1. INTRODUCTION:

Chemometrics, a discipline rooted in analytical chemistry, integrates advanced mathematical and statistical techniques to extract relevant information from complex chemical data. As modern analytical instruments generate vast datasets with multiple interdependent variables, traditional univariate approaches often fall short in capturing the true nature of such data. Chemometrics, rooted in the discipline of chemistry, has evolved to address the challenges posed by the vast and complex datasets generated by modern analytical instruments. Chemometrics has become an indispensable tool in transforming raw data into meaningful chemical knowledge. The integration of mathematical and statistical methods in chemometrics enables researchers to extract relevant information from intricate material systems, a task that has grown in significance with the advent of personal computers in the 1980s. As digital technologies advanced, so did the application of software-based mathematical tools, making a deep understanding of these approaches essential for scientists today¹. Chemometrics is the study of chemical data using statistical and mathematical techniques. Because it offers resources for deriving valuable information from intricate datasets, it is essential for multivariate data analysis. A key component of Process Analytical Technology (PAT) techniques is chemometrics. Understanding and diagnosing real-time processes, as well as keeping them under multivariate statistical management, requires it. The main goal of chemometrics techniques is to describe them with a focus on comprehension and interpretation. Chemometrics offers the instruments and techniques required for efficient multivariate data analysis, especially in process control and comprehension, with an emphasis on real-world implementation and outcome interpretation². The field of chemometrics, which has its roots in chemistry, is concerned with deriving useful information from data, especially when it comes to material systems. To do this, it makes extensive use of statistical and mathematical techniques³.

2. Fundamentals of Multivariate Data Analysis:

The fundamental aspects of multivariate data analysis, as described in this context, include several key methodologies: Design of Experiments: This involves structuring experiments to efficiently gather data and understand variable relationships. Exploratory Analysis: Techniques used to explore data and uncover initial patterns or relationships. Quantitative Predictive Modelling: Methods for building models to predict outcomes based on quantitative data. Classification: Techniques for categorizing data into predefined classes. Multivariate Process Monitoring: Approaches for observing and controlling processes using multiple variables simultaneously. Multi-block and Multi-way Analyses: Specialized methods for handling complex data structures involving multiple blocks or dimensions. When it comes to a large number of variables, graphical visualization is generally restricted to three variables, although a fourth dimension can occasionally be incorporated by changing the types and sizes of symbols. By defining a smaller number of linear combinations of the original data, referred to as principal components, MDA techniques seek to reduce the dimensionality of the data. Unsupervised Classification (Cluster Analysis): This method divides data into entities that are relatively based purely on the characteristics of the data, without any dependence/on prior knowledge.

Supervised Pattern-Recognition (Discriminant Analysis): This method, in contrast, assigns group membership to a given dataset based on prior classification⁴. PCA is a popular unsupervised technique mainly used for reducing dimensionality and visualizing data. It transforms correlated variables into main components, which are uncorrelated variables. Connections among two matrices. MLR is a statistical technique that predicts a response variable's result by using several explanatory variables. This is a supervised regression technique. PCA and MLR are combined in Principal Component Regression (PCR). Initially, it executes PCA on the independent variables to diminish dimensionality and address multicollinearity, subsequently employing the principal components in a linear regression model. Partial Least Squares (PLS): This technique integrates aspects of both PCA and regression, making it appropriate for modeling relationships among multiple independent variables and dependent responses Partial Least Squares Regression (PLSR): A regression method that establishes relationships between several independent variables and one or more dependent variables, especially valuable in the analysis of spectroscopic data Cluster Analysis: This method organizes observations that are alike, facilitating the identification of patterns and categorization within datasets⁵.

3. Types of Multivariate Data:

3.1. Categorical Data:

In multivariate analysis, particularly in educational and social science research, categorical data play a crucial role, as they represent variables that are measured in discrete categories rather than on a continuous scale. The levels of categorical variables can be categorized as nominal or ordinal based on their intrinsic characteristics and the context in which they are applied. Nominal Data: This category of categorical variable consists of categories that lack any inherent order. Ordinal Data: Unlike nominal data, ordinal variables consist of categories that have a natural order or ranking⁶. Multiple variables that are categorical in nature are referred to as multivariate categorical data. When working with multivariate categorical data, log-linear models, especially log-linear interaction models, are frequently used. The two main goals of modeling multivariate categorical data are: Smooth Estimation of Cell Probabilities: It acts as a mechanism for obtaining smooth estimated values for cell probabilities within the contingency table⁷.

