Multivariate Chemometric Methods Research Articles

Extended multivariate comparison of 68 cluster validity indices. A review

Clustering is an unsupervised machine learning methodology widely used in several sciences to find groups of similar patterns in complex data. The results generated by clustering algorithms generally depend on user-defined input parameters such as the number of expected clusters, which can have a great impact on the homogeneity of the identified clusters.Clustering validity indices (CVIs) are an effective method for determining the optimal number of clusters that best fit the natural partition of a dataset. They do not require any underlying assumption nor a priori knowledge about the true dataset structure. Since 1965, many cluster validity indices have been proposed in the literature and used in several different applications.In this paper, the performance of 68 cluster validity indices was evaluated on 21 real-life research and simulated datasets. CVIs were compared on the same partition for each dataset, which was searched for by the k-means clustering algorithm. Multivariate chemometric methods were applied to disclose mutual relationships among the indices and to select those that are more effective in terms of accuracy and reliability.

Spectral insights: advancing the authentication and quality assessment of Moroccan saffron through UV–visible spectroscopy and multivariate chemometric methods

Spectral insights: advancing the authentication and quality assessment of Moroccan saffron through UV–visible spectroscopy and multivariate chemometric methods

A novel and intelligent chemometric-electrochemical-enzymatic biosensing procedure and mimicking a clinical condition environment to trick the red blood cells for counting them under physiological conditions: A new connection among chemometry, electrochemistry and hematology

Here, a novel electrochemical biosensing procedure has been developed for determination of the number of red blood cells (RBCs) under physiochemical conditions based on chemometric modeling of hydrodynamic differential pulse voltammetric (HDPV), and amperometric data as responses of a modified edge plane pyrolytic graphite electrode (EPPGE). In order to obtain a good sensitivity from the EPPGE, its surface was modified with a thin layer of multiwalled carbon nanotubes-ionic liquid (MWCNTs-IL). Catalase (CAT) was immobilized onto the surface of MWCNTs-IL/EPPGE with help of nafion. The response of the biosensor was based on electrochemical reduction of oxygen of the blood samples which was enhanced by a trick based on addition of hydrogen peroxide (H2O2) to blood samples which can be reduced by the CAT to produce extra oxygen. Prior to experiments, the solution in electrochemical cell was bubbled with pure N2 to purge the oxygen in the solution, but in order to increase the selectivity of the biosensor towards detection of the oxygen obtained from the red blood cells, voltammetric responses of the biosensor were modeled by multivariate chemometric calibration methods with the help of radial basis function-partial least squares (RBF-PLS), least squares-support vector machines (LS-SVM), recursive weighted partial least squares (rPLS), ant colony optimization-mathematical pre-processing selection by genetic algorithm-sample selection through a distance-based procedure-partial least squares-1 (ACO-GA-SS-PLS1), and radial basis function-artificial neural networks (RBF-ANN) to select the best method for determination of the number of the RBCs. The results confirmed the amperometric methods modeled by RBF-ANN showed the best performance for supporting the biosensor in determination of the number of the RBCs with a performance which had an excellent compatibility with the results of a hemocytometer. The results of this study as the newest application of chemometric-electrochemical methods can make a strong connection among electrochemists, chemometricians and hematologists to expand their collaborations on determination of blood factors.

Novel hybrid ZnS:Mn2+quantum dots/N-methylpolypyrrole fluorescence probe for determination of nitro-aromatic compounds in water samples by using multivariate chemometric methods

Novel hybrid ZnS:Mn2+quantum dots/N-methylpolypyrrole fluorescence probe for determination of nitro-aromatic compounds in water samples by using multivariate chemometric methods

UV Spectrophotometry with Chemometric methods for Concurrent Assays of Antihypertensive Components in Tablets

Chemometrics is the precise and practice of analyzing data through various numerical techniques in order to develop useful information. Generally, it is better to measure many nonselective signals and then combine them in a multivariate model. Nowadays, the combinations of amlodipine, valsartan, and hydrochlorothiazide are effective antihypertensive drugs. The combination of active ingredients will be evaluated for its component content and validated using the chemometric spectrophotometric method paired with the multivariate partial least squares system. For modeling calibration and chemometric validation, a double divisor system was employed. An ultraviolet spectrophotometric measurement was performed by measuring the absorbance spectrum at a wavelength of 230-300nm of AML, 220-290nm of valsartan, and 230-300nm of hydrochlorothiazide at 2nm intervals. Partial Least Squares were used to calculate levels of AML is (99.59±0.28)%; VAL is (101.99± 0.44)% and HCT is (103.60±0.34)% and cross-validated using R2, PRESS, and RMSCEV. Concluded that the determination of amlodipine, valsartan, and hydrochlorothiazide mixtures by the partial least squares multivariate chemometric method met the requirements for tablet dosage forms, according to USP 43-NF38.

