The article by Bro and Smilde provides a comprehensive overview of Principal Component Analysis (PCA), a powerful method in chemometrics and other fields. PCA is introduced through an example of wine data, where 44 samples of Cabernet Sauvignon from different regions are analyzed using 14 parameters. The authors emphasize the importance of understanding and interpreting PCA, focusing on its application in chemometric areas. The paper begins with an intuitive example to illustrate the complexity of analyzing multiple variables and how PCA can simplify this by transforming the data into a new set of uncorrelated variables, called principal components (PCs). The first PC is derived from the linear combination of the original variables, weighted to maximize the variance explained. This process is formalized using matrix notation and eigenvalue decomposition. PCA is presented as a modeling activity, where the goal is to find the optimal weights for the linear combinations to maximize the variance explained. The explained variation is calculated by projecting the original data onto the PCs and assessing the residuals. The authors discuss the interpretation of scores, loadings, and residuals, emphasizing the importance of visualizing these components to understand the data structure. The article also covers practical aspects of PCA, including assumptions, preprocessing techniques, and the selection of the number of components. Preprocessing steps such as centering and scaling are crucial for meaningful analysis. The selection of the number of components can be guided by methods like the scree test, eigenvalue below one rule, broken stick rule, and the high fraction of variation explained. These methods help in determining the optimal number of components to retain while minimizing noise. Overall, the article provides a detailed guide to understanding and applying PCA, making it a valuable resource for researchers and practitioners in chemometrics and related fields.The article by Bro and Smilde provides a comprehensive overview of Principal Component Analysis (PCA), a powerful method in chemometrics and other fields. PCA is introduced through an example of wine data, where 44 samples of Cabernet Sauvignon from different regions are analyzed using 14 parameters. The authors emphasize the importance of understanding and interpreting PCA, focusing on its application in chemometric areas. The paper begins with an intuitive example to illustrate the complexity of analyzing multiple variables and how PCA can simplify this by transforming the data into a new set of uncorrelated variables, called principal components (PCs). The first PC is derived from the linear combination of the original variables, weighted to maximize the variance explained. This process is formalized using matrix notation and eigenvalue decomposition. PCA is presented as a modeling activity, where the goal is to find the optimal weights for the linear combinations to maximize the variance explained. The explained variation is calculated by projecting the original data onto the PCs and assessing the residuals. The authors discuss the interpretation of scores, loadings, and residuals, emphasizing the importance of visualizing these components to understand the data structure. The article also covers practical aspects of PCA, including assumptions, preprocessing techniques, and the selection of the number of components. Preprocessing steps such as centering and scaling are crucial for meaningful analysis. The selection of the number of components can be guided by methods like the scree test, eigenvalue below one rule, broken stick rule, and the high fraction of variation explained. These methods help in determining the optimal number of components to retain while minimizing noise. Overall, the article provides a detailed guide to understanding and applying PCA, making it a valuable resource for researchers and practitioners in chemometrics and related fields.