The International Committee on Taxonomy of Viruses authorizes and organizes the taxonomic classification of viruses. Thus
far, the detailed classifications for all viruses are neither complete nor free from dispute. For example, the current missing
label rates in GenBank are 12.1% for family label and 30.0% for genus label. Using the proposed Natural Vector
representation, all 2,044 single-segment referenced viral genomes in GenBank can be embedded in R^12. Unlike other
approaches, this allows us to determine phylogenetic relations for all viruses at any level (e.g., Baltimore class, family,
subfamily, genus, and species) in real time. Additionally, the proposed graphical representation for virus phylogeny provides
a visualization of the distribution of viruses in R^12. Unlike the commonly used tree visualization methods which suffer from
uniqueness and existence problems, our representation always exists and is unique. This approach is successfully used to
predict and correct viral classification information, as well as to identify viral origins; e.g. a recent public health threat, the
West Nile virus, is closer to the Japanese encephalitis antigenic complex based on our visualization. Based on cross validation
results, the accuracy rates of our predictions are as high as 98.2% for Baltimore class labels, 96.6% for family
labels, 99.7% for subfamily labels and 97.2% for genus labels.
Current methods cannot tell us what the nature of the protein universe is concretely. They are based on different models of amino acid substitution and multiple sequence alignment which is an NP-hard problem and requires manual intervention. Protein structural analysis also gives a direction for mapping the protein universe. Unfortunately, now only a minuscule fraction of proteins' 3-dimensional structures are known. Furthermore, the phylogenetic tree representations are not unique for any existing tree construction methods. Here we develop a novel method to realize the nature of protein universe. We show the protein universe can be realized as a protein space in 60-dimensional Euclidean space using a distance based on a normalized distribution of amino acids. Every protein is in one-to-one correspondence with a point in protein space, where proteins with similar properties stay close together. Thus the distance between two points in protein space represents the biological distance of the corresponding two proteins. We also propose a natural graphical representation for inferring phylogenies. The representation is natural and unique based on the biological distances of proteins in protein space. This will solve the fundamental question of how proteins are distributed in the protein universe.