© Published under licence by IOP Publishing Ltd. Asteroids have been observed both from the ground and through space missions for decades, which accumulated large amount of their observational data. These data are used to estimate the sizes, orbits, and even possible chemical compositions of asteroids. Even though the chemical composition is generally difficult to be accurately determined without a sample return or in-situ observation by a spacecraft, asteroids are classified based on their reflectance spectra, which are compared with those of meteorites, which are known to be mostly originated from asteroids. This scheme works reasonably well for some asteroid types, but others, mostly featureless ones in reflectance spectra, remained controversial due to the fact that the observational data of asteroids and measured data of meteorites are different in terms of the data coverage, precision and resolution. Our aim is to connect asteroids with meteorites based on sparse modelling in order to search for the optimal integration scheme for two different databases without relying on preliminary knowledge. For the above purpose, we develop large databases of asteroids and meteorites for easy application of sparse modelling. Through our analyses including principal component analysis, Bayesian spectral deconvolution and dimensionality reduction, we found that our data-driven approach can extract potential information without using empirical knowledge. Our methods show a new type of data handling scheme for asteroid and meteorite data, potentially having a significant contribution for future missions.