Chemometrics in forensic science

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Trends in Analytical Chemistry 105 (2018) 191e201

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Chemometrics in forensic science Raj Kumar, Vishal Sharma* Institute of Forensic Science and Criminology, Panjab University, Chandigarh, 160 014, India

a r t i c l e i n f o

a b s t r a c t

Article history: Available online 23 May 2018

This review represents a detailed discussion of the multivariate methods used in the examination of forensic exhibits; their advantages, disadvantages, and efficiency are compared. The last decade has seen the application of the chemometric methods combined with analytical techniques for characterization and discrimination of samples, which leads to the informative and representative examinations of the samples. Many research articles with reference to the use of chemometrics in forensic science have been published. This review has been divided into various sections which include chemometrics, its history, multivariate methods, and the application of chemometrics in various disciplines of forensic science. It is suggested that these new techniques and mathematical/statistical methods should be utilized in forensic science casework to get statistical confidence in the results. © 2018 Published by Elsevier B.V.

Keywords: Chemometrics Forensic science Analytical techniques Discrimination Characterization

1. Introduction Forensic science is a discipline in which the examination of complex evidence finds its most critical applications. It is important to identify the samples correctly and then classify them according to their class characteristics because the correct identification and classification of each forensic exhibit lead to unbiased verdict in the legal cases [1]. In this remark, now a day, the scientists have increased their interest in the analytical methods such as chromatographic and spectroscopic techniques for the analysis of complex mixtures such as inks, drugs, paints, glass, etc.

Abbreviations: AAS, Atomic Absorption Spectrometry; AFM, Atomic Force Microscopy; ANN, Artificial Neural Networks; ATR-FTIR, Attenuated Total Reflectance Fourier Transform Infrared; BLR, Binary Logistic Regression; CA, Cluster Analysis; CART, Classification and Regression Trees; CNN, Convolutional Neural Network; FID, Flame Ionization Detector; GA, Genetic Algorithm; GC-MS, Gas Chromatography Mass Spectrometry; HCA, Hierarchical Cluster Analysis; HPLC, High Pressure Liquid Chromatography; HSI, Hyperspectral Imaging; ICA, Independent Component Analysis; ICP-MS, Inductively Coupled Plasma Mass Spectrometry; kNN, k-Nearest Neighbor; LA-ICP-MS, Laser Ablation Inductively Coupled Plasma Mass Spectrometry; LDA, Linear Discriminant Analysis; LIBS, Laser-Induced Breakdown Spectroscopy; LR, Likelihood Ratio; MLR, Multiple Linear Regression Analysis; NAS, National Academy of Sciences; NIR, Near Infrared; PCA, Principal Component Analysis; PLSDA, Partial Least Squares-Discriminant Analysis; RDA, Regularized Discriminant Analysis; SERS, Surface-Enhanced Raman Spectroscopy; SIMCA, Soft Independent Modeling of Class Analogy; SPA, Successive Projection Algorithm; SW, Stepwise Formulation; ToF-SIMS, Time-of-Flight Secondary Ion Mass Spectrometry. * Corresponding author. E-mail address: [email protected] (V. Sharma). https://doi.org/10.1016/j.trac.2018.05.010 0165-9936/© 2018 Published by Elsevier B.V.

The analytical method produces masses of dataset even for a single sample. For a large number of samples, the amount of output data will increase tremendously and it makes the task of expert much tedious, time-consuming and also, the manual examination can provide false positive results. Therefore, the advanced chemometric methods are emerged to analyze the large and complex dataset. Moreover, chemometric methods provide accurate and significant results in the quick time domain. There are many chemometric methods and each method should be used according to the type of study: characterization, discrimination, model development, etc. The former tools and techniques might not be appropriate for today's work and will not solve future's challenges. Here, the conventional methods refer to oblique UVeVisible light scanning, compound microscopy, color/fluorescence test, a test based on physical parameters etc. Most of the conventional methods are destructive in nature, less reliable and non-significant whereas, in case of forensic science, advanced, nondestructive and reliable methods should be preferred. Therefore, the forensic science laboratories must be equipped with advanced techniques and methodology to face the forthcoming challenges significantly. In many forensic cases, only analytical methods are not sufficient to reach a conclusion because the obtained data are very vast and complex. Therefore, the researchers have been adopted chemometric methods to get desirable and significant results. The chemometric methods give better resolution or separation quality of the samples which define its incorporation with analytical (spectroscopic/ chromatographic) techniques in recent times [2]. The science of

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chemometrics initiates from the chemistry. Many books covering the topics of chemometrics have been published in the last two decade [3,4]. However, till date, a little information on the applicability of these techniques to the real casework is available. Moreover, these methods are not in practice in the forensic laboratories. The aim of this review is to discuss the various chemometric tools for the regular analysis and its applicability after fulfilling the pre-requisite criteria. As we know, there is a wide gap between forensic analysts and chemometricians, therefore this study will help the forensic expert to provide a detailed description of each chemometric methods along with their utility in forensic science. 2. Chemometrics and associated history

neural networks (ANN); 2nd based on modeling the individual classes, i.e., soft independent modeling class analog (SIMCA) [7]. 3.1.1. Linear discriminant analysis (LDA) LDA is a technique that builds a mathematical function to maximize the separation between known classes of samples. It condenses the dimensions of the complex dataset by reducing a huge number of original variables to few new composite dimensions (called as canonical functions), without or with a minimum loss of information from original [8]. LDA explains maximum dissimilarities among pre-defined groups of the sample and the developed model predicts the group membership of unknown samples. Wilks' l statistic is helpful for the calculation of the discrimination power of the model and is defined as;

