IN THE CURRENT WORK THE EFFECT OF APPLY MODEL FOR SPECTRAL PROFILES HAVE BEEN INVESTIGATED. HARD MODELING TECHNIQUES ARE UNDERSTOOD AS METHODS THAT EXPLOIT THE PHYSICAL STRUCTURE OF SPECTRA BY MODELING THE DATA WITH PEAK SHAPED FUNCTIONS, I.E. BY PEAK FITTING ...

MULTIVARIATE CURVE RESOLUTION – ALTERNATING LEAST SQUARE (MCR-ALS) WAS INTRODUCED BY TAULER ET. AL [1] AND IS A WELL-KNOWN METHOD AMONG SOFT-MODELING ALGORITHMS WITH BROAD RANGE OF APPLICATIONS IN DIFFERENT FIELDS OF SCIENCE. HOWEVER, THE MAIN DRAWBACK OF ALL MCR METHODS IS THE PRESENCE OF ROTATIONAL AMBIGUITY...

GAS CHROMATOGRAPHY–MASS SPECTROMETRY (GC–MS) COMBINED WITH CHEMOMETRIC RESOLUTION TECHNIQUES WERE PROPOSED AS A METHOD FOR THE ANALYSIS OF VOLATILE COMPONENTS OF STEVIA OIL. THE ESSENTIAL OIL OF STEVIA WAS EXTRACTED USING HYDRODISTILLATION METHOD AND ANALYZED WITH GC–MS IN OPTIMIZED CONDITIONS...

MULTIVARIATE CURVE RESOLUTION (MCR) METHODS SEEK TO DECOMPOSE A TWO WAY DATAMATRIX USING A BILINEAR MODEL INTO THE PRODUCT OF TWO SMALLER FACTOR MATRICES WITHOUT ANY PRIORINFORMATION OR USING ONLY A LIMITED KNOWLEDGE ABOUT THE INVESTIGATED SYSTEM. ALTHOUGH THE MAINGOAL OF SMCR METHODS HAS BEEN SPECIES RESOLUTION AND IDENTIFICATION FROM OVERLAPPINGMULTIVARIATE SIGNALS, BY ADOPTING A PROPER STRATEGY, THESE METHODS CAN ALSO BE APPLIED TO OBTAINQUANTITATIVE INFORMATION FROM COMPLEX MIXTURES ESPECIALLY IN PRESENCE OF UNKNOWN INTERFERENCES.THE MAIN DRAWBACK OF ALL MCR METHODS IS HOWEVER THE PRESENCE OF ROTATIONAL AMBIGUITIES IN THESOLUTIONS OBTAINED BY THESE METHODS WHICH USUALLY CAN BE REDUCED BY APPLYING DIFFERENT NATURALCONSTRAINTS.AN ASPECT WHICH IS SIGNIFICANTLY LESS WELL DOCUMENTED IN THE LITERATURES IS ACCURACY OFTHE OBTAINED QUANTITATIVE RESULTS IN PRESENCE OF NON-ELIMINATED PART OF ROTATIONAL AMBIGUITY.AN IMPORTANT TASK IN CHEMOMETRICSIS THE QUANTITATIVE EVALUATION OF THE RELIABILITY OFTHE PARAMETERS ESTIMATED BY MCR METHODS. IN THIS EVALUATION, TWO DIFFERENT BUT CORRELATED ASPECTS SHOULD BE CONSIDERED.THE FIRST ASPECT IS THE PROBLEM OF ROTATIONAL AMBIGUITIES ANDSCALE FREEDOM OF PARAMETER ESTIMATIONS, A UBIQUITOUS PROBLEMIN ALL FACTOR ANALYSIS TWO-WAY DATA BILINEAR DECOMPOSITIONMETHODS. THE SECOND ASPECT IS HOW EXPERIMENTAL ERRORSAND NOISE ARE PROPAGATED FROM EXPERIMENTAL DATA TO PARAMETERESTIMATIONS WHEN MCR CALCULATIONSARE PERFORMED. WHEN THERE IS NO NOISE, ONLY ROTATIONALAND SCALE AMBIGUITIES ARE PRESENT. ON THE OTHER HAND, WHENNOISE LEVELS IN EXPERIMENTAL DATA INCREASE, BOTH ASPECTS AREINTERMIXED AND IT IS RATHER DIFFICULT TO DISCERN BETWEEN THEMAND DIFFERENTIATE BETWEEN EFFECT AND CAUSE.IN THIS DISCUSSION THE EFFECT OF THE ROTATIONAL AMBIGUITY ON THE QUANTITATIVE RESULTS OBTAINED BY MCR METHODS WILL BE INVESTIGATED. ALSO PRECISION IN THE CALCULATED RESULTS IS CONSIDERED. ERROR PROPAGATION IN FEASIBLE SOLUTIONS OF BILINEAR CHEMICAL DATA FOR SINGLE AND MULTI-SET DATA ANALYSIS WILL EXPLAINED.