Comparative analysis of chemical components in fruits of Chebulae Fructus and its pulp based on chromatographic technology coupled with multivariate chemometric methods

Chebulae Fructus, was extensively used as a food supplement and medicinal herb, which contained two medicinal forms corresponding to the mature fruit of Chebulae Fructus (CF) and CF pulp. They were widely used in the Chinese clinical medicine and it played a significant role in the Mongolian and Tibetan medicine for the treatment of sore throat, asthma, diarrhea and other diseases. Both of them were recorded in the 2020 Edition (Volume I) of the Chinese Pharmacopoeia. However, the chemical components of CF and CF pulp have not been holistically explored, which seriously hindered its quality evaluation. This study investigated the overall chemical profile of the CF and CF pulp using ultra high-performance liquid chromatography coupled with quadrupole time of flight mass spectrometry (UHPLC-Q-TOF/MS) and ultra high-performance liquid chromatography-tandem mass spectrometry (UHPLC-MS/MS). Sixty-four chemical components were tentatively identified, and 13 components were quantified in Chebulae Fructus. Furthermore, multivariate chemometric methods were applied to compare the differences among CF samples, and all samples were classified by orthogonal partial least squares-discriminant analysis (OPLS-DA) based on the 13 quantified compounds. The results showed that CF and CF pulp were clustered in two different areas. Ellagic acid, chebulagic acid, chebulinic acid, corilagin and pentagalloyl glucose were selected as the significant constituents to different of CF and CF pulp. LC-MS coupled with chemometrics strategy analysis could comprehensively evaluate the holistic quality of CF, which provided a necessary information for the rational development and utilization of CF and CF pulp resource.

A Green-and-White Integrative Analytical Strategy Combining Univariate and Chemometric Techniques for Quantifying Recently Approved Multi-Drug Eye Solution and Potentially Cancer-Causing Impurities: Application to the Aqueous Humor.

Drug impurities are now seen as a major threat to the production of pharmaceuticals around the world and a major part of the global contamination problem, especially when it comes to carcinogenic impurities. We present the first spectrophotometric strategy based on a combination of univariate and multivariate methods as impurity profiling methods for the estimation of lignocaine (LIG) and fluorescein (FLS) with their carcinogenic impurities: 2,6-xylidine (XYL) and benzene-1,3-diol (BZD). The data processing strategy depends on overcoming unresolved bands by employing five affordable, accurate, selective, and sensitive methods. The methods applied were a direct UV univariate spectrophotometric analysis (D0) and four multivariate chemometric methods, including classical least squares (CLS), principal component regression (PCR), partial least squares (PLS), and genetic algorithm (GA-PLS). FLS analysis (1-16 μg/mL) was performed using the D0 method at 478 nm; then, the application of the ratio subtraction method (RSM) allowed the removal of interference caused by the FLS spectrum. From the resulting ratio spectra, LIG, XYL, and BZD can be efficiently determined by chemometrics. The calibration set was carefully selected at five concentration levels using a partial factorial training design, resulting in 25 mixtures with central levels of 160, 40, and 3 μg/mL for LIG, XYL, and BZD, respectively. Another 13 samples were applied to validate the predictive ability. The statistical parameters demonstrated exceptional recoveries and smaller prediction errors, confirming the experimental model's predictive power. The proposed approach was effectively tested using newly FDA-approved LIG and FLS pharmaceutical preparation and aqueous humor. Additionally, it was effectively assessed for whiteness, greenness, and sustainability using five assessment tools. With its remarkable analytical performance, sustainability, affordability, simplicity, and cost-efficiency, the proposed strategy is an indispensable tool for quality control and in situ analysis in little-equipped laboratories, increasing the proposed approach's surveillance ability.

A comprehensive quality evaluation of Cimicifugae Rhizoma using UPLC-Q-Orbitrap-MS/MS coupled with multivariate chemometric methods.