The exact meaning of Chemometrics is: e the utilization of mathematical and statistical operations in the field of Sciences (Chemistry) where the outcomes of the analytical methods are very complex. It extracts the maximum valuable information from the dataset by using the best measurement techniques/ optimal procedures and acquires most of the chemical information from the sample data. It correlates quality parameters or physical properties of the data. The term chemometrics was 1st used by scientists Swede, Bruce R. Kowalski and Svante Wold in 1972 [2]. In 1974, the establishment of International Chemometrics Society leads to the 1st explanation of the chemometrics. In the year 1980s, some international journals started special issues regarding the papers on chemometrics. After that, in 1986e87, two publishers, i.e. Wiley and Elsevier, started new chemometrics journals “the Journal of Chemometrics” and “Chemometrics and Intelligent Laboratory Systems” respectively [5]. The analytical methods generate a large amount of dataset posing difficulties in objective interpretation. This issue can potentially be overcome through the use of multivariate statistical methods. Normally, a chemist is less familiar with such statistical methods. So, to make the complicated statistical methods practicable for the chemist, the chemometrics is used. For the moment, many statistical and numerical software, i.e. SPSS, R, MATLAB, Minitab, Excel Stat, etc. are available commercially that simplifies this process. 3. Multivariate data analysis The spectra/chromatogram obtained through analytical methods vary for different kinds of samples and the chemometric methods extract different information to individualize and classify the particular class of samples, this is called as ‘chemical pattern recognition.’ These pattern recognition methods are further divided into two types i.e. supervised and unsupervised pattern recognition. 3.1. Supervised pattern recognitions Supervised pattern recognition methods have been currently used for a wide variety of analytical data, with different applications like individualization, classification, discrimination, fingerprinting of samples, and detection of impurities, etc. In these methods, a model is constructed on the basis of samples from the known class. This model is further used to predict the class of unknown samples [6]. There are two types of approaches for using supervised pattern recognition: 1st based on discrimination among the classes, i.e., partial least squares discriminant analysis (PLS-DA), linear discriminant analysis (LDA), k-nearest neighbor (kNN) and artificial



detðWÞ detðTÞ

where, det (W) ¼ determinant of with-in group variancecovariance matrix; det (T) ¼ determinant of the total varianceecovariance matrix. For the significant model, the value of Wilks' l must be smaller. In spite of this method, post hoc classification of the training dataset can also be used as a method to check the effectiveness of the discriminant model. The main drawback of LDA is that the matrix inversion is required by the software for the calculation of the matrix. So, this technique is practicable only when the numbers of variables are smaller than the number of samples. This reduction in data can be achieved by using principal component analysis (PCA) [2,5]. 3.1.2. Partial least squares discriminant analysis (PLS-DA) The problem of the smaller number of variables can be overcome by using PLS-DA. This method is based on partial least squares. It utilizes the independent variables of a matrix ‘X’ and categorical variables ‘Y’ of the pre-defined sample to develop a training model, and the group membership of unknown sample can be predictive by using the value of the partial least squares of unknown samples. In PLS-DA, a replica of the matrix is formed with ones and zeros. This matrix contained columns equal to the classes present and an observation had the value 1 for the class it belongs to and 0 for the rest. The original X matrix comprises the preprocessed dataset. The matrices X and Y are disintegrated into the product new two matrices that contained scores and loadings respectively. This method is different from PCA as PCA uses only the information of matrix X. However, the PLS method also takes into the account of matrix Y. Therefore, the loadings values of X block are calculated from the scores of the Y block and vice-versa [6,9]. 3.1.3. k-nearest neighbor (kNN) kNN is a non-parametric method which is mainly based on the calculation of the distance between the unknown object to the training objects. Generally, the method calculates the Euclidean distance but one can also use correlation-based measures if the variables are highly correlated with each other. On this basis, the unknown sample allocated to the groups that belong to closest of known group/training group on the basis of majority rule. The k shortest distance between known and unknown samples set is then calculated, with a small odd number value of k, the unknown is assigned to the class by kNN methods. The method has some advantages over the other supervised pattern recognition such as easy to conduct because of simple mathematical equations, no requirement of normalization, etc.

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However, kNN has the similar disadvantage that of LDA and it does not give good results when the distances among the samples are large. It doesn't provide a graphical representation of outcome and hence, has extremely slow computation.

space, without correcting the minor errors [12,13]. Other supervised techniques such as UNEQ and classification and regression trees (CART) also exist but there is no literature available for their application in the field of forensic science.

3.1.4. Soft independent modeling of class analogy (SIMCA) SIMCA is mainly based on the principal component analysis (PCA). Initially, PCA is utilized to get principal components (PCs) from sample classification, and later on, the best model developed from all kinds of samples is used to the prediction of unknown sample's class. Only those optimal PCs are retained for modeling which explains maximum amount of variation present in the sample dataset [6]. The model provides the best result when the difference between the classes is much larger than within-class differences. It also provides results in a graphical manner and hence, the computation is very fast. The plots of loading and scores value obtained after PCA analysis gives information about the outliers and grouping of samples. Moreover, there is the plot for interpretation of SIMCA results which is called as Coomans plot. This plot shows the differences between the two classes graphically. The main disadvantage of SIMCA is that it gives poor results when the differences between the classes are small.

