Accepted Manuscript

Title: Performance assessment of chemometric resolutionmethods utilized for extraction of pure components fromoverlapped signals in gas chromatography-mass spectrometry

Author: Hooman Seifi Saeed Masoum Soodabe Seifi

PII: S0021-9673(14)01377-6DOI: http://dx.doi.org/doi:10.1016/j.chroma.2014.08.095Reference: CHROMA 355786

To appear in: Journal of Chromatography A

Received date: 11-2-2014Revised date: 22-8-2014Accepted date: 27-8-2014

Please cite this article as: H. Seifi, S. Masoum, S. Seifi, Performance assessmentof chemometric resolution methods utilized for extraction of pure componentsfrom overlapped signals in gas chromatography-mass spectrometry, Journal ofChromatography A (2014), http://dx.doi.org/10.1016/j.chroma.2014.08.095

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Performance assessment of chemometric resolution methods utilized for extraction of pure 1

components from overlapped signals in gas chromatography-mass spectrometry2

3

Hooman Seifi a, Saeed Masoum *a, Soodabe Seifi b4

a Department of Analytical Chemistry, Faculty of Chemistry, University of Kashan, Kashan, Iran5

b Technical and Vocational University of Kermanshah, Girl's Technical College, Kermanshah, Iran6

Corresponding author Tel.: +98 361 5912338; fax: +98 361 5912397.7

E-mail address: masoum@kashanu.ac.ir (Saeed Masoum)8

Abstract9

Multivariate resolution technique is a set of mathematical tools that uncovers the underlying profiles from 10

a set of measurements of time evolving chemical systems. This technique was proposed for resolving the 11

overlapping GC-MS peaks into pure chromatogram and mass spectra. In this paper, several common 12

resolution chemometric techniques in GC-MS resolution such as mean field-independent component 13

analysis (MF-ICA), multivariate curve resolution-alternating least squares (MCR-ALS) and multivariate 14

curve resolution-objective function minimization (MCR-FMIN) were investigated. The obtained solutions 15

using chemometric methods are assessed by lack of fit (LOF) and R2. Results show that all solutions by 16

fulfillment the same constraints, have same performance in resolving high overlapping peaks. Also, the 17

differences obtained in each case should be related to the unresolved rotational ambiguity.18

Among of the different ambiguities such as intensity, permutation and rotation in resolution methods,19

rotational ambiguity is the most difficult and critical one. Because of rotational ambiguity, there is a set of 20

feasible MCR solutions, which explain equally well the observed experimental data, and fulfill 21

sufficiently the imposed constraints of the system. So in these methods, a range of feasible solutions exist. 22

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The rotational ambiguities of the profiles are a challenging fact which complicates the development of 23

stable and universal self-modeling curve resolution (SMCR) algorithms. The relative component 24

contribution (RCC) function values for the component profiles obtained by the different methods are 25

calculated by MCR-BANDS. The values of RCC for these three methods are equivalence. Rotational 26

ambiguities of the solutions of SMCR methods can be reduced by applying suitable constraints. The 27

obtained results show, using data sets, which are arranged in a single augmented data matrix could be the 28

best solution for reducing or removing of rotational ambiguity.29

Keywords: Chemometric resolution methods, Rotational ambiguities, Co-elution, Gas chromatography–30

mass spectrometry, Augmentation31

32

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1. Introduction32

Historically, analysis of essential oil is a significant challenge to analytical chemists and pharmacologists. 33

Hyphenated chromatographic techniques such as high performance liquid chromatography-mass 34

spectrometry (HPLC-MS) and gas chromatography-mass spectrometry (GC-MS) have been the powerful 35

tools in the analysis of essential oils [1]. However, in GC-MS analysis of EOs, even under the best 36

experimental conditions, there are various problems such as baseline drift, low signal to noise (S/N) ratio, 37

different types of noise, co-elution [2-7]. In practice, peak tailing and fronting as other problems appear in 38

some of the total ion chromatograms (TIC). The main reasons for this phenomenon may be the bad 39

column cutting and related to the high concentration of corresponding components. These difficulties can 40

be arisen from the complexity of EOs and the variability of GC-MS systems such as detection system, 41

chromatographic device and experimental conditions. Among these problems, co-elution (overlapped 42

and/or embedded peaks) is one of the most observed chromatographic difficulties that is due to 43

complexity of samples, inadequate peak capacity and need to faster chromatographic analysis. There are 44

two main approaches for solving the co-elution problem. In one hand, scientists attempt to reach perfect 45

separation by improving the temperature programming, stationary phase composition (generally classical 46

chromatographic parameters). In another hand, the co-eluted peaks are decomposed into the contribution 47

of the pure components using chemometric resolution methods. However, the first approach is time 48

consuming and, it is common to find some co-eluted chromatographic peaks that still remain after re-49

programming of the methods. Also, the second approach depends on the selective nature of the 50

chromatographic profiles [3,8-10].51

Chemometric resolution techniques based on bilinear models try to resolve the chemical constituents in a 52

mixture by mathematical resolution of their signal contribution. The goal of these techniques is to 53

mathematically decompose an instrumental response of a mixture into the pure contribution of each 54

component involved in the system [11-15]. The chemometric resolution methods are divided into two 55

groups. The first group is non-iterative methods such as evolving factor analysis (EFA), evolving window 56

orthogonal projection (EWOP), orthogonal projection resolution (OPR), sub-window factor analysis 57

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(SFA), window factor analysis (WFA) and heuristic evolving latent projections (HELP). The second 58

group is iterative methods such as multivariate curve resolution-alternating least squares (MCR-ALS), 59

mean field-independent component analysis (MF-ICA), multivariate curve resolution-objective function 60

minimization (MCR-FMIN) [14,16-23].61

Because of randomly generated initial values and local minimization problem, different results may be 62

produced through different runs of the MF-ICA and MCR-ALS procedures. Furthermore, sometimes MF-63

ICA and MCR-ALS cannot be converged and suitable results may not be achieved [24]. There are 64

numerous reasons for this problem, that one of them is the substantial dependency to the initial estimates 65

of the spectral or concentration profiles. So, these algorithms reach local minima instead of global 66

minima. Stuck in local minima can cause insufficient curve resolution. One powerful solution for this 67

problem is using the non-linear optimization techniques. These approaches are applied extensively for 68

finding the best solution in the SMCR techniques. MCR-FMIN is one of these methods that recently has 69

been proposed by Tauler [18]. 70

For run of the iterative resolution methods, initial estimates of concentration or spectral profiles are 71

needed. These can be helpful for faster convergence, obtaining the reproducible results and avoiding to be 72

stuck in local minima [24-26]. Hence, methods, which are based on pure variable selection such as OPA 73

and SIMPLISMA and also approaches that are based on evolutionary nature of data such as EFA are used 74

as initial estimation [27-29].75

However, though chemometric resolution solutions have sufficient physical meaning and easy 76

explanation, but they are not “unique” in general case, and they have an unknown amount of ambiguity. 77

Three types of ambiguities are distinguished in multivariate curve resolution techniques such as: 78

permutation (exchangeable order of the constituents in the row and columns of results), intensity and 79

rotational ambiguities. The permutation and intensity ambiguities are eliminated by aware of analyst and 80

external calibration information, respectively. Rotational ambiguity is a more significant problem in the 81

application of soft-modeling techniques, and this is the chief reason for “non-unique” solutions. 82

