Machine Learning (ML) has found several applications in spectroscopy, including recognizing minerals and estimating elemental composition. ML algorithms have been widely used on datasets from individual spectroscopy methods such as vibrational Raman scattering, reflective Visible-Near Infrared (VNIR), and Laser-Induced Breakdown Spectroscopy (LIBS). We firstly reviewed and tested several ML approaches to mineral classification from the existing literature, and identified a novel approach for using Deep Learning algorithms for mineral classification from Raman spectra, that outperform previous state-of-the-art methods. We then developed and evaluated a novel method for automatic mineral identification from combining measurements with two complementary spectroscopic methods using Convolutional Neural Networks (CNN) for Raman and VNIR, and cosine similarity for LIBS. Specifically, we evaluated fusing Raman + VNIR, Raman + LIBS or VNIR + LIBS spectra in order to classify minerals. ML methods applied to combined spectral methods presented here are shown to outperform the use of a single data source by a significant margin. Our approach was tested on both open access experimental Raman (RRUFF) and VNIR (USGS, RELAB, ECOSTRESS) libraries, as well as on synthetic LIBS (NIST) spectral libraries. Our cross-validation tests show that multi-method spectroscopy paired with ML paves the way towards rapid and accurate characterization of rocks and minerals. Future solutions combining Deep Learning Algorithms, together with data fusion from multi-method spectroscopy, could drastically increase the accuracy of automatic mineral recognition compared to existing approaches.