3.2 Continuous Data:

The term "multivariate continuous data" describes datasets that include measurements of several continuous variables at the same time. In many domains, such as biotechnology, the social sciences, and medicinal research, this kind of data is essential because it enables a thorough examination of the connections between variables. Continuous data are numerical values that fall anywhere in a specified range. Decimals and fractions can be included in these values, which are not limited to integers⁸. symbolizes a particular kind of multivariate data in which the variables are thought of as continuous curves or functions defined across a shared time period, this paradigm is altered by continuous-time multivariate analysis (CTMVA), which takes into functions or p curves defined on a single time interval as opposed to p distinct variables. This indicates that each variable is an infinitely dimensional function over time rather than having a finite number of observations. These continuous functions or curves can be represented as linear combinations of basis functions, like B-splines or Fourier bases, which effectively treat each variable as a continuous curve. This is a basic assumption in CTMVA ⁹.

3.3 Mixed Data Types:

Numerical and categorical variables are combined in multivariate mixed data types, which can make analysis more difficult but can improve the insights obtained from datasets. For the purpose of managing such mixed data, the R package PCA mixdata was created. Numerical variables, such as temperature, weight, or height, can have any value within a range. Categorical variables are those that reflect groups or categories, such as gender, car kind, or color. They are further separated into: Nominal: Does not have an innate order, such as fruit types.

Ordinal: Consists of a predetermined sequence (e.g., satisfaction ratings). Count Variables: These are discrete variables that can be used to model distributions like the generalized Poisson distribution. One illustration of this is the frequency of an event¹⁰.

4. Data Preprocessing Techniques:

4.1. Normalization:

Normalization adjusts numerical data to a uniform scale typically between 0 and 1, helping to eliminate scale discrepancies across variables. This is particularly crucial for machine learning algorithms that rely on distance-based computations. Normalization contributes to improved prediction accuracy by maintaining consistent data ranges¹¹.

4.2. Scaling:

Scaling is an essential data preparation method that standardizes the range of numerical features, improving the performance of machine learning models. For algorithms such as support vector machines and neural networks, scaling guarantees that no single feature dominates the model because of its range. In statistical analysis and machine learning, data scaling is an essential preprocessing method, particularly when dealing with algorithms that are sensitive to the size of input characteristics. Stops the dominance of features: Features with wider numerical ranges could significantly affect the model's performance if scaling isn't used ¹⁰. When the input variables have different scales, data scaling is frequently required to guarantee the validity of predictive modeling. most popular approaches in the construction industry, where μ is the mean and σ is the standard deviation, and min(x) and max(x) stand for the variable's minimum and maximum values¹².

4.3. Missing Value Treatment:

One important component of data preprocessing in data mining is the treatment of missing values. This procedure, which focuses on correcting missing values using unsupervised machine learning algorithms, is crucial when combined with other strategies like data standardization and noise reduction¹³. The effectiveness of data mining techniques can be greatly impacted by missing values in databases. Missing values can be overlooked in datasets with a large number of instances; however, deleting records with missing values in smaller datasets may result in incorrect categorization or predictions by data mining techniques. Common approaches for dealing with missing data include replacing them with the mean of the column. A regression-based methodology can be used to predict missing values¹⁴.

5. Exploratory Data Analysis:

5.1. Principal Component Analysis (PCA):

PCA reduces data dimensionality while preserving variability by transforming original variables into new uncorrelated variables (principal components). It enables visual inspection and feature extraction, even in time-series datasets with autocorrelation issues¹⁵. In order to comprehend complex information, exploratory data analysis (EDA) commonly uses the potent statistical method known as principal component analysis (PCA). PCA is essential for data analysis in a variety of fields. Finding underlying patterns and structures in the data is made easier by PCA, which converts the original variables into a new set of uncorrelated variables known as principal components. PCA makes it easier to visualize high-dimensional data. By displaying the information on the initial few main components, PCA makes it easier to visualize high-dimensional data. By displaying the information on the initial few main components¹⁶.

5.2. Cluster Analysis:

As a subset of exploratory data analysis (EDA), cluster analysis groups data into similar instances to reveal underlying patterns and relationships. Partitioning methods, such as K-means, divide data into discrete clusters and are effective for large datasets. Hierarchical clustering builds a tree-like structure, allowing visualization of relationships at multiple levels of granularity. Overlapping clustering is useful for complex datasets because it permits instances to belong to multiple clusters simultaneously. Overall, the primary goal of cluster analysis in EDA is to identify naturally occurring groupings in data by organizing points based on their similarity¹⁸.