Rotational ambiguity is reduced and totally avoided in some cases by intelligent use of data structure and 83

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imposing appropriate constraints [30]. Constraints like unimodality, non-negativity, selectivity, local rank 84

and equality or inequality have been proposed to limit rotational ambiguity [17,31-33]. In the absence of 85

this rotational ambiguity, all multivariate resolution techniques should give the same unique solution 86

which should be equal to the true one [34]. The calculative (and sometimes analytical) determination of 87

the range of feasible solutions has an advantage in the analysis of chemical systems.88

The range of acceptable solutions for a two-component system (F=2) was partially analyzed by Lawton 89

and Sylvestre [35]. In addition, Maeder et al. [36, 37] and Rajko and Istvan [36,37] in their papers 90

investigated two-component systems. For F > 2, a comparable analysis gets much harder. Borgen and his 91

coworkers contributed to this topic, did pioneering work for three-component systems [38,39]. The 92

analytical solution for these systems with computer tools was improved by Rajko et al. [40,41]. A new 93

approach to calculate the boundaries of the set of solutions for these systems has been proposed by 94

Abdollahi et al. [42].95

Essential oils (EOs) are complex mixtures of volatile organic compounds produced (as secondary 96

metabolites) in plants. EOs are constituted by hydrocarbons (terpenes and sesquiterpenes) and oxygenated 97

compounds (ethers, alcohols, esters, aldehydes, lactones, ketones, phenols and phenol ethers) [43-45]. A98

comprehensive knowledge of components of an EO will lead to a safe and better application of it, because 99

characteristics and properties of EOs are directly related to their compositions. Nevertheless, such a 100

comprehensive knowledge can only be obtained by utilizing appropriate extraction techniques and 101

accurately performed chromatographic analysis [43,46,47]. In another word, the effects of herb are 102

according to synergic effect (components that exist in each essential oil of herb if not a direct activity, at 103

least have a synergic effect on activities of others), so comprehensive knowledge is needed to correct 104

application in biological, pharmacological and food applications.105

In this study, volatile constituents of essential oils extracted from six Myrtus communis L. were analyzed 106

by GC-MS, and their components were identified assisted by chemometric methods. Then reliability of 107

results from several multivariate curve resolution methods in presence of rotational ambiguities was 108

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investigated and the effects of applying constraints and multi-set configurations on reducing ambiguity of 109

GC-MS data were surveyed. 110

2. Material and instrumentation111

2.1. Reagents112

All reagents and chemicals that were used in this work were of analytical grade. Anhydrous sodium 113

sulphate was purchased from Merck. Normal alkanes' standards were purchased from ULTRA Scientific 114

(North Kingstown, USA).115

2.2. Sample preparation116

Green parts of Myrtus communis L. were collected during September of 2011 from different area 117

(Noorabadand and Khoramabad) of Iran and confirming specimen of the plant was executed in the Barij 118

Essence Company (Kashan, Iran).119

Two of three samples (W: Noorabad Wild and K: Khoramabad Wild) were collected from hillsides that 120

grow wildly and third sample (E: cultivated from Noorabadand) was collected from cultivation area at 121

stead. In the next step, each sample was classified into two groups as fresh (F) and dried by sun (D). The 122

volatile constituents of Myrtus communis L. were extracted using Clevenger-type apparatus as proposed 123

by the European Pharmacopoeia [48]. The obtained essential oils were dried over anhydrous sodium 124

sulphate and after filtration, stored in a dark glass at low temperature (4 °C) prior to analysis.125

2.3. Gas chromatography–mass spectrometry126

Samples were analyzed with an Agilent HP-6890 gas-chromatograph combined to an Agilent HP-5973 127

mass spectrometer (that was supplied with an electron ionization and quadrupole analyzer) on a HP-5MS 128

capillary fused silica column (30 m×0.25 mm i. d. 0.25µm film thickness). The temperature of the ion 129

source was set at 230°C. Helium was used as carrier gas with a total flow of 5 ml/min. Interface 130

temperature was set at 280 °C. The mass scan range was from 40-300 amu (Ionization energy: 70 eV). A 131

split injection (split ratio, 1:20) and injector temperature of 250 °C were employed. The oven temperature 132

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was programmed to increase from 50 to 250 °C at a rate of 3 °C/min, and for post run step, kept constant 133

at 280 °C for 10 min.134

2.4. Data analysis135

Data analysis was carried out on a 4-GHz Pentium IV personal computer; all programs were coded in 136

MATLAB 7.14 for windows. Resolved spectra were identified by matching against the standard mass 137

spectral NIST 05 database, which contains 209311 compounds.138

3. Theory and methodology139

3.1. Theory140

The basic assumption of bilinear models is that multivariate experimental data is a linear sum of the pure 141

singular contributions of the different chemical components in the system. Contributions of each 142

component can be depicted by the product of two factors, one related to its pure spectrum and another one 143

related to the concentration.144

The two way data matrix X obtained from GC-MS can be represented by bilinear models as follows:145

MCR-ALS: TMCR ALS MCR ALS MCR ALSX X E CS E (1)146

MF-ICA: TMF ICA MF ICA MF ICAX X E AS E (2)147

MCR-FMIN: TMCR FMIN MCR FMIN MCR FMINX X E CS E (3)148

Where XMCR-ALS, XMF-ICA and XMCR-FMIN are the reconstructed data matrices by MCR-ALS, MF-ICA and 149

MCR-FMIN, respectively. C and A are the concentration profiles, and ST is the spectral profile obtained 150

by these three methods. EMCR-ALS and EMCR-FMIN are residual matrices with the data variance unexplained 151

by CST. EMF-ICA is a residual matrix with the data independent unexplained by AST. The dimensions of 152

matrices are: X (m×n), C and A (m×p), ST (p×n) and E (m×n); in GC-MS data, m is the time points in 153

chromatographic direction (the number of rows), n is mass-to-charge (m/z) values in spectral direction 154

(the number of columns of X), and p is the number of chemical constituents. The difference between 155

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MCR and ICA is that MCR methods attempt to maximize the data variance explained by the different 156

constituents under a set of constraints (i.e. non-negativity and other constraints in MCR method); in 157

another side, ICA attempts to maximize the independence among the resolved constituents with a 158

minimum loss of information [49].159

Assessment of the solutions of chemometric resolution methods is the main step in the chemometric 160

resolution analysis of analytical data, such as GC–MS. There are five different methods for evaluating the 161

chemometric resolution solutions for a GC–MS data: (1) main important aspect from the analytical 162

chemistry point of view is chromatographic shape recovery, (2) statistical parameters of lack of fit (LOF) 163

and variance explained (R2), (3) reverse match factor (RMF) for assessment of the resolved mass spectra 164

with the relative standards in the MS database, (4) assessment of the extent of rotational ambiguities, and 165

