What would be the best known method to transform a gene or proteine sequence to some coordinate space (so $t(G)$ is the transformed sequence) complying to following rules:
- similar sequences (phylogeny, function, ...) are transformed to similar coordinates
- the coordinate system has fixed dimension
- if sequence $G_1$ is a subsequence of $G_2$, a similar rule applies to the coordinates, e.g. $t(G_1) < t(G_2)$ (component-wise or on one line with origin) (the reversal is not necessary)
- the transformation only depends on the transformed gene sequence
- if possible: an one-pass algorithm is possible
A simple approach of counting the n-grams or frequencies of all k-words in all gene sequences does fulfill rules 2. to 5., but not 1. only partly.
problem with metrics/distances
I found enough approaches to fulfill 1., but they all calculate some distance between 2 sequences -- that's painfull to calculate beforehand even for $10^6$ sequences, since we need to calculate said distance for every pair of sequences.