5.3. Multidimensional Scaling:

Data scientists use Multidimensional Scaling (MDS) to compare and show similarities and differences in high-dimensional data. Because MDS reduces the dimensionality of multivariate data, it helps with visual evaluation and understanding in the context of geostatistics. These linkages are made visible by MDS, which projects multivariate distances between items into a best-fit configuration in lower dimensions¹⁹. Fundamentally, MDS is a technique for data visualization. In order to efficiently detect clusters of points, MDS projects high-dimensional data onto a lower-dimensional space. In MDS, the 'Stress' function is a crucial element for evaluating the quality of the dimensional reduction. MDS has been used in a number of domains, including social networks, marketing, ecology, and molecular biology, for exploratory purposes²⁰.

6. Regression Techniques in Chemometrics:

6.1. Multiple Linear Regression:

Multiple Linear Regression (MLR) is a fundamental technique in chemometrics, applied for estimating the connection between many independent factors and a dependent variable. A plot of x-loadings was used in MLR to extract a small number of variables. The input wavelengths were those linked to the positive and negative peaks. To optimize the model parameters, the full cross-validation method was used to validate all regression models²¹. A particular kind of regression analysis called multiple linear regression expands on simple linear regression by adding more than one independent variable. MLR is a model that uses a linear combination of two or more independent variables to predict the dependent variable. In chemometrics, regression methods such as multiple linear regression are essential. Predicting a substance's concentration using its spectral data is known as quantitative analysis. Creating models that connect instrument responses to known analyte concentrations is known as calibration. Process monitoring is the tracking and forecasting of chemical production process parameters. Predicting attributes using sensor data to ensure product quality is known as quality control²².

6.2. Partial Least Squares Regression (PLSR):

PLSR is intended to address multicollinearity by extracting orthogonal latent variables that maximize the covariance between predictors and outcomes. This approach is applicable in numerous sectors, including vegetation remote sensing and kinase signalling research. Partial Least Squares Regression (PLSR), sometimes known as PLS, is an effective dimensionality reduction technique that originated in the field of chemometrics. PLS components are derived by maximizing the covariance of linear combinations of the regressors²³. PLSR operates by projecting the predictor and response variables into a new space defined by a collection of latent variables. These latent variables are chosen to maximize the covariance between the X and Y spaces, so identify the underlying relationships that account for the highest variance in both sets of data. PLSR models accurately predicted physiological parameters despite noise and multicollinearity, with R² values typically exceeding 0.6. Stomatal conductance showed the best performance, with an R² of 0.7²⁴.

6.3. Support Vector Regression:

Support Vector Regression (SVR) is a potent technique in chemometrics. SVR's capacity to model complex connections with fewer calibration samples and its flexibility in loss functions are major characteristics that increase its use in chemometrics. In chemometrics, SVR is frequently used for jobs like: Quantitative Structure-Activity Relationship (QSAR) and Quantitative Structure-Property Relationship (QSPR) models: Predicting chemical, physical, or biological properties of substances using their molecular structure. Spectroscopic data analysis involves calibrating models to predict analyte concentrations from spectral data (e.g., NIR, IR, Raman spectroscopy). Process monitoring and control involve creating prediction models for real-time quality control in chemical processes. Drug discovery involves predicting drug efficacy or toxicity using molecular characteristics²⁵. SVR is an analytical technique that investigates the relationship between one or more predictor variables and a real-valued (continuous) dependent variable. SVR is ideal for such data because of its capacity to handle non-linear correlations and large dimensionality. SVR is noted for its robustness. In chemometrics, SVR can be used to develop prediction models for a variety of applications²⁶.

7. Classification Methods:

7.1. Linear Discriminant Analysis:

This method extends LDA to high-dimensional data, boosting performance when the number of observations is fewer than the number of features. RDA employs regularization to stabilize covariance estimations, therefore boosting classification accuracy²⁷. Conventional LDA is sensitive to departures from the norm. To reduce this susceptibility, new robust LDA models use winsorized and trimmed means, which show better classification rates in non-normal datasets. An innovative method that enables LDA to function in binary classification beyond one-dimensional reductions. By adding a continuous auxiliary variable, this technique enhances both the overall predictive accuracy and the extraction of local information²⁸.

