一个空间有效的字符串核框架
A framework for space-efficient string kernels
摘要：
字符串内核通常用于比较基因组规模的序列，其长度使得比对不切实际，但它们的计算基于空间效率低下或导致大幅减速的数据结构。我们表明，一些精确的字符串内核，如$k$ -mer内核，子串内核，一些长度加权内核，最小缺失字内核，和马尔可夫校正内核，都可以计算在$O(nd)$时间和$o(n)$空间位除了输入，只使用一个$\mathtt{rangeDistinct}$数据结构上的Burrows-Wheeler变换的输入字符串，其在其输出中的每个元素花费$O(d)$时间。相同的界限适用于基于$k$的多个值的组成复杂性的许多测量，如$k$ -聚体分布和$k$ -阶经验熵，以及用于使用数据校准$k$的值。
英文摘要：
String kernels are typically used to compare genome-scale sequences whose length makes alignment impractical, yet their computation is based on data structures that are either space-inefficient, or incur large slowdowns. We show that a number of exact string kernels, like the $k$-mer kernel, the substrings kernels, a number of length-weighted kernels, the minimal absent words kernel, and kernels with Markovian corrections, can all be computed in $O(nd)$ time and in $o(n)$ bits of space in addition to the input, using just a $\mathtt{rangeDistinct}$ data structure on the Burrows-Wheeler transform of the input strings, which takes $O(d)$ time per element in its output. The same bounds hold for a number of measures of compositional complexity based on multiple value of $k$, like the $k$-mer profile and the $k$-th order empirical entropy, and for calibrating the value of $k$ using the data.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