(5) co-injection (injection of the standards of recognized components at the similar instrumental 166

conditions and contrast of the retention indices) [8]. Among these methods, using chromatographic shape 167

recovery, statistical parameters and RMF are the most prevalent for the assessment of the resolved 168

profiles by chemometric resolution methods in the GC–MS analysis of EOs. Because of the application of 169

the proposed methods only for two- and/or three-component systems with a low quantity of artifacts, 170

investigating the feasible regions of MCR results of real data is limited. Co-injection is also a reliable 171

method to approve the results of chemometric resolution techniques; though, there are some limitations in 172

the accessibility of the standards for the EOs components.173

The lack of fit (LOF) and R2 parameters have used for satisfactory test of the results. LOF and R2 can be 174

calculated using Eqs. (4) and (5), respectively.175

2,1 1

2,1 1

,( )  100

i jI J

i ji j

I J

i ji j

d dLOF

d

(4)176

2

,1 12

2,1

,

1

1   100

I J

i ji j

I J

i ji j

i jd dR

d

(5)177

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where di,j is the element of the original data matrix and ljd is the recovered value using resolution 178

techniques. The sums are extended to i=1, . . ., I rows and j=1, . . ., J columns of the data matrix d. The 179

closer the lack of fit and R2 are, respectively, to zero and one, the best model fitting of the experimental 180

data has been achieved. The mathematical solutions of Eqs. (1), (2) and (3) for C (or A) and ST are 181

obviously “not unique” if no additional information is available. In other word, the decomposition of 182

matrix X according to these equations has been ambiguous. Here, rotational ambiguity of MCR solutions 183

was described (rotational ambiguity of ICA is similar to rotational ambiguity of MCR and describing of 184

it, was eliminated for brevity). Physical constraints such as non-negativity or other natural constraints like 185

closure, unimodality, and selectivity and especially local rank, significantly reduce the range of possible 186

solutions [30,34,40,50,51]. Rotational ambiguities can be described using the following equation:187

** 1 ( ) T Told newX X E CS E C T S E X ET (6)188

In this equation, from initial solutions C and ST, a new set of solutions C* and (ST)* can be obtained by 189

linear combination of the latter using a nonsingular matrix T, the so-called transformation (rotation) 190

matrix T. All C and ST solution fit the data matrix X equally well; they result in the same matrix Xold. For 191

a system that has no unique solution due to the presence of rotational ambiguity, a range of feasible MCR 192

solutions can be obtained via a range of different matrices T, and there is no way to be sure that one 193

solution is better than another one, i.e., that one particular solution is the true one, unless more 194

information is provided to the system [11,52].195

3.2. Methodology196

For studying the performance of chemometric resolution methods the following steps were performed:197

1. Data preprocessing: Since GC-MS data obtained in full scan mode includes many noise channels; 198

therefore, deleting these channels would result in a quicker computation. Noises channels consist of 199

random signals. Shen et al. [53] have proposed methods based on the frequency difference between 200

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the noise and the signal to distinguish the noises and the signal channels in GC-MS data. This 201

method is the so-called morphological score. It was used for decreasing the hemoscedastic noises in 202

GC-MS data. Also, Savitsky–Golay filter [54] which is a smoothing filter based on least squares for 203

smoothing and differentiating data, was used for decreasing the heteroscedastic noises in GC-MS 204

data. Baseline drift during the chromatographic elution is another problem in GC–MS analysis. 205

Presence of baseline drift in GC-MS analysis leads to requiring more complicated analysis to resolve 206

the data [55]. There are several methods that can deal with the difficulties of spectral background and 207

baseline drift, simultaneously. Congruence analysis method and least-squares fitting for correcting 208

the baseline drift and spectral background, have been developed by Liang et al. [56]. In another 209

preprocessing step, each data matrix is scaled to have a maximum signal intensity of 1.0.210

2. Determination of chemical constituents: Determination of chemical rank was performed by 211

morphological score method. In this technique key spectra are used instead of full rank matrices. 212

Therefore, the obtained results are more reliable [53].213

3. Chemometrics resolution: Using chemometric resolution methods, the pure profiles 214

(chromatographic and spectral profiles) of the constituents will be recovered.215

4. Valuation of the results: To confirm the reliability and quality of results, the similarity match with 216

MS database was used. The obtained results using these methods are evaluated by the statistical 217

parameters such as lack of fit (LOF) and variance explained (R2). When the LOF and R2 are close to 218

zero and one, respectively, the best model fitting of the multivariate instrumental measurements has 219

been achieved.220

5. Verifying of rotational ambiguities: Tauler showed that the MCR solutions are within the boundaries 221

which estimated by MCR-BANDS [18] and also he expressed that Gemperline’s concept was equal 222

to minimize and maximize the function in this Eq. [57]:223

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( )T

p p

p T

C Sf T

CS (7)224

Where T is the rotation (transformation) matrix; p represents the number of chemical constituents. The 225

optimization of this function (either maximized or minimized) will give the maximum and the minimum 226

boundary, respectively. For a particular species, these boundaries will describe the feasible concentration 227

and spectral profiles, executing the constraints of the problem and giving a maximum and a minimum 228

signal contribution [18,50,51,58].229

4. Results and discussion230

The six total ionic chromatograms (TICs) of essential oils from Myrtus communis L. are shown in Figure 231

1. The TICs show that some parts of the peaks practically overlap with each other. However, the 232

similarity indices (SIs) obtained from direct searching with the MS database, are very low for many 233

chromatographic peaks. Also, the same component is possibly searched at different chromatographic scan 234

points. In this study, as examples, three peak clusters (labeled by A, B, and C) are presented to show the 235

efficiency and performance of chemometric resolution methods for extracting more information from the 236

multi-component overlapping GC–MS data of essential oils. Here, the results of the peak cluster A 237

(Figures and Tables) are selected to display the chemometrics steps. Also, Tables of peak clusters B and 238

C are available as supplementary data. The aim of selecting these specific peak clusters are showing 239

performance and then assessment application of chemometric resolution methods in two- and three 240

components systems with various in degree in overlapping.241

Figure 1242

Steps of resolution process are shown by peak cluster A from EF sample. It seems that there is one 243

component in peak cluster A, but inspection of mass spectra of different part of the cluster indicates that 244

there could be more than one component or severe noises. As a result of the co-elution problems, 245

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presence of noises (heteroscedastic and homoscedastic) and baseline drift in these peak clusters; similarity 246

indices for simple search through the MS database were low. So, preprocessing was performed for each 247

data matrix, as first step in the resolution process. Critical step for reducing the complexity of the data 248

matrix is removing of the chromatogram baseline drift. In this study, the baseline correction was done by 249

using the methodology that was proposed by Liang et al.[56]. Therefore, morphological score method 250

[53] and Savitzky-Golay filter [54] were used for removing the homoscedastic and the heteroscedastic 251

noises in this peak cluster, respectively. In second step, chemical rank is determined. For this objective, 252

morphological score method was used. In this method, the numbers of constituents were concluded by 253

counting the number of singular vectors with morphological scores upper than noise levels. In Figure 2, 254

the result of morphological score method is shown. Results of morphological score show the presence of 255

two components in this peak cluster. Also, results of morphological score method show that the peak 256

cluster B and C contain two and three components, respectively (results are not shown).257

