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I'm currently dealing with large DNA sequences for machine learning purposes, I'm basically improving existing methods.

What I have is several millions of DNA sequences : ACGTAGGCAGGCTTTC ...

In the methods I'm currently reviewing they extracts the features like this : for every nucleobase they put 4 features, the first corresponding to A, the second to C, the third to G and the last to T. If for exemple the current base is G the corresponding 4 features will be 0 0 1 0.

The problem I have with that is that it multiply the number of "effective" feature by four and it will be very sparse.

I was wondering if there would be any disadvantages to put one feature per nucleobase which would be 0, 1, 2, 3 depending on the letter.

It is applied to DNA but my question extend to every kind of discrete features.

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The clear disadvantage is that in the 0..4 encoding, the nucleotides corresponding to closer numbers will appear to be more similar, which is not necessarily true. E.g. if A=1, C=2, G=3 and T=4, then sequences AAAA and CCCC will be more similar than sequences AAAA and TTTT.

However, there is no necessity for four dimensions -- three dimensions are sufficient; you just use the coordinates of the vertices of a tetrahaedron:

A = (1,1,1)
C = (1,−1,−1)
G = (−1,1,−1)
T = (−1,−1,1)

In fact, this is not much different from dummy variable encoding. The reasons for chosing this path in variable encoding (rather than assigning a different number for each factor level) are the same as in the case above.

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