title: Two Dimensional Yau-Hausdorff Distance with Applications on Comparison of DNA and Protein Sequences.
abstract: Comparing DNA or protein sequences plays an important role in the functional analysis of genomes. Despite many methods available for sequences comparison, few methods retain the information content of sequences. We propose a new approach, the Yau-Hausdorff method, which considers all translations and rotations when seeking the best match of graphical curves of DNA or protein sequences. The complexity of this method is lower than that of any other two dimensional minimum Hausdorff algorithm. The Yau-Hausdorff method can be used for measuring the similarity of DNA sequences based on two important tools: the Yau-Hausdorff distance and graphical representation of DNA sequences. The graphical representations of DNA sequences conserve all sequence information and the Yau-Hausdorff distance is mathematically proved as a true metric. Therefore, the proposed distance can preciously measure the similarity of DNA sequences. The phylogenetic analyses of DNA sequences by the Yau-Hausdorff distance show the accuracy and stability of our approach in similarity comparison of DNA or protein sequences. This study demonstrates that Yau-Hausdorff distance is a natural metric for DNA and protein sequences with high level of stability. The approach can be also applied to similarity analysis of protein sequences by graphic representations, as well as general two dimensional shape matching.
authors.affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China.
authors.forename: Kun
authors.initials: K
authors.lastname: Tian
authors.affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China.
authors.forename: Xiaoqian
authors.initials: X
authors.lastname: Yang
authors.affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China.
authors.forename: Qin
authors.initials: Q
authors.lastname: Kong
authors.affiliation: Department of Mathematics, Statistics and Computer Science, The University of Illinois at Chicago, Chicago, IL 60607-7045, United States of America.
authors.forename: Changchuan
authors.initials: C
authors.lastname: Yin
authors.affiliation: Department of Biological Sciences, Chicago State University, Chicago, IL 60628, United States of America.
authors.forename: Rong L
authors.initials: RL
authors.lastname: He
authors.affiliation: Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China.
authors.forename: Stephen S-T
authors.initials: SS
authors.lastname: Yau
mesh_terms: D008957:Models, Genetic; D010802:Phylogeny; D017422:Sequence Analysis, DNA / Q000379:methods*; D020539:Sequence Analysis, Protein / Q000379:methods*