Large-area nanoplasmonic structures with pillared metal-insulator geometry, also called nanomushrooms (NM), consist of an active spherical-shaped plasmonic material such as gold as its cap and silicon dioxide as its stem. NM is a geometry which evolves from its precursor, nanoislands (NI) consisting of aforementioned spherical structures on flat silicon dioxide substrates, via selective physical or chemical etching of the silicon dioxide. The NM geometry is well-known to provide enhanced localized surface plasmon resonance (LSPR) sensitivity in biosensing applications as compared to NI. However, precise optical phenomenon behind this enhancement is unknown and often associated with the existence of electric fields in the large fraction of the spatial region between the pillars of NM, usually accessible by the biomolecules. Here, we uncover the association of LSPR enhancement in such geometries with a hidden plasmonic mode by conducting magneto-optics measurements and by deconvoluting the absorbance spectra obtained during the local refractive index change of the NM and NI geometries. By the virtue of principal component analysis, an unsupervised machine learning technique, we observe an explicit relationship between the deconvoluted modes of LSPR, the differential absorption of left and right circular polarized light, and the refractive index sensitivity of the LSPR sensor. Our findings may lead to the development of new approaches to extract unknown properties of plasmonic materials or establish new fundamental relationships between less understood photonic properties of nanomaterials.