MULTIVARIATE CURVE RESOLUTION METHODS AIM AT PROVIDING A SCIENTIFIC MEANINGFUL DESCRIPTION OF THE VARIATION IN THE DATA SETS THROUGH A SMALL BILINEAR MODEL OF BASIC AND INTERPRETABLE CONTRIBUTIONS.THE MOST DISTINCT CHARACTERISTIC OF MCR METHODS IS THE STRAIGHT SCIENTIFIC MEANING OF THE RESULTS OBTAINED, WHICH IS A DIRECT CONSEQUENCE OF THE POSSIBILITY TO INTRODUCE CHEMICAL/SCIENTIFIC INFORMATION ABOUT THE PROPERTIES OF THE BASIC CONTRIBUTIONS SOUGHT (INSTRUMENTAL RESPONSES, CONCENTRATION PROFILES, ENVIRONMENTAL OR BIOLOGICAL PATTERNS, …) UNDER THE FORM OF CONSTRAINTS.ANOTHER RELEVANT ASPECT LINKED TO MCR IS THE POSSIBILITY TO WORK WITH MULTISET STRUCTURES THAT MAY ENCLOSE DATA COMING FROM DIFFERENT EXPERIMENTS, TECHNIQUES OR, IN A MORE GENERAL SENSE, COLLECTED UNDER DIFFERENT CONDITIONS OR IN DIFFERENT SCENARIOS. THIS APPROACH PROVIDES A MORE INTEGRAL AND RUGGED DESCRIPTION OF THE PROBLEM UNDER STUDY DUE TO THE ACTIVE USE OF MORE DIVERSE INPUT INFORMATION AND TO THE PARTICULAR PROPERTIES OF MULTISET STRUCTURES. SUCH AN ASPECT IS VERY RELEVANT IN AREAS, SUCH AS PROCESS ANALYSIS.THE UNDERLYING MCR BILINEAR MODEL OFFERS CERTAIN ADVANTAGES. ON THE ONE HAND, THE MATRICES OF BASIC CONTRIBUTIONS CAN BE USED AS EXCELLENT MEANINGFUL COMPRESSIONS OF THE RAW DATA SET FOR OTHER DATA ANALYSIS PURPOSES, E.G. IN THE CASE OF HYPERSPECTRAL IMAGES. ON THE OTHER HAND, THE SIMPLICITY AND INTERPRETABILITY OF THE MCR RESULTS MAKE THIS METHOD AN EXCELLENT OPTION TO EXPLORE DATA SETS WELL BEYOND THE TYPICAL ANALYTICAL FIELD, SUCH AS ENVIRONMENTAL OR -OMIC MEASUREMENTS.THIS WORK WILL GIVE AN OVERVIEW OF THE MAIN ASPECTS MENTIONED ABOVE, STRESSING BRIEFLY THE KIND OF DATA SETS AND INFORMATION THAT CAN BE USED WHEN APPLYING MCR METHODS AND ILLUSTRATING THE POWER OF THE METHOD WITH EXAMPLES FROM DIVERSE SCIENTIFIC FIELDS.