Figure 2258

In the next step, reliability of MCR-ALS method by changing initial estimation methods was surveyed. In 259

this study, SIMPLISMA, EFA and OPA [57] were used as an initial estimate in an iterative process. 260

SMCR process starts with the estimation of initial pure variables, such as concentration and or pure 261

spectral profile. ALS procedure is carried out using the initial set of estimates, either concentration or 262

spectral profile. Several studies have claimed that while a poor initial estimate has used, ALS algorithm 263

reaches the suboptimal local minimum (reach to local minima can cause inadequate curve resolution) and 264

using strong initial estimate, ALS algorithm reaches the global minimum [24,25].265

Because of inevitable experimental uncertainties (noise, etc.), this decomposition is not perfect, and the 266

differences between the measured data and their decomposition are collected in a matrix of error E (or 267

residuals). By comparing the results of different samples can find out that these three initial estimation 268

methods (SIMPLISMA, EFA and OPA) extract the same value of signal contribution and lose the same 269

value of information (that presumably are noises). Table 1 and Figure 3 show the results of changing the 270

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initial estimation methods for peak cluster A. Also, results of changing the initial estimation methods for 271

peak cluster B and C are available in supplementary data (Table S1B and Table S1C, respectively).272

Table 1273

These results confirm that the various types of initial estimation methods using in an iterative process of 274

MCR-ALS have been used to prevent it from likely getting stuck in the local minima as well as using 275

different types of initial estimation techniques lead to the same results (in terms of statistical parameters 276

such as LOF and R2) but due to presence of rotational ambiguities, RMF of constituents is different.277

Allowing the analysis to reach convergence is so important. Results show that SIMPLISMA method can 278

be helpful for faster convergence compared to the other initial estimation methods (results are not shown).279

For resolving the peak clusters, chemometric resolution methods such as MCR-ALS [17], MF-ICA [16]280

and MCR-FMIN [18] were applied. Required initial estimates for MCR-ALS and MF-ICA were obtained 281

by SIMPLISMA [59] and also required initial estimate for MCR-FMIN as a basic theory of this method 282

was obtained from PCA [18]. Non-negativity on chromatograms and spectral profiles and normalization 283

on spectral profiles as constraints were used. Results of these decompositions for peak cluster A are 284

shown in Table 2. Also, results of these chemometric resolution methods for peak cluster B and C are 285

available in supplementary data (Table S2B and Table S2C, respectively). Figure 3 shows the pure 286

concentration profiles for peak cluster A from EF sample.287

Figure 3288

Because of sever co-elution and only applying non-negativity and normalization as constraints, the 289

resolved profiles have peak shapes that are far from ideal, for example, they have more than one 290

maximum for their concentration profiles of their components. In this figure, resolved concentration 291

profiles of both components from SIMPLISMA-MCR-ALS and OPA-MCR-ALS with the blue dotted-292

line and orange triangle-line indicate the concentration profiles of 1,8-Cineol and D-limonene, 293

respectively. From EFA-MCR-ALS method, blue stared-line and blue circled-line show the concentration 294

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profiles of 1,8-Cineol and D-limonene, respectively. For solutions of MF-ICA, red dash-dot-line indicates 295

the concentration profile of 1,8-Cineol and blue crossed-line shows the concentration profile of D-296

limonene and for solutions of MCR-FMIN, violet solid-line shows the concentration profile of 1,8-Cineol 297

and green rhombic-line indicates the concentration profile of D-limonene.298

Table 2299

When each pure spectrum was obtained, then the constituents can be identified by similarity searches 300

using the NIST mass database and can be confirmed with retention indices [60]. In Figure 4 the mass 301

spectra and their relative standard spectra of constituents in peak cluster A from EF sample are shown 302

(obtained by SIMPLISMA-MCR-ALS). The library searches showed that the constituents of D-limonene 303

and 1, 8-Cineol are present in the peak cluster A, the constituents of Linalool and Hotrienol are existed in 304

peak cluster B; and the components of α-Terpineol, Estragole, and Myrtenol in peak cluster C. Also, the 305

reliability of the results was confirmed by comparing the Kovats retention indices of the resolved 306

components with those of the pure ones. 307

Figure 4308

In this study, Tauler’s algorithm [30] called MCR-BANDS was used for computing the minimum and the 309

maximum boundaries. Effect of different initial estimation methods on rotational ambiguity of MCR-ALS 310

in resolving of peak cluster A is shown in Table 3 with their relative component contribution (RCC) 311

function values (see caption) when only non-negativity and spectral normalization constraints were 312

applied (Table S3B and Table S3C for peak clusters B and C, respectively). In these Tables, for each 313

component, the function values for the initial profiles (finic), the maximum (fmax), minimum (fmin) 314

optimized functions and the difference between them (fmax-fmin) are given that allow an easy inspection of 315

the extent of remaining rotational ambiguities. When the difference is close to zero, it means that 316

practically there is no remaining rotational ambiguity.317

Table 3318

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In all cases, solutions of MCR-ALS with different initial estimates are going to the same loss of 319

experimental data value (lack of fitting) and the same value of ambiguity (feasible region), but the values 320

of qualitative analysis of final solutions with different initial estimates are not same and resolved 321

components have different RMF (finish in different feasible solutions).322

Table 4 shows the values of rotational ambiguities in SMCR methods for peak cluster A. Results of 323

SMCR methods for peak cluster B and C are available in supplementary data (Table S4B and Table S4C, 324

respectively). Results show that the performance of multivariate resolution techniques could be 325

influenced by level of overlapping or embedding and noise of dataset (these peak clusters in each sample 326

have different value of noise and degree of overlapping). Abdollahi and Tauler have claimed that in the 327

presence of rotational ambiguity and under a special set of constraints, the obtained solution by the 328

different multivariate curve resolution methods can differ among them and also from the true solution, 329

depending on the applies algorithm and initial estimates [42, 46]. But results of our research show that, all 330

iterative chemometric resolution methods with applied non-negativity on chromatogram and spectral 331

profiles and normalization on spectral profiles have the same and large values of rotational ambiguities. 332

Tauler reported that the maximum and the minimum band boundaries calculated for the solutions of 333

MCR-ALS and MCR-FMIN were different [18]. But, Rajko acclaim that the difference between the 334

maximum and the minimum band boundaries calculated for the solutions of MCR-ALS and MCR-FMIN 335

is impossible, because the rotational ambiguity belongs to the data matrix and is independent of the 336

algorithms of the curve resolution [51]. From comparison of RCC values in Table 4 for Peak cluster 337

A (peak cluster B and C in Table S4B and Table S4C, respectively), it is observed that each 338

solution of methods has RCC value in same feasible solution regions. For example, Fmin for peak 339

cluster A in EF sample by any of the three investigated methods are 0.754 and 0.397 for the first 340

and second components, respectively. Also, Fmax for peak cluster A in EA sample by any of the 341

three studied methods are 0.847 and 0.493 for the first and second components, respectively. In 342

other words, the range of the feasible region for this data set is independent of the algorithms that 343

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were used for resolution (0.093 and 0.096 for the first and second components, respectively). 344

