Non-linear methods for quantitative elemental analysis and mineral classification using laser-induced breakdown spectroscopy are disclosed. According to one embodiment, a method, comprises calculating concentrations of elements in a sample using a laser-induced breakdown spectroscopy (LIBS) instrument. The LIBS instrument implements a kernel partial-least-squares regression (KPLSR) analysis. The method further comprises displaying the concentrations of the elements according to the KPLSR analysis.
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