As shown in previous work discussed above [3,9,14-16], the fact that similar sequence distance is not equidistant (Euclidean) to the preceding position is a serious limitation to sequence comparison. On the other hand, it was also shown [17] that pursuing discriminant analysis using representations that are not constrained by predefined scales or succession orders, even when those scales are systematically screened such as in variable length Markov models [18-20], leads to more accurate models of sequences. The two results put together point to the need for a density kernel that resolves scale (succession order) such that predictive patterns can be investigated more efficiently in the iterative map representation.