论文标题
频谱重建的分析公式
An Analytical Formula for Spectrum Reconstruction
论文作者
论文摘要
我们研究频谱重建技术。众所周知，特征值在许多研究领域都起着重要作用，并且是PCA（主要成分分析）等许多实用技术的基础。我们认为，相关算法应通过更准确的频谱估计来更好地发挥作用。提出了一个近似公式，但是他们没有提供任何证据。在我们的研究中，我们展示了该公式为什么有效。当空间的特征数量和空间尺寸都达到无穷大时，我们找到了近似公式的错误顺序，这与恒定的$ c $ - 空间维度和特征数量的比率有关。
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.
