Spectroscopy rapidly captures a large amount of data that is not directly interpretable. Principal Components Analysis (PCA) is widely used to simplify complex spectral datasets into comprehensible information by identifying recurring patterns in the data with minimal loss of information. The linear algebra underpinning PCA is not well understood by many applied analytical scientists and spectroscopists who use PCA. The meaning of features identified through PCA are often unclear. This manuscript traces the journey of the spectra themselves through the operations behind PCA, with each step illustrated by simulated spectra. PCA relies solely on the information within the spectra, consequently the mathematical model is dependent on the nature of the data itself. The direct links between model and spectra allow concrete spectroscopic explanation of PCA, such the scores representing âconcentrationâ or âweightsâ. The principal components (loadings) are by definition hidden, repeated and uncorrelated spectral shapes that linearly combine to generate the observed spectra. They can be visualized as subtraction spectra between extreme differences within the dataset. Each PC is shown to be a successive refinement of the estimated spectra, improving the fit between PC reconstructed data and the original data. Understanding the data-led development of a PCA model shows how to interpret application specific chemical meaning of the PCA loadings and how to analyze scores. A critical benefit of PCA is its simplicity and the succinctness of its description of a dataset, making it powerful and flexible.
Designing a Reliable and Application Specific Controller Area Network Protocol for Intra-Communication of an Embedded System
