1 isomeric mixtures, reacted with Bu₃SnSnBu₃ and Pd(PPh₃)₄ to afford (1Z, 3Z)-2,3-difluoro-1,4-disubstituted-buta-1,3-dienes in good yield. (Z)-1-Bromo-1-fluoroalkenes, which were prepared by kinetic reduction from 1-bromo-1-fluoroalkenes (E/Z ≈ 1:1), can undergo similar reaction with Bu₃SnSnBu₃ and Pd(PPh₃)₄/CuI to prepare (1E, 3E)-2,3-difluoro-1,4-disubstituted-buta-1,3-dienes.     

Correlation between crystal symmetry and the splitting of d orbital in the thiocyanate nickel(II) complexes

New [Ni(SCN)₂(L)_4/2] complexes, where L = py (1), γ-pic (2), pyCH₂OH (3), py(CH₂)₃OH (4) were synthesized in simple reactions of NiCl₂·6H₂O with ammonia thiocyanate and pyridine type ligands in methanol solutions. Blue crystals of [Ni(SCN)₂(py)₄] (1), [Ni(SCN)₂(pyCH₂OH)₂] (3) and [Ni(SCN)₂(py(CH₂)₃OH)₂] (4) crystallize in the monoclinic system, blue crystal of [Ni(SCN)₂(γ-pic)₄] (2) – in the tetragonal one, and red crystal of [Ni(SCN)₂(PPh₃)₂] (5) – in the triclinic one. The ligands of complexes (1) and (3) were indicated as rather strong π-acceptors while that of complex (4) one has some π-donor properties. When the aliphatic chain (CH₂) elongates in the sequence: (1), (3) and (4), an increase in the orbital contribution to the magnetic moment and a decrease in the 10Dq value of the d orbital splitting are related to the change of the point group symmetry from D_2h, via D_2v to C_2h.     

Efficient synthesis of (R)- and (S)-3-octanol, (R)-2-dodecanol, (R)-2-methyl-4-heptanol and (R)-2-methyl-4-octanol: the pheromones of Myrmica scabrinodis, Crematogaster castanea, C. liengmei, C. auberti and Metamasius hemipterus

A simple and efficient synthesis of optically active insect pheromones, such as (R)- and (S)-3-octanol, (R)-2-dodecanol, (R)-2-methyl-4-heptanol and (R)-2-methyl-4-octanol starting from non-racemic β-hydroxy sulfides has been established.     

Stereoselective total synthesis of (S)-Virol C and (S)-1-dehydroxyvirol A

A stereoselective total synthesis of (S)-Virol C and (S)-1-dehydroxyvirol A has been developed, based upon the selective and sequential substitution of the two trimethylsilyl groups of readily available 1,4-bis(trimethylsilyl)-1,3-butadiyne.     

Efficient PhB(OH)2-catalyzed one-pot synthesis of 3-substituted isoindolin-1-ones and isobenzofuran-1(3H)-ones under solvent free conditions

An efficient and practical one-pot synthesis of 3-substituted isoindolin-1-ones and isobenzofuran-1(3H)-ones has been developed under solvent free-conditions using non-toxic and cheap phenylboronic acid as excellent catalyst. This strategy involves the sequential two-step Mannich/lactamization cascade reaction of inexpensive 2-formylbenzoic acid with primary amines and a wide variety of ketones, and an aldol/lactonization cascade reaction of 2-formylbenzoic acid with a broad range of ketones.     

(Z)-Ethyl 2-phenyl-1-(2-vinylphenyl)vinylcarbamates. Part 1: Synthesis and preliminary studies on their divergent transformation into benzo[c]phenanthridines and 2-phenyl-1,4-naphthoquinones

Treatment of N-carbethoxy-1-benzylideneisoquinolines with LDA gives N-ethoxycarbonyl-1-amino-1-(2-vinylphenyl)-2-phenylethylenes, which can easily be transformed into N-carbethoxy-1-amino-2-phenylnaphthalenes. Bischler-Napieralski reaction of these latter compounds affords the corresponding benzo[c]phenanthridines, while their hydrolysis and subsequent oxidation constitutes a novel route to 2-phenyl-1,4-naphthoquinones.     

A simple and practical method for the stereoselective synthesis of (Z)-1-iodo-1-alkenes from 1,1-diiodo-1-alkenes

Treatment of the 1,1-diiodo-1-alkenes 8, prepared from the corresponding aldehydes with CI₄/PPh₃, with ZnCu/AcOH in THF-MeOH gave the (Z)-1-iodo-1-alkenes 9, selectively, in good yields.     

A facile synthesis of (6S,1′S)-(+)-hernandulcin and (6S,1′R)-(+)-epihernandulcin

A facile total synthesis of (+)-hernandulcin (1) was accomplished from (−)-isopulegol in 6 steps with 15% overall yield. Epoxidation of (−)-isopulegol with m-chloroperbenzoic acid followed by opening of the epoxide 3a with prenyl Grignard afforded the tertiary alcohol 4a with correct C-6 and C-1′ stereochemistry as a major product. Oxidation of the secondary alcohol in compound 4a to the ketone 5a was accomplished in high yield by using TPAP and N-methylmorpholine N-oxide. Conversion of the ketone 5a to α,β-unsaturated ketone via organoselenium intermediate gave (+)-hernandulcin (1). This method was also successfully applied to the synthesis of (+)-epihernandulcin (2).