One can see from Tables 3, S3B, S3C, 4, S4B and S4C that Fmin and Fmax values are rather 345

similar when the same system was investigated by any of the three methods (MCR-ALS, MFICA 346

or MCR-FMIN). The results of this study approve the Rajko acclaim, that the maximum and the 347

minimum band boundaries calculated for the solutions of MF-ICA, MCR-ALS and MCR-FMIN 348

are the same, in other words, rotational ambiguity belongs to the data matrix is independent of 349

the algorithms of the curve resolution.350

NIST library by comparing the fragmentation patterns composed of all fragment ions of unknown 351

component with its standards (supported by both reasonably good spectral matches and close time 352

matching with a database) lists the formula and name of the most likely compound. While one or more of 353

resolving fragmentation ions (abundance or pattern in spectral profile) are affected with each of common 354

problems, such as rotational ambiguity and noise, different component may be characterized. For 355

example, in peak cluster A of WF sample, in spite of obtaining good values of LOF and R2, similarity 356

index (RMF2) is poor (noted by (-) in Tables 1 and 2). This means that the model fits well the data but the 357

solutions are not the true ones, because rotational ambiguities are still present. Existence of rotational 358

ambiguities had led to obtaining odd profiles for peak cluster A of WF sample that does not pertain to D-359

limonene or 1, 8-Cineol, and the obtained profile could not be identified. As another example, in peak 360

cluster B of EF sample, in spite of obtaining good values of LOF and R2, similarity index (RMF4) is poor 361

(noted by (-) in Tables S1B and S2B in supplementary data). As mentioned above, this means that 362

rotational ambiguities are still present. Results show that, SMCR methods by non-negativity and 363

normalization as constraints are not reliable for quantitative and qualitative analysis.364

Table 4365

Iterative techniques try to find a rational solution. The important differences between the iterative 366

approaches can be related to the initial estimates used, the sort of profiles that are iteratively optimized, or 367

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the nature and application of the constraints. In these methods, at each cycle of an optimization process, 368

some constraints such as non-negativity, normalization, unimodality, local rank/selectivity, are exerted on 369

the algorithms to obtaining meaningful solutions. Constraints force the profiles in C and/or ST to comply 370

some predefined mathematical or chemical properties. In MF-ICA, MCR-ALS and MCR-FMIN some 371

constraints such as non-negativity and normalization are common. But algorithms of MCR-ALS and 372

MCR-FMIN have an advantage that they could impose other constraints such as unimodality, local 373

rank/selectivity, trilinearity (MF-ICA algorithm could not comply these important constraints). Also, in 374

contrast to MF-ICA algorithm, resolution of augmentation data is another MCR algorithms advantage. In 375

another word, MCR algorithms are proffered to resolution of several runs and or several samples.376

Several factors such as intense of complexity, intense of components, and value of noises have effect on 377

ambiguity of resolved results [42]. Therefore, each type of chromatograms, which has the diverse nature 378

of the data set, has a different amount of rotational ambiguity. 379

Because of unknown concentrations of components in GC-MS, the constraint of equal unit concentration 380

profile (closure) cannot be used. So non-negativity, unimodality, and selectivity play a major role in these 381

analysis [52,61]. In this paper, for reducing rotational ambiguity the following constraints have been 382

applied; non-negativity for the concentration and spectral profiles, unimodality and selectivity for the 383

concentration profile and normalization for the spectral profile. In this case, for the analysis of 384

experimental systems, the information needed for the application of the local rank/selectivity constraints 385

can be obtained from preliminary evolving factor analysis (EFA) of the data sets [62]. Results of peak 386

cluster A of EF sample are shown in Table 5. In supplementary data, Tables S5B and S5C have shown the 387

results of applying constraints on peak cluster B and C of EF sample, respectively.388

Table 5389

Results show that rotational ambiguities are reduced by applying appropriate constraints. Imposing of 390

only non-negativity and normalization constraints leave a wide range of possible elution profiles (see 391

Tables 3, S3B and S3C, Tables 4, S4B and S4C). Also, the spectral profiles can be very different if only 392

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these constraints were applied. When unimodality was applied, this range of possible solutions was 393

narrowed (see Tables 5, S5B and S5C), and when local rank constraint was applied, this range of possible 394

solutions was narrowed significantly. From these results can be clearly concluded that imposing any 395

additional information on the chemical system could be reduced the rotational ambiguity of the solutions 396

of a SMCR method [57,61]. Results show that, MCR-ALS and MCR-FMIN did not produce the unique 397

solutions because rotational ambiguity could not be totally solved in these cases by the proposed 398

constraints.399

As mentioned above, the first possible strategy to decrease or overcome on the influence of rotational 400

ambiguities could be the use of additional information (applying constraints) for each of the co-eluted 401

components. The second strategy is arranging data sets in a single augmented data matrix (data 402

augmentation of the several samples or runs). Data can be augmented by the three options of matrix 403

augmentation (column-wise, row-wise or column- and row-wise augmented data matrix). When the data 404

matrix is arranged in a row - or a column -wise augmented matrix, the algorithm is started by spectral or 405

concentration profile as an initial estimate, respectively [42]. GC-MS data, including those of essential 406

oils are naturally three-way (samples × retention time × m/z) and therefore, are candidates for analysis by 407

chemometric resolution methods.408

From the fact that the positions and shapes of the elution of the two co-eluted components in peak clusters 409

A (as well as B) and the three co-eluted components in peak cluster C are different in the six different 410

samples and can be found out that they could not be described by only two elution profiles for peak 411

clusters A (as well as B) and only three elution profiles for peak clusters C. In the other words, each 412

component in each sample needs a specific concentration profile to describe its elution profile. In this 413

study, because of using several samples, matrices of experimental data have some deviation from tri-414

linearity. MCR-ALS belongs to the methods that could work even with some deviation from tri-linearity 415

in data set. MCR-ALS works with the unfolding three-way data array which breaks the tri-linear 416

structure in the data set [63].417

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Results from augmentation of these six samples proven that the peak cluster A includes two components, 418

D-limonene and 1, 8-Cineol. The RMF of D-limonene and 1, 8-Cineol are 880 and 945, respectively. 419

Results from augmentation of these samples confirmed that the peak cluster B includes two components, 420

Linalool and Hotrienol. The RMF of Linalool and Hotrienol are 925 and 931, respectively. Also, results 421

from augmentation of these samples confirmed that the peak cluster C includes three components such as 422

α-Terpineol, Estragole, and Myrtenol. The RMF of α-Terpineol, Estragole, and Myrtenol are 945, 932 and 423

905, respectively. By augmentation of datasets from only six samples, the value of rotational ambiguity 424

reaches to zero. This proves the importance of using augmentation data to get optimal solutions in MCR 425

analysis. Thus, by applying the strategy of augmentation, the concentration and spectral profiles of the 426

main components were obtained truly. Therefore, using augmentation of datasets is one of the best 427

solutions for reducing or removing the rotational ambiguity.428

5. Conclusion429

Gas chromatography-mass spectrometry is common hyphenated chromatography technique for 430

identification volatile constituents of essential oils, but because of baseline drift, noises and co-elution, 431

this technique has unreliable performance. Chemometric resolution methods for resolving overlapping 432

peaks into pure profiles were applied. In this work, several results of common resolution techniques such 433

as MF-ICA, MCR-ALS and MCR-FMIN have been surveyed. Self-modeling curve resolution techniques 434

are hard model-free methods in a sense that no a-priori information on the chemical system is needed for 435

the construction of profiles. These results confirm that, when non-negativity and normalization are 436

applied, results of these three methods almost were the same. In general, because of the so-called 437

rotational ambiguity, a range of feasible solutions exist. The rotational ambiguities of the profiles are a 438

challenging fact which complicates the development of stable and universal SMCR algorithms. The 439

calculative determination of the range of feasible solution has an advantage in the analysis of chemical 440

systems. These results approve that, chemometric resolution techniques with imposed non-negativity and 441

normalization as constraints have much value of ambiguities on rotational ambiguities that approximately 442