Cimicifugae Rhizoma, known in Chinese as Shengma, is a common medicinal material in traditional Chinese medicine (TCM), mainly used for treating wind-heat headaches, sore throat, uterine prolapse, and other diseases. An approach using a combination of ultra-performance liquid chromatography (UPLC), mass spectrometry (MS), and multivariate chemometric methods was designed to assess the quality of Cimicifugae Rhizoma. All materials were crushed into powder and the powdered sample was dissolved in 70% aqueous methanol for sonicating. Chemometric methods, including hierarchical cluster analysis (HCA), principal component analysis (PCA), and orthogonal partial least squares discriminant analysis (OPLS-DA), were adopted to classify and perform a comprehensive visualization study of Cimicifugae Rhizoma. The unsupervised recognition models of HCA and PCA obtained a preliminary classification and provided a basis for classification. In addition, we constructed a supervised OPLS-DA model and established a prediction set to further validate the explanatory power of the model for the variables and unknown samples. Exploratory work research found that the samples were divided into two groups, and the differences were related to appearance traits. The correct classification of the prediction set also demonstrates a strong predictive ability of the models for new samples. Subsequently, six chemical makers were characterized by UPLC-Q-Orbitrap-MS/MS, and the content of four components was determined. The results of the content determination revealed the distribution of representative chemical markers caffeic acid, ferulic acid, isoferulic acid, and cimifugin in two classes of samples. This strategy can provide a reference for assessing the quality of Cimicifugae Rhizoma, which is significant for the clinical practice and quality control of Cimicifugae Rhizoma.

Maximum likelihood factor analysis for resolution of noisy smartphone based diffuse reflectance data from CdS pigments

This study aims to use multivariate chemometric methods such as principal component analysis (PCA), maximum likelihood common factor analysis (MLFA), and multivariate curve resolution alternating least squares (MCR-ALS) to analyze a designed data set and obtain an estimation of measurement error structure in the absence of replicates. For this purpose, we developed a smartphone-based diffuse reflectance spectrophotometer (smartDRS) with the advantage of being rapid, simple, and cost-effective in acquiring spectral information from the produced pigment samples based on a designed experiment. In our experimental design, the effects of different factors on the color of synthesized cadmium sulfide (CdS) pigment are investigated. DR spectral data from synthesized CdS samples were rapidly and successfully measured using the homemade device. The contribution of three forms (two crystalline and one amorphous) of CdS with three different spectra in each of the 16 synthesized pigment samples was illustrated and confirmed by using MLFA-MCR-ALS. Based on RGB values obtained from spectral information, the concentration profile of the brightest form of CdS was considered as a quantitative criterion of the whiteness of CdS samples and the response in the experimental design. The experimental design results showed pH, use of the furnace, and time for CdS drying as the main factors, in addition to a two-factor (Cd/S molar ratio × drying time) and a three-factor (pH × furnace × drying time) interactions are statistically significant on experimental design response. MLFA results also showed that independent noise in the measured diffuse reflectance data is heteroscedastic but not simply proportional to the signal intensities. This study shows the success of maximum likelihood-based multivariate analysis of diffuse reflectance spectral data from smartDRS for quantitatively investigating affecting factors on synthesized CdS color. Results from the application of PCA before MCR-ALS were considerably different from what was obtained from MLFA and MCR-ALS and were not in accordance with the previous reports.

A multi-evaluating strategy for raw and processed Veratrum nigrum L.: Fingerprinting combined with quantitative analysis based on multivariate chemometric methods

Veratrum nigrum L. (VN) is a well-known herbal medicine and rich in chemical components with multiple pharmacological activities including antihypertensive, anticancer, and antifungal effects. In the current experiment, the quality of VN from different habitats was evaluated based on combinative method of fingerprint, multi-component quantification and chemical pattern recognition. Fifteen batches of VN were collected, and intrinsic chemical composition were identified using ultra-performance liquid chromatography coupled with quadrupole time-of-flight mass spectrometry, which is a method for analyzing the similarity between samples, coupled with fingerprint of traditional Chinese medicine. The fingerprint similarity model show that 22 common peaks were selected covering 15 batches of and the similarity > 0.963. The total of 22 joint components were tentatively identified by comparison with standard substances or literature. A ultra-high performance liquid chromatography coupled with triple quadrupole mass spectrometry method for simultaneous determination of 8 compounds was established to evaluate the contents of raw and processed Veratrum nigrum L. Multivariate analysis was then applied to compare different batches of herbs based on ultra-high performance liquid chromatography coupled with triple quadrupole mass spectrometry data. All raw and processed samples were classified by partial least squares discriminant analysis based on the 8 analyzed compounds. The findings suggested that veratramine and polydatin with a variable importance for the project (VIP) > 1 were identified as significant constituents, the presence of which can be used to differentiate between raw and processed Veratrum nigrum L. samples. These results indicate that processing methods show important effects on the composition of Veratrum nigrum L..

