Xianfeng Hu | Searcharxiv

arXiv2016

Rapidly Computing Sparse Legendre Expansions via Sparse Fourier Transforms

In this paper we propose a general strategy for rapidly computing sparse Legendre expansions. The resulting methods yield a new class of fast algorithms capable of approximating a given function $f:[-1,1] \rightarrow \mathbb{R}$ with a near-optimal linear combination of $s$ Legendre polynomials of degree $\leq N$ in just $(s \log N)^{\mathcal{O}(1)}$-time. When $s \ll N$ these algorithms exhibit sublinear runtime complexities in $N$, as opposed to traditional $Ω(N \log N)$-time methods for computing all of the first $N$ Legendre coefficients of $f$. Theoretical as well as numerical results demonstrate the promise of the proposed approach.

math.NA↗

arXiv2014

Multiple Authors Detection: A Quantitative Analysis of Dream of the Red Chamber

Inspired by the authorship controversy of Dream of the Red Chamber and the application of machine learning in the study of literary stylometry, we develop a rigorous new method for the mathematical analysis of authorship by testing for a so-called chrono-divide in writing styles. Our method incorporates some of the latest advances in the study of authorship attribution, particularly techniques from support vector machines. By introducing the notion of relative frequency as a feature ranking metric our method proves to be highly effective and robust. Applying our method to the Cheng-Gao version of Dream of the Red Chamber has led to convincing if not irrefutable evidence that the first $80$ chapters and the last $40$ chapters of the book were written by two different authors. Furthermore, our analysis has unexpectedly provided strong support to the hypothesis that Chapter 67 was not the work of Cao Xueqin either. We have also tested our method to the other three Great Classical Novels in Chinese. As expected no chrono-divides have been found. This provides further evidence of the robustness of our method.

cs.LG↗