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is the same for all methods. Also, results show that using additional information on the chemical system 443

can be reduced the rotational ambiguity of the solutions of chemometric resolution techniques. From the 444

obtained results, it is deduced that augmentation of data decreases considerably the extent of rotational 445

ambiguities in multivariate resolution methods. So, using augmented data with MCR-ALS technique by 446

applying appropriate constraints is the best solution for obtaining resolved profiles that are most similar to 447

the true profiles..448

6. Acknowledgements449

The authors are grateful to University of Kashan for supporting this work by Grant NO. 256727/1 and 450

would like to thank from Dr. Hadi Parastar from Department of Chemistry, Sharif University of 451

Technology for his helpful discussion and thankful to Barij Essence Pharmaceutical Company (Kashan, 452

Iran) for help us in preparing samples.453

454

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References454

455

[1] M. Jalali-Heravi, B. Zekavat, H. Sereshti, Use of gas chromatography–mass spectrometry 456combined with resolution methods to characterize the essential oil components of Iranian cumin 457and caraway, J. Chromatogr. A 1143 (2007) 215-226.458

[2] C. Brunelli, C. Bicchi, A. Di Stilo, A. Salomone, M. Vincenti, High‐speed gas chromatography in 459

doping control: Fast‐GC and fast‐GC/MS determination of β‐adrenoceptor ligands and diuretics, 460

J. Sep. Sci. 29 (2006) 2765-2771.461[3] J.M. Amigo, M.J. Popielarz, R.M. Callejón, M.L. Morales, A.M. Troncoso, M.A. Petersen, T.B. 462

Toldam-Andersen, Comprehensive analysis of chromatographic data by using PARAFAC2 and 463principal components analysis, J. Chromatogr. A 1217 (2010) 4422-4429.464

[4] X. Shao, G. Wang, S. Wang, Q. Su, Extraction of mass spectra and chromatographic profiles 465from overlapping GC/MS signal with background, Anal. Chem. 76 (2004) 5143-5148.466

[5] W. Windig, J.M. Phalp, A.W. Payne, A noise and background reduction method for component 467detection in liquid chromatography/mass spectrometry, Anal. Chem. 68 (1996) 3602-3606.468

[6] C.-J. Xu, Y.-Z. Liang, F.-T. Chau, Identification of essential components of Houttuynia cordata 469by gas chromatography/mass spectrometry and the integrated chemometric approach, Talanta 68 470(2005) 108-115.471

[7] L.W. Hantao, H.G. Aleme, M.P. Pedroso, G.P. Sabin, R.J. Poppi, F. Augusto, Multivariate curve 472resolution combined with gas chromatography to enhance analytical separation in complex 473samples: A review, Anal. Chim. Acta 731 (2012) 11-23.474

[8] M. Jalali-Heravi, H. Parastar, Recent trends in application of multivariate curve resolution 475approaches for improving gas chromatography–mass spectrometry analysis of essential oils, 476Talanta 85 (2011) 835-849.477

[9] J.M. Amigo, T. Skov, R. Bro, ChroMATHography: solving chromatographic issues with 478mathematical models and intuitive graphics, Chem. Rev. 110 (2010) 4582-4605.479

[10] G. Lubec, L. Afjehi-Sadat, Limitations and pitfalls in protein identification by mass spectrometry, 480Chemical Reviews-Columbus 107 (2007) 3568-3584.481

[11] A. de Juan, R.A. Tauler, Multivariate curve resolution (MCR) from 2000: progress in concepts 482and applications, Crit. Rev. Anal. Chem. 36 (2006) 163-176.483

[12] M. Garrido, F. Rius, M. Larrechi, Multivariate curve resolution–alternating least squares (MCR-484ALS) applied to spectroscopic data from monitoring chemical reactions processes, Anal. Bioanal. 485Chem. 390 (2008) 2059-2066.486

[13] J.-H. Jiang, Y. Liang, Y. Ozaki, Principles and methodologies in self-modeling curve resolution, 487Chemom. Intell. Lab. Syst. 71 (2004) 1-12.488

[14] S. Masoum, H. Ghasemi-Estarki, H. Seifi, E.H. Ebrahimabadi, H. Parastar, Analysis of the 489volatile chemical constituents in Mindium laevigatum by Gas chromatography–Mass 490spectrometry and correlative chemometric resolution methods, Microchem. J. (2012) 276-281.491

[15] H. Seifi, S. Masoum, S. Seifi, E.H. Ebrahimabadi, Chemometric Resolution Approaches in 492Characterisation of Volatile Constituents in Plantago ovata Seeds using Gas Chromatography–493

Page 22 of 35

Accep

ted

Man

uscr

ipt

Mass Spectrometry: Methodology and Performance Assessment, Phytochem. Anal. 25 (2014) 494273–281.495

[16] A. Hyvärinen, E. Oja, Independent component analysis: algorithms and applications, Neural 496networks 13 (2000) 411-430.497

[17] J. Jaumot, R. Gargallo, A. de Juan, R. Tauler, A graphical user-friendly interface for MCR-ALS: 498a new tool for multivariate curve resolution in MATLAB, Chemom. Intell. Lab. Syst. 76 (2005) 499101-110.500

[18] R. Tauler, Application of non-linear optimization methods to the estimation of multivariate curve 501resolution solutions and of their feasible band boundaries in the investigation of two chemical and 502environmental simulated data sets, Anal. Chim. Acta 595 (2007) 289-298.503

[19] H. Li, J. Hou, K. Wang, F. Zhang, Resolution of multicomponent overlapped peaks: A 504comparison of several curve resolution methods, Talanta 70 (2006) 336-343.505

[20] S. Masoum, H. Seifi, E.H. Ebrahimabadi, Characterization of volatile components in calligonum 506comosum by coupling gas chromatography-mass spectrometry and mean field approach 507independent component analysis, Anal. Methods 5 (2013) 4639-4647.508

[21] M. Jalali-Heravi, B. Zekavat, H. Sereshti, Characterization of essential oil components of Iranian 509geranium oil using gas chromatography–mass spectrometry combined with chemometric 510resolution techniques, J. Chromatogr. A 1114 (2006) 154-163.511

[22] G. Wang, W. Cai, X. Shao, A primary study on resolution of overlapping GC-MS signal using 512mean-field approach independent component analysis, Chemom. Intell. Lab. Syst. 82 (2006) 137-513144.514

[23] M. Vosough, Using mean field approach independent component analysis to fatty acid 515characterization with overlapped GC–MS signals, Anal. Chim. Acta 598 (2007) 219-226.516