Characterization and Classification of Spanish Honey by Non-Targeted LC–HRMS (Orbitrap) Fingerprinting and Multivariate Chemometric Methods

A non-targeted LC-HRMS fingerprinting methodology based on a C18 reversed-phase mode under universal gradient elution using an Orbitrap mass analyzer was developed to characterize and classify Spanish honey samples. A simple sample treatment consisting of honey dissolution with water and a 1:1 dilution with methanol was proposed. A total of 136 honey samples belonging to different blossom and honeydew honeys from different botanical varieties produced in different Spanish geographical regions were analyzed. The obtained LC-HRMS fingerprints were employed as sample chemical descriptors for honey pattern recognition by principal component analysis (PCA) and partial least squares-discriminant analysis (PLS-DA). The results demonstrated a superior honey classification and discrimination capability with respect to previous non-targeted HPLC-UV fingerprinting approaches, with them being able to discriminate and authenticate the honey samples according to their botanical origins. Overall, noteworthy cross-validation multiclass predictions were accomplished with sensitivity and specificity values higher than 96.2%, except for orange/lemon blossom (BL) and rosemary (RO) blossom-honeys. The proposed methodology was also able to classify and authenticate the climatic geographical production region of the analyzed honey samples, with cross-validation sensitivity and specificity values higher than 87.1% and classification errors below 10.5%.

Big (Bio)Chemical Data Mining Using Chemometric Methods: A Need for Chemists

AbstractThis Review summarizes how big (bio)chemical data (BBCD) can be analyzed with multivariate chemometric methods and highlights some of the important challenges faced by modern analytical researches. Here, the potential of chemometric methods to solve BBCD problems that are being encountered in chromatographic, spectroscopic and hyperspectral imaging measurements will be discussed, with an emphasis on their applications to omics sciences. In addition, insights and perspectives on how to address the analysis of BBCD are provided along with a discussion of the procedures necessary to obtain more reliable qualitative and quantitative results. In this Review, the importance of “big data” and of their relevance to (bio)chemistry are first discussed. Thereafter, analytical tools which can produce BBCD are presented as well as the theoretical background of chemometric methods and their limitations when they are applied to BBCD. Finally, the importance of chemometric methods for the analysis of BBCD in different chemical disciplines is highlighted with some examples. In this work, we have tried to cover many of the current applications of big data analysis in the (bio)chemistry field.

Big (Bio)Chemical Data Mining Using Chemometric Methods: A Need for Chemists.

This Review summarizes how big (bio)chemical data (BBCD) can be analyzed with multivariate chemometric methods and highlights some of the important challenges faced by modern analytical researches. Here, the potential of chemometric methods to solve BBCD problems that are being encountered in chromatographic, spectroscopic and hyperspectral imaging measurements will be discussed, with an emphasis on their applications to omics sciences. In addition, insights and perspectives on how to address the analysis of BBCD are provided along with a discussion of the procedures necessary to obtain more reliable qualitative and quantitative results. In this Review, the importance of "big data" and of their relevance to (bio)chemistry are first discussed. Thereafter, analytical tools which can produce BBCD are presented as well as the theoretical background of chemometric methods and their limitations when they are applied to BBCD. Finally, the importance of chemometric methods for the analysis of BBCD in different chemical disciplines is highlighted with some examples. In this work, we have tried to cover many of the current applications of big data analysis in the (bio)chemistry field.

Quality Evaluation of Crude and Salt-Processed Cuscutae Semen through Qualitative and Quantitative Analysis of Multiple Components Using HPLC Combined with Chemometrics

Cuscutae Semen (CS; Chinese common name “Tusizi”) is one of the most common traditional herbal medicines used to treat liver and kidney diseases in China. Although it is most commonly used as a processed product, little progress has been made on the quality control of CS and salt-processed Cuscutae Semen (PCS). The purpose of this study was to establish a comprehensive strategy integrating chromatographic analysis and chemometric methods for quality evaluation and discrimination of CS and PCS. An accurate and reliable HPLC method was established for the simultaneous quantification of 12 analyte compounds in CS and PCS. The results showed that this method exhibited desirable sensitivity, precision, stability, and repeatability. Multivariate chemometric methods were applied to analyze the obtained HPLC fingerprints, including hierarchical cluster analysis (HCA), principle component analysis (PCA), and partial least squares discriminant analysis (PLS-DA). The results indicated that CS and PCS samples showed a clear classification of the two groups, and three chemical markers with great contributions to the differentiation were screened out. Collectively, the chemometrics combined with the quantitative analysis based on HPLC fingerprint results indicated that salt processing may change the contents and types of components in Cuscutae Semen.