3.2. Unsupervised pattern recognition

3.1.5. Artificial neural networks (ANN) An Artificial neural network (ANN) is a parallel computing device, which is basically an attempt to make a computer model of the brain. The main objective is to develop a system to perform various computational tasks faster than the traditional systems [10]. These tasks include pattern recognition and classification, approximation, optimization, and data clustering. ANN acquires a large collection of units that are interconnected in some pattern to allow communication between the units. These units also referred to as nodes or neurons, are simple processors which operate in parallel [11]. Each neuron has an internal state, which is called an activation signal. Output signals, which are produced by combining the input signals and activation rule, may be sent to other units. A great advantage of ANNs is that causal knowledge of the relationship between the input and the output variables is not required. Instead, they learn these relationships through successive training. Moreover, ANNs present remarkable and attractive information processing characteristics: (i) non-linearity, allowing better fit to the data; (ii) noise insensitivity, providing accurate prediction in the presence of uncertain data and measurement errors; (iii) high parallelism, which implies fast processing and hardware failure tolerance; and (iv) generalization, enabling application of the model to unlearned data [8]. 3.1.6. Support vector machine (SVM) Support vector machine is a statistical method which requires learning theory of statistics [12]. This method is applicable for the classification and regression related problems. For classification, it creates a boundary between the two classes which is independent of the distributions of sample vectors in the dataset. When the classes are linearly separated, it develops optimal boundaries which exactly distinguish both the classes and also classify the unknown samples to representative class. The ‘optimal’ boundary is defined as the most distant hyperplane from both sets, i.e. the ‘middle point’ between these sets. The sample vectors which are closest to the boundary are called support vectors. However, in case of non-linear separation, the boundary is developed by using the kernel method. In this method, a transformation of the original vector towards the higher dimensional space takes place, leading to linear separation of the classes. In regression method, SVM functions as a linear regression in this

The main unsupervised pattern recognition method is principal component analysis (PCA). It is the 1st step of data analysis in order to detect the patterns in the dataset. PCA primarily reduces the dimension of the dataset without losing any information from original data. The newly generated few principal components explain most of the information from the dataset. In addition to PCA analysis, cluster analysis such as K-mean and hierarchical cluster analysis (HCA) is also used as unsupervised pattern recognition method for classification purposes. 3.2.1. Principal component analysis (PCA) The main purpose of PCA is to retain most of the variation that is present in the given data set by reducing the dimensions of a large number of interconnected variables to few Principal Components (PCs). From these Principal Components, first few PCs, which are uncorrelated with each other, explain the most of variation present in the dataset. Among all PCs, those PCs are selected whose eigenvalue is greater than unity [14]. Thus, the interpretation of principal components is easy, but, this simple looking technique has vast applications in many disciplines along with a number of different derivations. The linear coefficients of the inverse relation of linear combinations are called the component loadings. The values that represent the samples in the space defined by the principal components are the component scores. The scores can be used as input to other multivariate techniques, instead of the original measured variables [15]. Before analyzing the data by PCA method, there are some assumptions that should be followed to get valid, significant and accurate results. However, there is often a solution to overcome this problem if your data violated (not met) certain assumptions. The assumptions are as follow; a) There should be multiple variables in dataset measured at continuous (i.e. ratio or interval) level. Although, ordinal variables can also be used. b) The selected variables should be in a linear relationship because this method is based on Pearson correlation coefficients and hence needs to be in a linear relationship. c) The sample size should be adequate. The sample size should be large enough to provide a reliable result. There are two methods which detect sampling adequacy (1): the KaisereMeyereOlkin (KMO) and [2] Bartlett's test of Sphericity. d) The data should be suitable for data reduction. For this, adequate correlations between the variables should be there in order for variables to be reduced to the smaller number of principal components (PCs). e) The data should be free from any significant outliers.

3.2.2. Cluster analysis It is an exploratory technique used for grouping of samples according to the types of similarity measures used. The samples having similar signatures of spectra are most likely to get arranged by themselves in the cluster. The number of clusters (fixed) which is a priority of this technique, is decided by hierarchical cluster analysis (HCA). For HCA, Ward's method is used as clustering algorithm and Euclidean distance is used as the similarity measure to explain the scheme of clustering. The best results are obtained with

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the PCA loading (10 PCs) as an input variable for HCA. The fixed number of clusters is entered to Kemean clustering, which distributes the samples to different clusters according to the method employed. This method is used as a combined tool to PCA and for pairwise comparison of the samples. Further information about exploratory data analysis (EDA) techniques (e.g., the algorithm of PCA, the definition for the distance measures and clustering algorithms) can be found in standard chemometric articles and textbooks [2,16]. 4. Application of chemometric methods in the examination of forensic exhibits Forensic science is a combination of all the branches of natural science and allied disciplines, the knowledge of which is essential and efficient in the dispensation of justice in civil, criminal, and social contexts. The National Academy of Sciences (NAS, USA) [17] in their report on the current status of forensic science, have stressed upon the problems being faced by the experts and have also suggested the necessary remedies to overcome these problems. It is emphasized that in order to achieve better results from the analysis, the analytical techniques should be computable and correlated with statistical confidence, with the purpose of minimizing the errors. Fig. 1 shows different areas of forensic science that utilizes the principles of chemometrics. In forensic science, the main aim of research is to characterize/ identify a suspected sample or to discriminate/classify a disputed sample to/with its respective groups or to detects the adulteration/ counterfeiting for quality assurance purposes or some other miscellaneous applications such as nuclear forensics, soil quality assessment, estimation of age/sex, fingerprint enhancement, etc. For the accomplishment of these aims, various analytical methods i.e. spectroscopy, chromatography, thermal methods, X-Ray based methods and microscopic methods are utilized and for the significant result, chemometric methods are employed. The detailed investigation procedure is represented in Fig. 2 in the form of a flow diagram. Quantitative techniques coupled with statistical software are used to view the similarity or dissimilarity between the sample under investigation and standard material used for comparative analysis. In the field of forensic science, the statistical interpretation