[24] M. Jalali-Heravi, H. Parastar, H. Ebrahimi-Najafabadi, Self-modeling curve resolution techniques 517applied to comparative analysis of volatile components of Iranian saffron from different regions, 518Anal. Chim. Acta 662 (2010) 143-154.519

[25] M. Jalali-Heravi, H. Parastar, Assessment of the co-elution problem in gas chromatography-mass 520spectrometry using non-linear optimization techniques, Chemom. Intell. Lab. Syst. 101 (2010) 1-52113.522

[26] A. Cichocki, R. Zdunek, Advances in Neural Networks, Springer, 2007.523[27] S. Navea, R. Tauler, A. de Juan, Monitoring and modeling of protein processes using mass 524

spectrometry, circular dichroism, and multivariate curve resolution methods, Anal. Chem. 78 525(2006) 4768-4778.526

[28] A. de Juan, M. Maeder, T. Hancewicz, R. Tauler, Use of local rank‐based spatial information for 527

resolution of spectroscopic images, J. Chemometrics 22 (2008) 291-298.528[29] T. Azzouz, R. Tauler, Application of multivariate curve resolution alternating least squares 529

(MCR-ALS) to the quantitative analysis of pharmaceutical and agricultural samples, Talanta 74 530(2008) 1201-1210.531

[30] J. Jaumot, R. Tauler, MCR-BANDS: A user friendly MATLAB program for the evaluation of 532rotation ambiguities in Multivariate Curve Resolution, Chemom. Intell. Lab. Syst. 103 (2010) 96-533107.534

[31] M.H. Van Benthem, M.R. Keenan, D.M. Haaland, Application of equality constraints on 535variables during alternating least squares procedures, J. Chemometrics 16 (2002) 613-622.536

[32] A. de Juan, M. Maeder, M. Martı́nez, R. Tauler, Combining hard-and soft-modelling to solve 537kinetic problems, Chemom. Intell. Lab. Syst. 54 (2000) 123-141.538

Page 23 of 35

Accep

ted

Man

uscr

ipt

[33] M. Sawall, C. Fischer, D. Heller, K. Neymeyr, Reduction of the rotational ambiguity of curve 539resolution techniques under partial knowledge of the factors. Complementarity and coupling 540theorems, J. Chemometrics 26 (2012) 526-537.541

[34] H. Abdollahi, R. Tauler, Uniqueness and rotation ambiguities in Multivariate Curve Resolution 542methods, Chemom. Intell. Lab. Syst. 108 (2011) 100-111.543

[35] W.H. Lawton, E.A. Sylvestre, Self modeling curve resolution, Technometrics 13 (1971) 617-633.544[36] R. Rajkó, Additional knowledge for determining and interpreting feasible band boundaries in 545

self-modeling/multivariate curve resolution of two-component systems, Anal. Chim. Acta 661 546(2010) 129-132.547

[37] R.b. Rajkó, Comments on Near-Infrared Hyperspectral Unmixing Based on a Minimum Volume 548Criterion for Fast and Accurate Chemometric Characterization of Counterfeit Tablets, Anal. 549Chem. 82 (2010) 8750-8752.550

[38] O.S. Borgen, N. Davidsen, Z. Mingyang, Ø. Øyen, The multivariate N-component resolution 551problem with minimum assumptions, Microchim. Acta 89 (1986) 63-73.552

[39] O.S. Borgen, B.R. Kowalski, An extension of the multivariate component-resolution method to 553three components, Anal. Chim. Acta 174 (1985) 1-26.554

[40] R. Rajkó, Some surprising properties of multivariate curve resolution‐alternating least squares 555

(MCR‐ALS) algorithms, J. Chemometrics 23 (2009) 172-178.556

[41] R. Rajkó, Studies on the adaptability of different Borgen norms applied in self‐modeling curve 557

resolution (SMCR) method, J. Chemometrics 23 (2009) 265-274.558[42] A. Golshan, H. Abdollahi, M. Maeder, Resolution of rotational ambiguity for three-component 559

systems, Anal. Chem. 83 (2011) 836-841.560[43] S. Burt, Essential oils: their antibacterial properties and potential applications in foods—a review, 561

Int. J. Food Microbiol. 94 (2004) 223-253.562[44] L.S. Nerio, J. Olivero-Verbel, E. Stashenko, Repellent activity of essential oils: a review, 563

Bioresour. Technol. 101 (2010) 372-378.564[45] E. Guenther, The production of essential oils, The essential oils 1 (1972) 87-226.565[46] D.J. Charles, J.E. Simon, Comparison of extraction methods for the rapid determination of 566

essential oil content and composition of basil, J. Am. Soc. Hortic. Sci. 115 (1990) 458-462.567[47] M. Godefroot, P. Sandra, M. Verzele, New method for quantitative essential oil analysis, J. 568

Chromatogr. A 203 (1981) 325-335.569[48] S. A. Maisonneuve, European Pharmacopoeia, Sainte-Ruffine, France 3 (1975) 68-80.570[49] H. Parastar, M. Jalali-Heravi, R. Tauler, Is independent component analysis appropriate for 571

multivariate resolution in analytical chemistry?, TrAC, Trends Anal. Chem. 31 (2012) 134-143.572[50] H. Abdollahi, M. Maeder, R. Tauler, Calculation and meaning of feasible band boundaries in 573

multivariate curve resolution of a two-component system, Anal. Chem. 81 (2009) 2115-2122.574[51] R. Rajkó, Computation of the range (band boundaries) of feasible solutions and measure of the 575

rotational ambiguity in self-modeling/multivariate curve resolution, Anal. Chim. Acta 645 (2009) 57618-24.577

Page 24 of 35

Accep

ted

Man

uscr

ipt

[52] R. Tauler, Multivariate curve resolution applied to second order data, Chemom. Intell. Lab. Syst. 57830 (1995) 133-146.579

[53] H. Shen, L. Stordrange, R. Manne, O.M. Kvalheim, Y. Liang, The morphological score and its 580application to chemical rank determination, Chemom. Intell. Lab. Syst. 51 (2000) 37-47.581

[54] A. Savitzky, M.J.E. Golay, Smoothing and differentiation of data by simplified least squares 582procedures, Anal. Chem. 36 (1964) 1627-1639.583

[55] P.H.C. Eilers, Parametric time warping, Anal. Chem. 76 (2004) 404-411.584[56] Y.Z. Liang, O.M. Kvalheim, A. Rahmani, R.G. Brereton, A two-way procedure for background 585

correction of chromatographic/spectroscopic data by congruence analysis and least-squares fit of 586the zero-component regions: comparison with double-centering, Chemom. Intell. Lab. Syst. 18 587(1993) 265-279.588

[57] R. Tauler, Calculation of maximum and minimum band boundaries of feasible solutions for 589species profiles obtained by multivariate curve resolution, J. Chemometrics 15 (2001) 627-646.590

[58] G. Ahmadi, H. Abdollahi, A systematic study on the accuracy of chemical quantitative analysis 591using soft modeling methods, Chemom. Intell. Lab. Syst. 120 (2012) 59-70.592

