This thesis is dedicated to developing innovative methodologies that improve elemental quantification in scanning transmission electron microscopy (STEM) using energy-dispersive X-ray spectroscopy (EDXS). The primary motivation stems from a geochemistry problem concerning Si deficiency in the Earth's upper mantle. To address this, mantle melting experiments were conducted on pyrolite composition under lower mantle conditions, followed by the characterization of the synthesized mineral phases using STEM-EDXS. The results reveal that within the investigated lower mantle pressure range, bridgmanite, a silicate mineral, is the first phase to crystallize during mantle solidification, supporting the hypothesis of a Si-rich lower mantle that could account for the Si depletion in the upper mantle. The mineral specimens exhibiting complex phase features provide opportunities for the development of advanced data processing techniques, including classical machine learning and deep learning approaches. These techniques have been employed to overcome challenges in phase segmentation and improve elemental quantification, particularly for trace elements. Two novel methodologies, non-negative matrix factorization (NMF) aided and pan-sharpening fused non-negative matrix factorization (PSNMF), have been developed. These methodologies effectively unmix overlapping phases, enhance chemical sensitivity, and improve the precision of STEM-EDXS quantification. Additionally, this thesis combines the complementary techniques of EDXS and EELS (electron energy-loss spectroscopy) using a deep learning approach to enhance elemental analysis. The preliminary results of this methodology show promising potential. In summary, this thesis significantly advances the analytical capabilities of STEM-EDXS and deepens our understanding of the Earth's mantle. The proposed methodologies are applicable to the analysis of various materials that exhibit complex volumetric phase relationships, low signal-to-noise ratios (SNR), or contain vital trace constituents.