7.2. K-Nearest Neighbors:

A popular non-parametric classification technique, K-Nearest Neighbor (KNN), uses data points' proximity to categorize new instances. Numerous studies have looked into ways to improve KNN, with an emphasis on handling missing data, measuring distance, and increasing computational efficiency. Two primary criteria have a significant impact on the quality of KNN classification results: Distance between objects: The categorization result is greatly influenced by the technique used to calculate the distance between data points. The value of 'k'. Another important factor in deciding the classification results is the selection of the 'k' value, which denotes the number of nearest neighbors taken into account²⁹. It is especially intended for categorization in the situation of lacking data. The proposed method, entitled 'k-nearest centroid neighbour', leverages a local mean-based vector of k centroid neighbors for each class. The novel method greatly outperforms current advanced KNN-based algorithms, particularly when dealing with datasets that include missing values³⁰.

7.3. Random Forest Classifier:

The Random Forest classifier is a strong ensemble learning algorithm commonly utilized for classification tasks across multiple domains. Random Forest frequently beats alternative classifiers such as decision trees, support vector machines, and logistic regression in terms of accuracy. For example, in land cover categorization, it demonstrated greater performance compared to other methods. The Random Forest Classifier was one of the supervised machine learning algorithms used in a study to categorize various forest cover types. This classification was based on cartographic features, to automate the process of understanding tree types in different forest locations³¹. In a study comparing Random Forest and SVM for classifying students' adaptation to distance learning, Random Forest outperformed SVM with 91.5% accuracy and 73.36% error rate. Despite being more accurate, Random Forest had a greater number of wrong classifications than SVM, demonstrating a trade-off between accuracy and error distribution³².

8. Validation of Chemometric Models:

8.1. Cross-Validation Techniques:

Validation of chemometric models is critical to their predicted accuracy and reliability. Cross-validation techniques, specifically k-fold cross-validation, are commonly used to analyze model performance. Cross-validation is an iterative method that uses the calibration set several times by resampling. This entails developing many models from different subsets of the calibration data. The change seen between these models can offer an estimate of the sampling error, allowing cross-validation to check both fitting and sampling errors concurrently. Some academics believe that cross-validation does not effectively account for sample variance and that test set validation is a more accurate approach. This viewpoint highlights the necessity for a second dataset to reduce bias and improve model evaluation. Unlike cross-validation, which is a generally established method³³.

8.2. Performance Metrics:

By measuring the difference between expected and actual values, these measures evaluate how well models predict outcomes. Mean Squared Error (MSE) and Root Mean Squared Error (RMSE) are two common loss functions used to measure model performance. This includes estimating the uncertainty associated with model predictions, which is critical for determining reliability. Bootstrapping and cross-validation are common techniques used to produce confidence intervals for predictions³⁴. Validation factors include specificity and selectivity, which refer to the ability to discriminate between analytes. Accuracy refers to how closely measurements match the genuine value. Repeatability and Intermediate Precision: The consistency of findings under the same and different settings, respectively. Robustness: The model's ability to withstand alterations in experimental settings³⁵.

9. Applications of Multivariate Analysis in Chemistry:

9.1. Quality Control:

Multivariate analysis is important in chemical quality control, especially for monitoring complicated processes and maintaining consistent product results. These analytical tools help improve process monitoring and control, leading to higher quality standards. Monitoring multivariate analytical data helps firms attain consistent product outcomes. Example: White Wine Production: The application of these algorithms to the white wine manufacturing process has demonstrated their efficacy in assessing complex multivariate chemical data³⁶. The standard univariate technique is constrained since it only evaluates one variable at a time, which might result in underutilization of the global data structure and an incomplete view. In contrast, multivariate approaches allow for a more full interpretation and use of the information included in the data. Multivariate approaches are commonly used for modeling, especially in predictive applications. When utilized for prediction, comprehensive model validation is always required to assure reliability³⁷.

Multivariate methods are used for qualitative or quantitative modeling as well as for exploratory purposes. This is especially helpful for process monitoring, because control and optimization depend on an awareness of the interdependencies between variables. Multivariate methods enable better use of the given information and provide a more thorough analysis of the data³⁷. In process industries, process monitoring is a state-of-the-art system that guarantees both product quality and process safety. The size, complexity, and intelligence of manufacturing processes have grown as a result of recent technological advancements in contemporary industry. Plant safety, reduced downtime, and improved product quality can all be achieved through early fault detection and diagnosis (FDD). Furthermore, process companies stand to save billions of dollars by using sophisticated process monitoring systems. To be effective, a defect diagnostic system needs to contain a number of features. These features are useful for comparing and standardizing different approaches to enhance the design system's execution and design³⁸.