[59] W. Windig, C. Heckler, F. Agblevor, R. Evans, Self-modeling mixture analysis of categorized 593pyrolysis mass spectral data with the SIMPLISMA approach, Chemom. Intell. Lab. Syst. 14 594(1992) 195-207.595

[60] R.P. Adams, Identification of essential oil components by gas chromatography/mass 596spectrometry, B R.P. Adams (Ed.), Allured Publishing Corporation, 2007.597

[61] R. Tauler, A. Smilde, B. Kowalski, Selectivity, local rank, three‐way data analysis and ambiguity 598

in multivariate curve resolution, J. Chemometrics 9 (1995) 31-58.599[62] M. Maeder, A.D. Zuberbuehler, The resolution of overlapping chromatographic peaks by 600

evolving factor analysis, Anal. Chim. Acta 181 (1986) 287-291.601[63] A. Olivieri, G. Escandar, A. Peña, Second-order and higher-order multivariate calibration 602

methods applied to non-multilinear data using different algorithms, TrAC Trends in Anal. Chem. 60330 (2011) 607-617.604

605

606

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606

Table 1. Effects of different initial estimation methods to launch MCR-ALS 607algorithm in resolving of peak cluster A.608

EFa WDb EDc KDd WFe KFf

RMF1 938 923 974 885 954 911

RMF2 782 799 844 801 - 759

LOF 8.79 7.27 5.44 9.56 10.55 12.45SIMPLISMA

R2 99.23 99.47 99.70 99.09 99.89 98.45

RMF1 938 906 974 885 954 911

RMF2 799 798 844 801 - 759

LOF 8.79 7.27 5.44 9.56 10.55 12.45

OPA

R2 99.23 99.47 99.70 99.09 99.89 98.45

RMF1 938 902 974 885 954 911

RMF2 782 799 844 801 - 759

LOF 8.79 7.27 5.44 9.56 10.55 12.45EFA

R2 99.23 99.47 99.70 99.09 99.89 98.45

a Fresh sample cultivated in Noorabad; b Dried sample collected from hillsides of 609Noorabad; c Dried sample cultivated in Noorabad; d Dried sample collected from hillsides 610of Khoramabad; e Fresh sample collected from hillsides of Noorabad; f Fresh sample 611collected from hillsides of Khoramabad.612The database lists the name and formula of the most likely compound in accordance with 613the NIST search that matches an unknown compound and how similar the two compounds 614are in terms of their peaks (match/ reverse match factor). Reverse match factor (RMF) is a 615peak comparison between the unknown and the known spectra. As a general guide, 900 or 616greater is an excellent match; 800–900, a good match; 700–800, a fair match. Less than 600 617is a very poor match. RMF1 and RMF2 show reverse match factor (RMF) of 1, 8-Cineol and 618D-limonene, respectively.619b LOF and R2 values are calculated according to Equation (4) and (5), respectively.620

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Table 2. RMF of resolution chemometric methods for peak cluster A.621622

EFa WDb EDc KDd WFe KFf

RMF1 938 923 974 885 954 911MCR-ALS

RMF2 782 799 844 801 - 759

RMF1 946 940 975 878 954 911MF-ICA

RMF2 800 752 892 812 843 800

RMF1 943 941 930 816 948 850MCR-FMIN

RMF2 800 741 909 816 - 804

623

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623Table 3. Effect of different initial estimation methods with their relative component contribution (RCC) function 624values on rotational ambiguity of MCR-ALS in resolving of peak cluster A.625

626EF WD ED KD WF KF

1 2 1 2 1 2 1 2 1 2 1 2

fmin 0.754 0.397 0.811 0.332 0.203 0.851 0.834 0.339 0.869 0.347 0.724 0.349

finic- SIMPLISMA 0.825 0.423 0.864 0.366 0.203 0.897 0.885 0.464 0.869 0.382 0.724 0.533

finic-OPA 0.825 0.423 0.864 0.366 0.203 0.897 0.885 0.339 0.869 0.382 0.724 0.533

finic- EFA 0.842 0.427 0.871 0.351 0.203 0.897 0.884 0.341 0.879 0.367 0.807 0.410

fmax 0.847 0.493 0.888 0.424 0.281 0.897 0.885 0.502 0.896 0.382 0.867 0.533

fmax-fmin 0.093 0.096 0.077 0.092 0.078 0.046 0.051 0.163 0.027 0.035 0.143 0.184

627

Values of the relative component contribution (RCC) function (fp), for component p obtained using 628

different techniques under non-negativity constraints. fp is defined as: ( )T

p p

p T

C Sf T

CS , where T

p pC S is 629

the norm of the contribution of component p calculated as the norm of the product of its concentration 630profile Cp by its spectrum profile T

pS . TCS provides the global contribution of all resolved 631

components calculated as the norm of the product of the concentration matrix C by the spectra matrix ST. 632fmax – fmin corresponds to the difference between fmax and fmin values.633

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634

Table 4. The results of MCR-BANDS with their relative component contribution (RCC) function values635in resolving of peak cluster A with multivariate resolution techniques.636

637638639640641642643644

EF WD ED KD WF KF1 2 1 2 1 2 1 2 1 2 1 2

fmin 0.754 0.397 0.811 0.332 0.203 0.851 0.834 0.339 0.869 0.347 0.724 0.349

finic- MCR-ALS 0.825 0.423 0.864 0.366 0.203 0.897 0.885 0.464 0.869 0.382 0.724 0.533

finic-MF-ICA 0.815 0.493 0.811 0.424 0.203 0.897 0.836 0.479 0.877 0.377 0.792 0.486

finic-MCR-FMIN 0.830 0.441 0.853 0.382 0.203 0.897 0.847 0.472 0.869 0.347 0.724 0.533

fmax 0.847 0.493 0.888 0.424 0.281 0.897 0.885 0.502 0.896 0.382 0.867 0.533

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Table 5. Effects of different constraints on 644rotational ambiguity for peak cluster A of EF 645sample.646

647648649650651652653654655656657

Constraints: 1 normalization; 2 non-negativity; 3 658unimodality; 4 Selectivity/local rank.659a: fmax – fmin corresponds to the difference between 660fmax and fmin values for MCR-ALS and MCR-661FMIN solutions.662

663

fmax-fmin a

1 2

1, 2 0.093 0.096

1, 2, 3 0.051 0.063

1, 2, 4 0.014 0.012

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Figure Caption663

Figure 1. Total ion chromatogram of all samples.664

Figure 2. Morphological score plot for peak cluster A.665

Figure 3. Results of resolution for peak cluster A of EF sample by different multivariate resolution 666methods.667

Figure 4. Resolved mass spectra and their corresponding standard mass spectra for peak cluster A of EF 668sample. Resolved (a) and standard (c) mass spectra of 1, 8-Cineol; resolved (b) and standard (d) mass 669spectra of D-limonene.670

671

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Highlights:

Initial estimates have no effect on extraction of information from overlapped signals.

MCR-ALS results are favorably compared to results obtained by MF-ICA and MCR-FMIN.

Physical constraints were implemented to reduce the rotational ambiguities.

Using augmentation data is the best way to overcome on rotational ambiguity.

*Highlights (for review)

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Figure 1

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Figure 2

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Figure 3

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Figure 4