基于拉普拉斯矩阵的流形UniFrac算法  

A Manifold UniFrac Algorithm Based on the Laplacian Matrix

作　　者：范业田 宋博 FAN Ye-tian;SONG Bo(School of Mathematics and Statistics,Liaoning University,Shenyang 110036,China;College of Computing&Informatics,Drexel University,Philadelphia,PA 19104 USA)

机构地区：[1]辽宁大学数学与统计学院,辽宁沈阳110036 [2]德雷塞尔大学计算与信息学院,费城19104

出　　处：《辽宁大学学报(自然科学版)》2025年第1期79-85,共7页Journal of Liaoning University:Natural Sciences Edition

基　　金：教育部“春晖计划”合作科研项目(HZKY20220439)。

摘　　要：UniFrac距离是衡量微生物群落关系的重要且稳健的算法之一,它可以比较不同环境样本的微生物菌群组成,以分析微生物群落结构和功能多样性.但是现有算法没有考虑微生物菌群在生物流形上的分布,并且因为微生物菌群数据的维度高、系统发生树结构复杂,导致UniFrac算法的计算复杂度极高.为此,基于生物流形局部同构于欧式空间,本文提出了流形UniFrac算法,该算法利用局部生物流形上的UniFrac距离,将样本间的距离由局部推广到全局.此外,通过对流形UniFrac算法进行理论分析,发现其降低了算法的复杂度.数值实验表明,使用不同的UniFrac距离定义,流形UniFrac算法均可以提高微生物菌群的类聚集性,并且随着近邻阶数的增加,流形UniFrac的降维可视化结果可以逐渐收敛到原始UniFrac距离的降维可视化结果.UniFrac distance is an important and robust algorithm for measuring the relationship between microbial communities,which can compare the composition of microbial communities in different environmental samples to evaluate microbial communities’structure and functional diversity.However,the existing algorithms do not consider the distribution of microbial communities on the biological manifolds,and the computational complexity of UniFrac is high due to the high dimension of data and the complex structure of the phylogenetic tree.Inspired by the idea that biological manifolds are locally isomorphic to Euclidean space,we propose a manifold UniFrac algorithm in this paper,which calculates the UniFrac distances based on the local manifold and generalizes to the global distances.In addition,the theoretical analysis reveals that the manifold UniFrac algorithm can reduce the computational complexity.Finally,numerical experiments show that the proposed manifold UniFrac algorithm can improve the clustering performance of microbial communities based on different UniFrac distances.With the increasing order of neighbors,the visualization results of manifold UniFrac can converge to the original results.

关 键 词：UniFrac距离 流形 拉普拉斯矩阵 微生物组 

分 类 号：Q811.4[生物学—生物工程]