Unsupervised verification of laser-induced breakdown spectroscopy dataset clustering

Laser-induced breakdown spectroscopy is a versatile, optical technique used in a wide range of qualitative and quantitative analyses conducted with the use of various chemometric techniques. The aim of this research is to demonstrate the possibility of unsupervised clustering of an unknown dataset using K-means clustering algorithm, and verifying its input parameters through investigating generalized eigenvalues derived with linear discriminant analysis. In all the cases, principal component analyses have been applied to reduce data dimensionality and shorten computation time of the whole operation. The experiment was conducted on a dataset collected from twenty four different materials divided into six groups: metals, semiconductors, ceramics, rocks, metal alloys and others with the use of a three-channel spectrometer (298.02-628.73nm overall spectral range) and a UV (248nm) excimer laser. Additionally, two more complex groups containing all specimens and all specimens excluding rocks were created. The resulting spaces of eigenvalues were calculated for every group and three different distances in the multidimensional space (cosine, square Euclidean and L1). As expected, the correct numbers of specimens within groups with small deviations were obtained, and the validity of the unsupervised method has thus been proven.