Forensic Physical Sciences

Forensic Biological Sciences

Forensic Seience & Chemometrics

Forensic Questioned Document

5. Discussions and prospect A survey of literature on the use of multivariate analysis in forensic science from 2007 to 2018 is performed using the ISI web of knowledge. Most of the articles found which are related to forensic science and chemometrics. The range of forensic examination by chemometrics methods is certainly wide, including pharmaceutical tablets, medicines, drugs, cigarette and tobacco, wine, soft drinks, paint, textile fibers, gunshot residues, soil, hair dye, bloodstain, semen, bones, saliva, currency note, ballpoint pen ink, cultural heritage, toners, etc. Tables 1e4 summarizes the information about sample type, publication year, the aim of the research and chemometric method utilized in the forensic science disciplines. 5.1. Forensic chemical science

Forensic Chemical Sciences

Forensic Anthropology

of multidimensional data is generally executed on either raw data or log-transformed data. However, the data obtained from a spectroscopic or chromatographic technique are very complex in nature. Therefore, these data are first normalized to either mean 0 or 100 by using various normalization methods. The correct pretreatment of raw data is an essential part of the valuable and effective analysis. The understanding of basic statistics/mathematics is a prerequisite for using such techniques, otherwise nonesignificant and misleading results might be obtained. The use of chemometrics in forensic science is dynamically increasing from last two decades. Scientists around the world have published various research and review on chemometrics, but none of them has compiled comprehensive information covering up all the aspects of multivariate analysis in the forensic science discipline. Therefore, the current review amalgamates the different aspects of multivariate modeling for the investigation of exhibits related to forensic discipline. It also covers usefulness of mathematical information of multivariate models along with their utilization in forensic chemical, physical, biological sciences and questioned document examination. Some review articles on some specific areas of forensic science have been published; application of serology and gunshot residue analysis [18], crossing ink lines [19], Application of SurfaceEnhanced Raman Spectroscopy (SERS) [20], atomic force microscopy (AFM) [21], infrared (IR) spectroscopy and IR imaging [22], wildlife forensic [23], analysis of questioned documents [24], bite mark identification [25] etc. However, no review is available on recent developments and trends of multivariate analysis in forensic science.

Forensic Toxicology

Forensic Ballistic

Fig. 1. Different areas of forensic science which are currently using the principle of natural science along with the utilization of chemometric methods.

The forensic chemical sciences deal with the exhibits such as medicine, soft drinks, wine adulteration, etc. and their identification. The spectroscopic methods i.e. Raman Spectroscopy [26e28,32], Fourier Transform infrared spectroscopy (FTIR) [29,32] and fluorescence spectroscopy [31], UVeVisible spectroscopy [30], are favored in most of the studies because these methods are nondestructive. Some of the researchers utilize GCeMS [33] and UHPLC-MS [34] techniques. The output data are analyzed by different multivariate methods to get effective, fast, reliable and bias results. Some good examples are given as follow; 5.1.1. Y. Roggo et al. Y. Roggo et al. [26] utilize Raman spectroscopy coupled with multivariate analysis for the quality control and detection of counterfeits of pharmaceutical tablets. Experimental Procedure: The authors have analyzed 25 different pharmaceutical tablets by using PhAT probe that generates a 6 mm diameter spot which covers the main part of

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Fig. 2. Flow chart of investigation procedures involved for the examination of forensic exhibits.

tablets. The scanning is performed in 150e1890 cm1 region with 785 nm laser excitation source. SNV and SavitzkyeGolay methods are used for data pretreatment. SVM method is used for identification and classification of the tablets. Findings: The main purpose of the research is to find out the concentration of API (Active pharmaceutical ingredients) in the

tablet. For that, a linear relationship of the area under the curve and API concentration is observed. The limit of detection obtained is 0.59% API. Secondly, with the help of SVM model, all 25 pharmaceuticals tablets are correctly identified and classified without any error. The developed model has passed the correlation and API peak test.

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Table 1 Multivariate analysis of forensic exhibits encountered in forensic chemical science. Samples types

Publication year

Aims of the research

Analytical techniques

Applied statistical methods if any

Refs.

Pharmaceutical tablets Medicine

2010 2011

Identification of Pharmaceutical tablets Counterfeits Detection of Medicine

Raman Spectroscopy Raman Spectroscopy

[26] [27]

Viagra counterfeiting Fireworks Cigarette tobacco Wine

2011 2016 2011 2016

Counterfeit Viagra Detection Post-blast residues analysis Discrimination of Cigarette Tobacco Discrimination of Wine

Raman microspectrometry imaging FTIR UVeVis Spectrophotometry Fluorescence Spectroscopy

Soft drinks Oil contaminated soils Ethanol biomarkers

2015 2013 2017

Contamination of Soft Drinks Removal of Oil contamination from Soils For identification of chronic alcohol abusers

FTIR and Raman spectroscopy GC-MS UHPLC-MS/MS

SVM SVM, PCA, and Correlation Analysis PCA, LDA, k-NN, SIMCA PCA PCA and DA Independent Component Analysis Carbon Dots methods CHEMSIC method PCA and LDA

[28] [29] [30] [31] [32] [33] [34]

Table 2 Multivariate analysis of forensic exhibits encountered in forensic physical science. Samples types

Publication year

Aims of research

Analytical techniques

Applied statistical methods

Refs.

