Based on the k-mer model for protein sequence, a novel k-mer natural vector method is proposed to characterize the features of k-mers in a protein sequence, in which the numbers and distributions of k-mers are considered. It is proved that the relationship between a protein sequence and its k-mer natural vector is one-to-one. Phylogenetic analysis of protein sequences therefore can be easily performed without requiring evolutionary models or human intervention. In addition, there exists no a criterion to choose a suitable k, and k has a great influence on obtaining results as well as computational complexity. In this paper, a compound k-mer natural vector is utilized to quantify each protein sequence. The results gotten from phylogenetic analysis on three protein datasets demonstrate that our new method can precisely describe the evolutionary relationships of proteins, and greatly heighten the computing efficiency.
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