Methods and systems for creating ensembles of hypersurfaces in high-dimensional feature spaces, and to machines and systems relating thereto. More specifically, exemplary aspects of the invention relate to methods and systems for generating supervised hypersurfaces based on user domain expertise, machine learning techniques, or other supervised learning techniques. These supervised hypersurfaces may optionally be combined with unsupervised hypersurfaces derived from unsupervised learning techniques. Lower-dimensional subspaces may be determined by the methods and systems for creating ensembles of hypersurfaces in high-dimensional feature spaces. Data may then be projected onto the lower-dimensional subspaces for use, e.g., in further data discovery, visualization for display, or database access. Also provided are tools, systems, devices, and software implementing the methods, and computers embodying the methods and/or running the software, where the methods, software, and computers utilize various aspects of the present invention relating to analyzing data.