9.3. Environmental Analysis:

In chemistry, multivariate analysis is an effective method for managing and interpreting big datasets, especially in environmental studies. Understanding the complex interactions between many chemical, physical, and biological aspects in environmental systems requires this method. To help with pollution assessment and control, multivariate approaches are employed to study changes in physical circumstances and chemical concentrations. These techniques aid in characterizing phenomena, minimizing the dimensionality of data, and Water quality is continuously monitored and evaluated using automated multivariate algorithms, guaranteeing adherence to environmental regulations. Water quality is continuously monitored and assessed using automated multivariate approaches, which ensure adherence to environmental requirements and raise the sensitivity of environmental research³⁸.

10. Software and Tools for Chemometric Analysis:

10.1. R Packages:

A range of tools allows chemometric analysis in R, making it easier to process and analyze chemical data. These packages provide tools for data preprocessing, exploratory analysis, modeling, and validation, making them indispensable for researchers in the natural and life sciences. The offered information does not specifically define specific R packages used for chemometric analysis. R is an open-source language that provides a wide range of statistical and graphical tools, making it a strong tool for numerous types of data analysis, including chemometrics. Using scripts encourages repeatability and transparency in research³⁹. R packages are made to increase R's capabilities so that users may efficiently carry out intricate analyses and data manipulations⁴⁰.

10.2. Python Libraries:

In several domains, including analytical chemistry, where reliable data analysis is essential for instrumental analysis, Python is becoming a useful tool for data analysis. Multivariate analysis, or chemometrics, is frequently used to analyze data from instrumental analysis to get around challenges with precise analysis⁴¹. Python is a popular option for resolving chemical challenges because of its extensive library environment and versatility. Its libraries ease these activities by facilitating data processing and visualization in chemistry. Python is utilized in software development and laboratory automation. Advanced data-driven chemical research using Python, which may include chemometrics. Python is used in lab automation and software development⁴².

10.3. Commercial Software:

MATLAB: A popular numerical computer environment with a wealth of tools and capabilities that facilitate chemometric applications. It is renowned for having a user-friendly interface and numerical stability, which makes it appropriate for complex data processing. A free exploratory data analysis application that enables multivariate analysis without the need for complex programming skills. It has been verified against MATLAB findings and supports several techniques, including PCA and HCA⁴³. A Python module that combines the scikit-learn machine learning framework with chemometrics. By offering a consistent platform for spectral data analysis, it makes the process of creating chemometric models easier. More than 200 functions for different chemometric investigations, such as regression and multidimensional analysis, are included in this free MATLAB toolbox. It is made to efficiently manage physicochemical sensory data⁴⁴.

11. Challenges in Multivariate Data Analysis:

11.1. Overfitting:

Overfitting is a major issue in multivariate data analysis, particularly in areas such as immunology. By understanding its causes and applying appropriate mitigation strategies, researchers can develop models that are more reliable and widely applicable. Overfitting occurs when a prediction model performs extremely well on training data but fails to generalize to new, unseen observations. This is especially problematic in medical applications, such as predicting vaccination responses or disease outcomes in cancer and infectious disease studies, because it reduces the accuracy and utility of predictive models⁴⁵.

Several factors contribute to overfitting. Noise in the training data can cause the model to learn patterns that do not accurately represent the true data distribution. Limited training data may lead the model to memorize specific examples instead of learning generalizable features. Classifier complexity also plays a role: overly complex models with too many parameters can fit the training data, including noise, too closely, and generalize new data difficult⁴⁶. Overfitting can result in instability, higher computational costs, and unnecessarily complex models. To prevent overfitting, various strategies can be applied. Regularization adds a penalty term to the loss function during model training to discourage overly complex models. Ensemble methods combine multiple models to improve predictive performance and reduce variance. By creating altered versions of preexisting data, data augmentation broadens the training dataset, assisting the model in learning more reliable features and improving generalization⁴⁶.

