An Analytical Formula for Spectrum Reconstruction
This work provides theoretical justification for spectrum estimation methods used in techniques like PCA, but it appears incremental as it focuses on proving and analyzing an existing formula rather than introducing new algorithms.
The paper tackles the problem of spectrum reconstruction by providing a theoretical proof for an existing approximation formula and analyzing its error behavior as both the number of features and space dimension approach infinity, with the error order depending on a constant ratio c.
We study the spectrum reconstruction technique. As is known to all, eigenvalues play an important role in many research fields and are foundation to many practical techniques such like PCA(Principal Component Analysis). We believe that related algorithms should perform better with more accurate spectrum estimation. There was an approximation formula proposed, however, they didn't give any proof. In our research, we show why the formula works. And when both number of features and dimension of space go to infinity, we find the order of error for the approximation formula, which is related to a constant $c$-the ratio of dimension of space and number of features.