  The taxonomic classification of asteroids has been mostly based on
spectroscopic observations with wavelengths spanning from the VIS to the NIR.
VIS-NIR spectra of $\sim$2500 asteroids have been obtained since the 1970s; the
SDSS MOC 4 was released with $\sim$4 $\times$ 10$^{5}$ measurements of asteroid
positions and colors in the early 2000s. A number of works then devised methods
to classify these data within the framework of existing taxonomic systems. Some
of these works, however, used 2D parameter space that displayed a continuous
distribution of clouds of data points resulting in boundaries that were
artificially defined. We introduce here a more advanced method to classify
asteroids based on existing systems. This approach is simply represented by a
triplet of SDSS colors. The distributions and memberships of each taxonomic
type are determined by machine learning methods in the form of both
unsupervised and semi-supervised learning. We apply our scheme to MOC 4
calibrated with VIS-NIR reflectance spectra. We successfully separate seven
different taxonomy classifications with which we have a sufficient number of
spectroscopic datasets. We found the overlapping regions of taxonomic types in
a 2D plane were separated with relatively clear boundaries in the 3D space
newly defined in this work. Our scheme explicitly discriminates between
different taxonomic types, which is an improvement over existing systems. This
new method for taxonomic classification has a great deal of scalability for
asteroid research, such as space weathering in the S-complex, and the origin
and evolution of asteroid families. We present the structure of the asteroid
belt, and describe the orbital distribution based on our newly assigned
taxonomic classifications. It is also possible to extend the methods presented
here to other photometric systems, such as the Johnson-Cousins and LSST filter
systems.