Paint Textile fibers Lipstick Cigarette

2017 2017 2017 2009

FTIR ATR-FTIR ATR-FTIR NIR spectroscopy

ANOVA-PCA, AComDim method PCA PCA, CA LDA, SIMCA

[35] [36] [37] [38]

Nuclear forensic

2017

[39]

2015

ANN, HCA, SIMCA, PLS-DA, PCA

[40]

Glass Soil

2017 2017

Differentiation of Glass samples Find the Soil Trace Origin

Likelihood Ratio PCA Analysis

[41] [42]

GSR

2012

Differentiation of Ammunitions

LIBS and laser Raman spectromicroscopy (LRS) Energy dispersive X-ray fluorescence and scattering spectroscopy LA-ICP-MS XRD, TGA and Hyper-spectral color reflectance (HSI) AAS and ICP-AES

ANN, PCA

Soil

Gamma radiations effects on iodine/epoxy paint Identification and classification of textile fibers Differentiation of red lipsticks Classification of cigarette by successive projection algorithm Rapid Nuclear Forensics Analysis via Laser-Based Microphotonic Techniques Challenges in Soil quality assessment

Regularized discriminant analysis

[43]

Table 3 Multivariate analysis of forensic exhibits encountered in forensic biological science. Samples types

Publication year

Aims of research

Analytical techniques

Applied statistical methods

Refs.

Hair dye Blood stain Semen, Vaginal fluid, and Urine Semen Body fluids Brain cancer Human bone

2017 2017 2017

Dyed hairs were differentiated by using ATR-FTIR Identification and Classification of Bloodstain Revealing the location of semen, vaginal fluid, and urine

ATR-FTIR NIR Spectroscopy NIR-HSI

PLSDA SIMCA, PLS-DA, LDA-GA PCA

[44] [45] [46]

2017 2016 2018 2015

Non-destructive screening of Semen samples Identification and differentiation of body fluids Discrimination of human brain tumors from normal structures Supervised chemometric methods for sample classification

2017 2017

Discrimination of patients with lung cancer and controls Determine the distribution map of protein contents (PC), carbohydrate contents (CC) and sialic acid Contents (SAC) on Edible bird's nest

PCA PLS-DA PLS-DA LDA, CART, SIMCA, PLS-DA, BLR, NN SVM, PCA-LDA, PLS-DA Genetic algorithm PLS (GA-PLS)

[47] [48] [49] [50]

Urine Edible Bird's nest

ATR-FTIR Raman Spectroscopy Raman Spectroscopy and AFM Laser-Induced Breakdown Spectroscopy Mass spectrometry Hyper-spectral Imaging

5.1.2. P.Y. Sacr e et al. The authors have investigated the Viagra® counterfeiting by using chemometrics and Raman microspectroscopic imaging [28]. Experimental Procedure: A total of 26 counterfeit and imitation tablets of Viagra® and 08 reference tablets are used in this study. Each sample is smoothly cut into two parts to avoid spectral difference caused by the distance between sample and probe. The laser wavelength of 785 nm is used throughout the experiments. The data pretreatment is done by MATLAB and SIMCA modeling is performed by using the PLS_toolbox. PCA is used for reducing the multidimensional dataset into two dimensional. Findings: The spectra of genuine and counterfeit Viagra® show no visible differences in the peak position. However, the intensity of counterfeit Viagra® is high in comparison to genuine

[51] [52]

sample. Further, PCA is able to differentiate between counterfeit and genuine Viagra® on the basis of PC3 because the counterfeit colored tablets have more intensity. It also confirms the presence of lactose in the spectral region 830e880 cm1 belongs to illegal Viagra. The kNN and SIMCA models provide 100% correct classification of genuine and counterfeit Viagra when analyzed the complete spectral range of 200e1800 cm1 whereas LDA model gives 95.5% of cross-validation results. 5.1.3. R. Saad et al. R. Saad et al. [31] explain the importance of fluorescence spectroscopy in the discrimination of wine samples by using independent component analysis (ICA) methods. Experimental Procedure: In this study, 09 wines belonging to three different grape varieties (Shiraz, Cabernet Sauvignon and

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Table 4 Multivariate analysis of forensic exhibits encountered in forensic questioned document analysis. Samples types

Publication year

Aims of research

Analytical techniques

Applied statistical methods

Refs.

