After a very long time, this will be my first post. I hope that it will not be the last, and the rest will come. For a project about taxi trajectory prediction, I have applied k-NN algorithm on coordinate sequence of taxi trips. Did I have promising results? Well, it is arguable, but I have discovered some good techniques. One of them is Z-order curve (Figure 1). Figure 1: Four levels of Z-ordering (taken from Wikipedia page) I was looking for a technique to decrease dimensionality of 2-D coordinate representation (lat-lon) into 1-D . But on this 1-D value, I would like to apply k-NN algorithm. For this purpose, 1-D values must preserve the closeness of two different coordinates. If I do linear ordering of latitude and longitude values, I couldn't achieve this goal, because closeness will depend on only one value which is placed on the right-most. Let's assume I do linear ordering as lat-lon:
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