Simultaneous spectrophotometric determination of fluphenazine HCl and nortriptyline HCl in presence of their potential impurities perphenazine and dibenzosuberone in bulk and pharmaceutical formulation

Fluphenazine HCl (FLU) is an anxiolytic, while Nortriptyline HCl (NOR) is an anti-depressant. They are co-formulated together to treat depression and schizophrenia. Perphenazine (PER) and dibenzosuberone (DBZ) are the pharmacopeial impurities of FLU and NOR, respectively. Four spectrophotometric and multivariate chemometric methods were developed to determine the two drugs together or in presence of their two impurities in their bulk and pharmaceutical formulation. Method (A) is the triple divisor-ratio derivative (TDR) method, where the zero order spectrum of each component was divided by a mixture of the other 3 components, then the peak amplitudes of the first derivative spectra of FLU, NOR and DBZ were measured at 265, 245.4 and 283.2 nm, respectively. Method (B) is the double divisor-ratio difference-dual wavelength (DD-RD-DW) method, in which each component spectrum mixture was divided by a binary mixture of 2 of the interfering components. In the resulting ratio spectra, the amplitude difference is calculated between 2 wavelengths at which the third interfering component has zero difference. Methods (C and D) are the principle component analysis (PCA) and partial least squares (PLS) models. Methods (A and B) failed to quantify PER (FLU impurity), while (C and D) succeeded to quantify all components. The four methods have been applied for the prediction of the FLU and NOR in their pharmaceutical formulation with good accuracy and precision. The proposed methods have been validated according to the ICH guidelines and the results were within the acceptable limits.

Critical assessment of smart calculation-based spectroscopy versus chemometric-assisted methods: Application to combined antibiotic formulations

This work describes a comparative study of two multivariate chemometric and univariate spectrophotometric methods for the determination of a ternary drug mixture containing oxytetracycline HCl, bromhexine HCl, and lidocaine HCl. All methods show high sensitivity and similar linearity range. Meanwhile, the chemometric method has the advantage of higher accuracy, higher specificity and better regression parameters. The two spectrophotometric methods are constant multiplication coupled with spectrum subtraction and successive ratio subtraction coupled with spectrum subtraction while the chemometric method used partial least square and principal component regression models. In addition, a spiking technique was used to increase the concentration of bromhexine HCl in the dosage form, allowing its determination despite its low contribution. Methods were successfully applied in the dosage form Oxyclear® veterinary injection in pure powder as well as in its pharmaceutical formulation. Statistical comparison showed no significant difference between the developed methods and the reference method.

Multivariate chemometric methods and Vis-NIR spectrophotometry for monitoring plutonium-238 anion exchange column effluent in a radiochemical hot cell

The Plutonium-238 Supply Program at Oak Ridge National Laboratory has developed the capability to inform process decisions during full-scale 238Pu anion exchange column runs using multivariate chemometrics and visible-near infrared (Vis-NIR) absorption spectroscopy. Multivariate analytical methods provided a suitable option for real-time analysis of complex neptunium (Np) and plutonium (Pu) absorption spectra. Thousands of spectra from multiple production campaigns were analyzed by principal component analysis and Kennard-Stone sample selection to select a training set composed of 60 spectra. Multivariate curve resolution–alternating least squares analysis (MCR-ALS) identified spectral components and component concentrations. A partial least squares regression (PLSR) model was built using the spectra and concentration values determined by these virtually unsupervised methods. Next, a supervised PLSR model was built by scaling the MCR-ALS–selected concentration matrix using molar epsilon values. Both PLSR models predicted the concentrations of Np(IV), Np(V), Pu(III), Pu(IV), and Pu(VI) in the column effluent and identified nearly identical product cut decisions. The time-dependent Np and Pu concentration profiles provided valuable insight into column dynamics and the predictions agreed with traditional methods including alpha spectrometry and inductively coupled plasma mass spectrometry. These results establish a resourceful avenue for modeling multicomponent systems with convoluted absorption bands without significant user input. It is particularly advantageous for production-oriented radiochemical applications in restrictive hot cell environments.

