Applications of Singular Value Decomposition part1(Machine Learning)

Abstract: Currently, the engineering of miniature spectrometers mainly faces three problems: the mismatch between the number of filters at the front end of the detector and the spectral reconstruction accuracy; the lack of a stable spectral reconstruction algorithm; and the lack of a spectral reconstruction evaluation method suitable for engineering. Therefore, based on 20 sets of filters, this paper classifies and optimizes the filter array by the K-means algorithm and particle swarm algorithm, and obtains the optimal filter combination under different matrix dimensions. Then, the truncated singular value decomposition-convex optimization algorithm is used for high-precision spectral reconstruction, and the detailed spectral reconstruction process of two typical target spectra is described. In terms of spectral evaluation, due to the strong randomness of the target detected during the working process of the spectrometer, the standard value of the target spectrum cannot be obtained. Therefore, for the first time, we adopt the method of joint cross-validation of multiple sets of data for spectral evaluation.