Currency notes

2013

Raman Spectroscopy

PCA, PLS-DA

[53]

Black ballpoint Inks

2008

UVeVis spectroscopy

PCA

[54]

Cultural heritage

2017

Discrimination between authentic and counterfeit banknotes Classification and individualization of black ballpoint pen inks Non-invasive characterization of colorants

PCA-DA

[55]

Blue ballpoint pen inks

2017 2017

K-mean Cluster, PCA PCA

[56]

Paper

diffuse reflectance infrared Fourier transform (DRIFT) spectroscopy Diffuse reflectance UVeViseNIR spectroscopy FTIR

Toners

2017

Near Infrared Spectroscopy

PCA

[58]

Dating of writing inks

2017

UVeVis Spectroscopy

PCA, Multiple Regression Analysis

[59]

Fraudulent documents

2017 2017

PCA and Projection Pursuit (PP) PCA

[60]

Writing/printing papa

Near and middle infrared hyperspectral imaging TGA

Non-destructive examination of blue ballpoint pen inks in forensic application Characterization and discrimination of writing/photocopier paper types Identify the chemical composition of black toners in questioned documents. Developed two Models, i.e. curve estimation model and MLR model for the dating of blue ballpoint pen ink Hyperspectral infrared images techniques for fraud detection Characterization and Discrimination of paper samples

[57]

[61]

Pinot Noir) and from 09 different producers are analyzed over a wide range of pH. The opaque nature of sample leads the examination by front face fluorescence spectroscopy because this technique examines only the surface of the sample. The spectra are acquired with two excitation wavelengths i.e. 269e490 nm and 250e490 nm and two emission wavelengths i.e. 286e540 nm and 286e520 nm. The obtained data are analyzed by ICA method in MATLAB software. Findings: The fluorescence intensity increases with increase in the pH because increasing pH leads to the change in the structure of molecules. The discrimination of 45 wine samples altogether is achieved by ICA method of 1st 7 ICs. Amongst all plots, a scatter plot of IC7 against IC5 provides clear differentiation of wine samples. The fluorescence signals varied according to the pH of wine samples resulting in better discrimination of wine samples by ICA method.

Experimental Procedure: 38 red lipsticks from 20 different manufacturers are used to determine the differentiation. All spectra are collected from 650 to 4000 cm1 region. The cleaning of the crystal is done by 50% isopropanol followed by the method to avoid any contamination. PCA, cluster analysis, and correlation method are used to get significant/desirable results. Findings: The presence of various oils and waxes are observed in all the lipstick samples below 1800 cm1 spectral range. With the help of PCA and CA analysis, 9 groups are created: G1eG5 and G6 aed. The PCA and CA provide a preliminary classification of red lipstick as they give 0.29% and 0.51% discriminating power respectively and correlation coefficient provides 0.93% discriminating power and hence, the best discrimination of lipstick samples.

The fundamental ideas of these studies that are still present in the nowadays researches are: (1) Comparison of different algorithms shows that they could all be applied to model similar type of dataset. The k-NN and SIMCA give best results in comparison to LDA. However, it should be kept in mind that these algorithms are case sensitive and can change in function of the data (2) these methods should be followed in the routine workflow of forensic science laboratory (3) the pretreatment of data is an essential step of multivariate analysis, otherwise false positive results can be obtained.

5.2.2. R.S. Corr^ ea et al. ^a et al. [42] proposed that soils can be differentiated R.S. Corre via analyzing their clay fraction alone and also, the same soil type can be varied according to the distance they are collected from each other by using hyperspectral color reflectance and XRD techniques.

5.2. Forensic physical sciences The forensic physical science cases involve paints [35], fibers [36], lipsticks [37], cigarettes [38], nuclear forensic [39], soils [40,42], glass [41], GSR [43], etc. for the examination of trace and unknown samples with the help of analytical methods combined with chemometrics. After the detailed analytical examination, the forensic expert decides, whether the two items/exhibits are same or not. Experimental procedure and findings of some of the studies are as follow. 5.2.1. M. Gładysz et al. M. Gładysz et al. [37] uses ATR-FTIR spectroscopy combined with chemometrics for the identification and differentiation of different types of lipstick brands.

Experimental Procedure: 16 each collected soil samples of Oxisol and Inceptisol respectively are air dried and homogenized before the analysis. The organic digestion is done with the help of 30% H2O2. The slit and clay fraction are separated by partial sedimentation process. The clay fraction is examined by HSI and XRD methods. The obtained data are submitted for PCA analysis in the origin software. Findings: XRD analysis significantly differentiated the soil clay samples. On the basis of clay components, this technique is able to discriminate Oxisol soil samples over a range of 1 km. The color analysis is the most accurate method to group the Inceptisol samples. This methodology is more effective for discrimination of Inceptisol samples than Oxisol samples. PCA is able to discriminate 97% between Inceptisol and Oxisol samples when clay þ XRD and HSI þ clay þ XRD respectively are subjected to the analysis. Only XRD and HSI þ XRD in combination with PCA provide 100% discrimination.

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~ ez et al. 5.2.3. J. Yan ~ ez et al. [43] proposed the conventional as well as a cheJ. Yan mometric method for the differentiation of gunshot residues (GSR) on the basis of metallic components present in ammunition brands.

5.3.2. C.K. Muro et al. C.K. Muro et al. [48] use Raman spectroscopy in combination with different classification models for the identification and differentiation of various body fluids.

Experimental Procedure: 66 samples from two different manufactures i.e. FAMAE and CBC are taken from individuals' hands with a cotton swab moistened with 2% EDTA immediately after shooting with the firearm. 10% HNO3 is used for dissolution of metallic residues. GF-AAS and ICP-OES are used for the detection of metallic components. PCA and Regularized discriminant analysis are used as the multivariate methods. Findings: The higher concentrations of Al, Ba, Ca, Cd, Co, Cu, Fe, K, Hg, Mg, Mo, Pb, Sn and Zn metallic elements in the CBC brand in comparison to FAMAE brands of gunshot residue is determined by AAS and ICP-OES. By the conventional method, two brands are differentiated without quantitative certainty. With the help of regularized discriminant analysis, 100% discrimination and classification of ammunition brands are observed with quantitative certainty.