Geographical origin identification and chemical markers screening of Chinese green tea using two-dimensional fingerprints technique coupled with multivariate chemometric methods

Identifying the geographical origins of green teas produced in specific regions is of significance since the geographical origin of tea influences its quality and price greatly. In this work, a novel two-dimensional (2D) fingerprints acquired by high-performance liquid chromatography-diode array detector (HPLC-DAD) was firstly proposed to identify geographical origins of Chinese green teas. A total number of 62 chemical components were extracted from 2D HPLC-DAD fingerprints of 78 tea samples by multivariate curve resolution-alternating least squares (MCR-ALS) algorithm. Afterward, principal component analysis (PCA) and orthogonal partial least squares-discriminant analysis (OPLS-DA) were used to classify tea samples based on the extracted components. Inspection of PCA score plots of two scaling types (UV and Par) showed that tea samples from two different geographical origins have an obvious clustering tendency. As for the OPLS-DA analysis, the Q 2 cum of two types-scaling OPLS-DA models are greater than 0.75, and the total recognition rates for test set are 92.86%. What's more, according to p value of t -test, VIP values, V-plot and S-plot, 17 characteristic components were screened and identified as chemical markers to distinguish between Zhejiang teas and Shandong teas. This work indicated that the proposed strategy is suitable for identifying geographical origins of Chinese green teas. • 2D HPLC-DAD fingerprints was proposed to identify geographical origins of tea. • 62 chemical components were extracted from 2D HPLC-DAD fingerprints by MCR-ALS. • PCA and OPLS-DA were used to classify tea samples using the extracted components. • 17 characteristic components were screened and identified as chemical markers. • There are correlations between chemical components and geographical origins of tea.

Extraction and determination of phenolic compounds in Chinese teas using a novel compound salt aqueous two-phase system coupled with multivariate chemometric methods

The phenolic compounds are the primary ingredients contributing to the color, fragrance, and health care functions of tea. The present study sought to extract the phenolic compounds from Chinese tea samples using a novel compound salt aqueous two phase system (ATPS) with iso-propanol and two inorganic salts (sodium citrate and ammonium sulfate). The results showed that the analytes were mainly distributed in the alcohol-rich top phase within the recovery range of 82.54–110.73%. Additionally, the alternating trilinear decomposition (ATLD) algorithm combined with HPLC-DAD was employed for the simultaneous rapid quantitative analysis of six phenolic compounds in four Chinese tea samples within 7.0 min. Based on the quantitative data obtained by the proposed ATPS-ATLD method, the principal component analysis (PCA) and hierarchical cluster analysis (HCA) methods were adopted to classify and analyze the four types of Chinese teas. Overall, the proposed ATPS-ATLD method could be a potential approach for distinguishing the types of Chinese teas.

Parametric study of spot size and multi-elemental quantification of geomaterials under complex matrix conditions using fiber-optic laser-induced breakdown spectroscopy

Laser-induced breakdown spectroscopy (LIBS) has provided an optional access method to analyze multiple components of geomaterials with the advantages of rapid detection and minimal damage and preprocessing of samples compared with other conventional analytical methods. A fiber-optic LIBS (FO-LIBS) system with a compact laser probe was established to analyze ten different sediment samples, with Al, Fe, Ca, Mg, Ti, Mn, V, and Cr successfully detected. The spectra from the different samples are quite different due to matrix effects, and the spot size has a great influence on both plasma evolution and emission spectra for the same sample. The laser irradiance decreased from 1.382 to 0.855 GW/cm2 with increasing the spot diameter from 480 to 610 μm as the spectral fluctuation was gradually aggravated. Internal standardization (IS) was utilized to decline the spectral fluctuations caused by the spot size and matrix effects for the quantification of multiple elements. By adopting the most suitable combinations of emission lines, the fluctuation of emission lines caused by the spot size was also limited with a relative standard deviation lower than 30%. The R2 of all the calibration curves was higher than 0.9 with the major element Si out of the detection range and spectra mixed at different spot sizes, which outperformed normalization by the whole spectrum. Two multi-variate chemometric methods, including partial least squares regression and support vector regression, were also applied to establish quantitative models for the sediments. It was found that three methods provided similar prediction results, while IS could establish a more robust calibration model that was less sensitive to spot size. This study also demonstrated that FO-LIBS has the potential to quantitatively analyze the chemical compositions of geomaterials combined with IS and machine learning.