What are the differences between Dynamic Time Warping and Needleman-Wunsch algorithm?
Both of these algorithms use dynamic programming to determine an alignment of sequential data. The major difference here is how the score for i,j is determined.
In Dynamic Time Warping, a cost (determined by a function of i, j) is added to the minimum value of the set (i-1, j), (i-1, j-1), (j, i-1).
In NW, the maximum of the set (i-1, j) + weight, (i-1, j-1) + S(Ai, Bi), (j, i-1) + weight is taken, such that S(A, B) is determined by a look up in the similarity matrix.
If you would like to make an alignment through enumerable space and can create a similarity matrix, (such as a protein sequence or words), use NW, however, if you are aligning data where you can't make a similarity matrix (like a time series), and need to use a function, go with DTW.
Alignments can be a tricky thing, and you may have to tweak parameters to get things right.
The fundamental difference between Dynamic Time Warping (DTW) and the Needleman-Wunsch algorithm (NW) is in the way the sequence elements are accounted for in the alignment.
A basic assumption of DTW is that one sequence is a "time-warped" version of the other, in the sense that the target sequence is either stretched (one-to-many alignment), condensed (many-to-one alignment), or non-warped (one-to-one alignment) with respect to the source sequence.
Thus, DTW is not compatible with the notion of gaps, where one or more elements in one sequence are not matched by any elements in the other sequence (one-to-none or none-to-one alignment). By contrast, NW accounts for gaps explicitly with a penalty that is not a function of the elements to be inserted/deleted.
If you need to align character sequences, DTW is only appropriate in the unlikely case that the sequences are strictly "time warped" versions of each other, such as "wow" and "wwooowww". As soon as one sequence contains elements that cannot be construed as the result of stretching the other sequence, such as the exclamation marks in "wow" vs "wwooowww!!!", DTW is not appropriate, since it forces you to define the cost of inserting a "!" in terms of the distance with respect to a "w" or an "o".