11.2. Interpretability:

Interpretability is essential, particularly in sectors where achieving interpretability presents a number of difficulties, including both philosophical and technical ones. The main obstacles and factors to take into account while attempting to make multivariate data analysis interpretable are listed below. Because of the intricacy and high dimensionality of the data involved, interpretability in multivariate data analysis poses a number of difficulties. Dimensionality reduction techniques are frequently needed for high-dimensional data in order to make analysis possible and comprehensible. Nevertheless, these methods may mask the underlying data structure, which makes it challenging to meaningfully evaluate the findings. It can be difficult to optimize sparse logical models, such as decision trees, because it requires striking a balance between interpretability and model complexity. Although they may be less accurate, sparse models are typically easier to understand⁴⁷. Highly linked variables are frequently present in multivariate data, which can cause multicollinearity problems that make it more difficult to understand the findings. To solve this, careful feature extraction and selection are required. The lack of a consensus definition for interpretability in multivariate analysis makes it challenging to create standardized techniques for assessing and enhancing interpretability. For instance, in neuroimaging, the interpretability of brain maps is associated with their representativeness and reproducibility, both of which are challenging to measure and optimize at the same time⁴⁸.

12. Future Trends in Chemometrics:

12.1. Big Data and Chemometrics:

In contemporary analytical chemistry, big data and chemometrics are becoming more and more integrated, improving the capacity to examine intricate chemical systems. While big data includes enormous amounts of heterogeneous information produced by numerous analysis approaches, chemometrics uses mathematical and statistical tools to extract relevant information from large datasets. Chemometrics is expected to have a very bright future, partly because big data technologies are developing so quickly. Chemometrics is becoming increasingly important in decision-making processes in a variety of chemical sectors as data collection and analysis in analytical chemistry grow easier and more accessible⁴⁹. The development of artificial intelligence (AI) and new machine learning algorithms will have a big impact on the future of chemoinformatics, especially in the setting of Big Data. Novel deep learning architectures such as Transformers, Long Short-Term Memory, Recurrent Neural Networks, and Convolutional Neural Networks (CNN) are becoming more popular in the field. These approaches are more creative and frequently call for a high level of programming proficiency as well as familiarity with contemporary toolkits like TensorFlow, Keras, and PyTorch. One important area of progress is the use of GMs for molecular de novo design in drug development. The use of RNNs with variational autoencoders and reinforcement learning for molecular designs has been pioneered by projects such as BIGCHEM⁵⁰. There are still issues to be resolved, like guaranteeing data quality and tackling the limitations of machine learning algorithms in chemistry, even if the developments in big data and chemometrics provide tremendous prospects. It is anticipated that the convergence of big data and the Internet of Things (IoT) would propel advancements in chemical sensing and materials discovery, broadening the use of chemometrics⁵¹.

12.2. Machine Learning Integration:

The incorporation of machine learning (ML) into chemometrics is set to transform analytical chemistry by boosting data analysis abilities and refining the precision of chemical evaluations. Neural networks and support vector machines, among other ML methods, are being employed more and more for the analysis of complex chemical data. Their use enhances the interpretation of outcomes from techniques such as mass spectrometry and surface-enhanced Raman spectroscopy (SERS). Machine learning contributes to the optimization of experimental conditions for electrochemical sensors, facilitating improved calibration and analyte classification⁵². ML models are employed to identify complex connections between chemical structures and their electrochemical properties. They are utilized for the analysis of intricate electrochemical data, enhancing calibration and analyte classification. This includes their application in electronic tongue machine learning algorithms such as linear and logistic regressions, neural networks, and support vector machines⁵³. By automating data analysis and enhancing predictive modeling, ML is revolutionizing these fields and speeding up research and development processes. By incorporating ML into spectroscopy, microscopy, and chromatography, the efficiency and reliability of chemical analyses are improved. The incorporation of ML into chemometrics brings about considerable progress; however, issues like data availability and reproducibility continue to be vital problems that must be tackled for more widespread use in chemistry⁵⁴.

13. CONCLUSION:

In 'Multivariate Data Analysis (Chemometrics), chemometrics is positioned as an essential component of PAT strategies, with an emphasis on its use for comprehending processes, diagnosing issues, and regulating activities. It aims to provide a comprehensive overview of various chemometric methods, with a strong emphasis on practical understanding, interpretation, and assessment of their applicability and usefulness. Chemometrics includes a variety of multivariate statistical techniques tailored for chemical data. Although it is already widely accepted in the chemistry community, its use is increasing in forensic science.

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Received on 12.12.2025 Revised on 17.01.2026

Accepted on 19.02.2026 Published on 04.07.2026

Available online from July 18, 2026

Asian J. Pharm. Tech. 2026; 16(3):293-301.

DOI: 10.52711/2231-5713.2026.00041

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