Experimental Procedure: A total of 75 samples including peripheral blood, semen, saliva, sweat and vaginal fluid are purchased. The samples are air dried on microscopic slides. The laser of 785 nm is used for spectra collections. The spectral data are pre-processed in MATLAB software before used for model development. PLS_toolbox is used for SVM-DA and PLS-DA modeling analysis and processing. Findings: All the blood and related products are accurately characterized by Raman spectroscopy. Further, the combined classification modeling with different variable selection procedures is evaluated and it is found that the chemometric SVMDA model with GA algorithm variable selection provides 99.9% correct classification internally. Moreover, the external crossvalidation provides 100% correct classification of body fluid samples. The PLS-DA model and SVM-DA model without any variable selection algorithm provide internal validation errors of 2.3% and 0.9% and external validation errors of 2.1% and 0.5% respectively.

The PCA analysis is a most utilized method in recent time as it reduces the data matrix into few PCs. Some considerations are; (1) One should follow all the prerequisites prior to the analysis (2) cross-validation of obtained results should be done (3) it is better to apply PCA before any model development to estimate the linear relationship among the dataset (4) the advance form of discriminant analysis may provide better results.

5.3. Forensic biological sciences The forensic biology includes evidence related to hairs, body fluids, bones, urine, etc. Recent literature suggests that chemometrics in combination with analytical methods [44e52] gives useful information about the discrimination of individuals prior to DNA analysis. This combined approach provides most promising results of discrimination/individualization of the suspected person on the basis of biological evidence as follow;

5.3.1. J.F.Q. Pereira et al. J.F.Q. Pereira et al. [45] describe the method of identification of dry blood stains on different surfaces by using NIR spectroscopy and multivariate analysis. Experimental Procedure: 31 human blood samples, two animal i.e. cat and dog blood samples and different red colored products perceived as blood are collected. NIR spectral ranges of 908e1676 nm are used for spectra collection. The undesirable effects such as noise, uncontrolled amount of samples etc. are corrected by various data pre-processing methods. Different modeling methods such as SIMCA, SPA-LDA, GA-LDA, and PLSDA are utilized. Findings: The developed SIMCA model helps in 100% correct classification of blood stains deposition on porcelain and glass substrate but failed in 100% classification of blood stains deposited on metal and ceramic substrates (80% and 90% classification respectively). Again, genetic algorithm (GA) variable selection provides better results than successive projection algorithm (SPA). GA-LDA model gives 100% correct classification than SPA-LDA model which provide one false positive and one false negative result. PLS-DA model is able to discriminate human blood and other stains on all substrates significantly.

 G. Ramos et al. 5.3.3. A.  G. Ramos et al. [51] analyzed urine samples of 14 patients A. with cancer and 24 control volunteers in order to check the differentiation between them. Experimental Procedure: The urine samples from 38 individuals i.e. 1e24 healthy persons and 25e38 persons having lung cancerous are collected. Samples are first treated with NaCl and then, examined with the help of headspace mass spectroscopy. Various statistical methods are employed for model development. Findings: Among different models, PLS-DA provides 91% specificity and 100% sensitivity. The proposed model didn't provide any false negative results in the screening method. The PCA-LDA and SVM models provide 100% specificity as well as 100% sensitivity. The selection of urine samples has advantages over other fluid such as saliva as it contains more volatiles components than other biological fluids. In most of the aforementioned studies, the authors have developed multiple models for the comparison of classification of their samples and in general, it is a good practice because (1) the accuracy and significance of model depends on the sensitivity of instruments and the output data (2) parameters like resolution, scanning area, scanning speed, etc. used for the analysis of exhibits (3) data pre-treatment methods such as normalization, baseline corrections, noise reduction, etc. This is the reason why one model provides better efficiency than others. Therefore, it is suggested that in one type of analysis, the methodology should remain same throughout the study. 5.4. Forensic questioned document examination The questioned documents are examined consistently in forensic science laboratories for their authenticity. This includes documents associated with checks, question papers, passport duplicity, driving license, or document linked with personal identification such as Aadhar card, voter card, pan card, etc. With their widespread use, it is necessary to develop a method through which

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the source, individuality, and age of the concerned document can be established. Some recent studies are as follow; 5.4.1. R. Kumar et al. R. Kumar et al. [57] explored the non-destructive application of ATR-FTIR technique for characterization and discrimination of paper samples. Experimental Procedure: Twenty-four types of paper brands are used in this study. The qualitative feature and chemometrics of the obtained spectral data are used for characterization and discrimination. Three different regions of IR, i.e. 400e2000 cm1, 2000e4000 cm1 and 400e4000 cm1 are selected for differentiation by chemometrics analysis. Findings: The characterization is achieved by matching the peaks with standards of cellulose and inorganic fillers, the usual constituents of paper. It is observed that maximum discrimination has been procured in the wavenumber range of i.e. 2000e4000 cm1. Again, the discriminating power is better achieved by chemometrics analysis, PCA i.e. 99.64% rather than qualitative features i.e. 97.83%.

5.4.2. V. Sharma and R. Kumar V. Sharma and R. Kumar [59] proposed a method of the dating of ink by utilizing UVeVis spectroscopy and multiple regression analysis approaches. Experimental Procedure: The ink entries are aged for approx. nine months (267 Days) and then analyzed by using UVeVis spectroscopy as shown in Fig. 3. Curve estimation and multiple regression analysis are used to build the models for ink dating. Before developing the model, the factors like the best solvent for ink extraction and the conditions through which maximum ink is extracted has been determined. The variables are selected by visual inspection as well as by PCA analysis. Findings: The cross-validation of curve estimation model provides an error of ±19 days in dating. However, the MLR model provides an error of ±10 days in dating which is much significant than curve estimation model. Moreover, all the assumptions are met in MLR model significantly.