RESOLUTION AND QUANTIFICATION OF TARGET COMPOUNDS IN THE ANALYSIS OF COMPLEX MIXTURES BY COMPREHENSIVE TWO-DIMENSIONAL GAS CHROMATOGRAPHY (GC´GC) [1, 2] IN THE CASE OF INCOMPLETE SEPARATION AND CO-ELUTION PROBLEMS IS A CHALLENGING AND ACTIVE RESEARCH FIELD. IN THIS STUDY, COMBINATION OF PEAK ALIGNMENT METHODS AND MULTIVARIATE CURVE RESOLUTION (MCR) [3] IS PROPOSED FOR HANDLING RETENTION TIME SHIFTS AND MODELING OF GC´GC DATA IN THE CASE OF UNIVARIATE DETECTOR RESPONSE LIKE FOR THE FLAME IONIZATION DETECTOR (FID) OR FOR TIME-OF-FLIGHT MASS SPECTROMETER (TOFMS) DETECTOR IN TOTAL ION CHROMATOGRAM (TIC) MODE. A NEW “BILINEAR PEAK ALIGNMENT” METHOD BASED ON MCR IS FIRST PROPOSED TO CORRECT FOR PROGRESSIVE WITHIN RUN RETENTION TIME SHIFTS IN GC´GC DUE TO THE TEMPERATURE PROGRAM ON SECOND DIMENSION. THE PERFORMANCE OF THIS PEAK ALIGNMENT METHOD IS COMPARED TO THE CORRELATION OPTIMIZED WARPING (COW) [4] METHOD WHICH IS PROBABLY THE MORE POPULAR PEAK ALIGNMENT METHOD FOR CHROMATOGRAPHIC DATA. IN ADDITION, MULTIVARIATE CURVE RESOLUTION-ALTERNATING LEAST SQUARES (MCR-ALS) [5] METHOD UNDER PROPER CONSTRAINTS IS ALSO PROPOSED TO ANALYZE THE THREE-WAY GC´GC DATA FOR THE RESOLUTION AND QUANTIFICATION OF THE TARGET COMPOUNDS IN COMPLEX SAMPLES IN CASE OF INCOMPLETE SEPARATION AND CO-ELUTION PROBLEMS. COLUMN-WISE DATA AUGMENTATION WITH THE FIRST DIMENSION RETENTION TIME IN THE COMMON COLUMN MODE WAS A GOOD DATA ARRANGEMENT FOR THE ANALYSIS OF THREE-WAY GC´GC RUNS AND MCR-ALS ANALYSIS. FOR THOSE DIFFICULT CASES IN WHICH LARGE BETWEEN GC´GC RUN RETENTION TIME SHIFTS EXIST IN BOTH DIMENSIONS, A PRELIMINARY BETWEEN RUNS FIRST DIMENSION PEAK ALIGNMENT METHOD BY CORRELATION OPTIMIZED SHIFTING (COSHIFT) [6] IS USED TO PRESERVE THE BILINEARITY MODEL ASSUMPTION NEEDED FOR MCR-ALS APPLICATION. THE RESULTS SHOWED THE SUCCESSFUL APPLICATION OF THE PROPOSED STRATEGY FOR RESOLUTION AND QUANTIFICATION OF SOME TARGET COMPOUNDS IN THE GC´GC ANALYSIS OF HEAVILY OVERLAPPED CO-ELUTED PEAKS IN THE ANALYSIS OF POLYCYCLIC AROMATIC HYDROCARBONS (PAHS) USING GC´GCTOFMS IN TIC MODE AND OF GASOLINE SAMPLES BY GC´GC-FID.