  In this paper, we propose two-dimensional signal path classification (2D-SPC)
for reconfigurable intelligent surface (RIS)-assisted near-field (NF)
localization. In the NF regime, multiple RIS-driven signal paths (SPs) can
contribute to precise localization if these are decomposable and the reflected
locations on the RIS are known, referred to as SP decomposition (SPD) and SP
labeling (SPL), respectively. To this end, each RIS element modulates the
incoming SP's phase by shifting it by one of the values in the phase shift
profile (PSP) lists satisfying resolution requirements. By interworking with a
conventional orthogonal frequency division multiplexing (OFDM) waveform, the
user equipment can construct a 2D spectrum map that couples each SPs time of
arrival (ToA) and PSP. Then, we design SPL by mapping SPs with the
corresponding reflected RIS elements when they share the same PSP. Given two
unlabeled SPs, we derive a geometric discriminant from checking whether the
current label is correct. It can be extended to more than three SPs by sorting
them using pairwise geometric discriminants between adjacent ones. From
simulation results, it has been demonstrated that the proposed 2D SPC achieves
consistent localization accuracy even if insufficient PSPs are given.