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5.4.3. J.F. Pereira et al. J.F. Pereira et al. [60] evaluate the alteration and deletion in a questioned document by applying the principle of chemometrics and HSI in NIR and MID regions. Experimental Procedure: Sixteen black ink pen samples are used in this study. A straight line is drawn on A4 paper and analyzed by HSI-MIR and HSI-NIR. Different data pre-processing methods are used before the analysis. The projection pursuit (PP) and PCA methods are used to discriminate the ink samples. Findings: It is found that PP shows better results in comparison to PCA analysis in HSI-MIR ranges (discrimination of 97.5% and 87.5% ink respectively). The HSI-NIR method with PCA and PP models describe 76.7% and 83.3% of cross-validation of test ink sample respectively while HSI-MIR provides 90% of crossvalidation. Therefore, it is concluded that HSI-MIR provides better results in comparison to HSI-NIR. PCA, LDA and regression analysis is used in this discipline of forensic science. The conditions of PCA and LDA are the same as aforementioned. However, there are some prerequisites one should keep in his mind while estimating the relative age of the document by the regression model. These are as follows; ○ The storage condition of the document must be same till the document aged. ○ High humidity conditions enhance the dye degradation. Therefore, a dry environmental storage should be preferred. ○ The initial composition of used ink should match with the dated ink. ○ High temperature and heating conditions should be avoided for storage of document. Therefore, here it is to be noted that the interpretation of the analytical data requires a sound knowledge of prerequisites as well as the statistical techniques. These methods are now becoming an essential need for the forensic examiner as well as the basic chemist, physicist, and biologist working in these areas since they provide accurate and subjective conclusions when applied correctly. Nonetheless, the established statistical protocols provide a logical reason that can authenticate the findings of examiners in

Fig. 3. Decrease in absorption of dye w.r.t. increase in time of writing (days).

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Fig. 4. Percentage utilization of chemometric methods on forensic exhibits.

the court of law. The implementation of such methodology also affords less human errors, less subjectivity, and quick time domain. Along with these statistical methods, the market survey is also vital to ascertain the exact source of suspected samples by using a database approach. This type of survey helps in the developing a forensic database which can further be used for the prediction the future unknown samples by using pattern recognition methods. This type of practices could be used as a complementary method to classical forensic investigation offering inexpensive, easy, fast and non-destructive analysis. Moreover, this strategy fastens the investigation and hence, helpful in reducing the number of backlogged cases in forensic laboratories. The authors feels that still, there is lots of scope in the research area of chemometric coupled with the analytical methods applied to basic as well as applied sciences.

investigation such as identification, differentiation, and classification of exhibits. The present review indicates that the fundamental knowledge of mathematical modeling is still required because without the basic information of chemometrics, the experts will not able to get reliable, accurate and significant model for the predictive data analysis. The current review summarized the detail description of supervised and unsupervised pattern recognition methods along with their application in the field of forensic science. The advantages of automated chemometric methods are discussed in the present review in the light of amalgamation of these methods into standard operating procedures. Some special point should be considered for good results like; sample size should be large enough to represent variability in the dataset; use of numerical variables in spite of string variables; and the developed model should be cross-validated. It also suggests that the fundamental knowledge of statistics is still needed. Some non-crossvalidated studies would have facilitated so that these studies could have acquired descriptive and cross-validated results. For the significant number of samples, the multivariate statistical analysis is expedient due to its ease of interpreting results, reliability, and speed. It is suggested that one should apply PCA method before developing any mathematical models as it reduces the chances of misclassification many folds. The DA model is the primary choice of authors for the classification purposes. However, advanced modeling methods such as SIMCA and SVM gain popularity in recent time. The UNEQ and CART modeling is rarely used in forensic studies. Acknowledgments This work has been financially supported by the Department of Science and Technology (Govt. of India) through sanction no. EMR/ 2016/001103 and PURSE-II grant. References

6. Future trends The pattern recognition statistical methods are used for individualization and separation of elements from multi-elements evidence/exhibit. In this review, the maximum research articles utilized PCA (36.23%) and discriminant analysis (33.33%) whereas kNN and others (CHEMSIC Model, Likelihood ratio, etc.) are least utilized chemometric methods as shown in Fig. 4. The analytical techniques with advantages like fast, reliable, cost-effective, reproducible and multiple element analysis are frontier in the analysis of forensic samples, i.e. questioned document, biological samples, chemical samples and other traces. However, the main problem for the analytical technique is to improve the accuracy of qualitative and quantitative analysis by extracting the useful information from a large number of complex data i.e. spectra or chromatogram. The aforementioned chemometric methods will help the forensic experts to correctly identify the exhibits belongs to the crime and hence the criminals and their modus operandi. In the light of the above discussion, some of the above-mentioned examples explain the usefulness of chemometric methods in forensic science as chemometrics provide robust and accurate results when utilized correctly. It is advisable to follow all the prerequisites of multivariate analysis before applying to real casework otherwise false positive results might be obtained. 7. Conclusions The incorporation of multivariate methods in forensic analysis is increasing tremendously as it helps in deciphering all the aspects of

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