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Here too, spaced words was the best alignment-free method, followed by kmacs.
For each pattern length ℓ > k, spaced words outperformed the standard contiguous words (ℓ = k).
As in most previous examples, spaced words and kmacs outperformed other alignment-free approaches and, as on BAliBASE, kmacs was slightly better than spaced words if k was sufficiently large.
We show that the variance of N is smaller for spaced words than for contiguous words, and that the variance is further reduced if our spaced-words approach is used with multiple patterns of 'match positions' and 'don't care positions'.
In general, spaced words used with the single-pattern option is only slightly slower than the k-mer approach.
Surprisingly, on these benchmark sequences spaced words and kmacs even outperformed Clustal W and Maximum Likelihood, although not dramatically.
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To calculate the frequencies of spaced words in a sequence with respect to a pattern P, we implemented a hash function that maps each spaced word to an integer in.
While the expected number of (spaced) word matches is essentially the same for contiguous words and for spaced words of the corresponding weight, we have showed that the variance of N is considerably lower for spaced-words than for the traditionally used contiguous words.
Figure 2 shows that the distance matrices produced by Spaced-Words with the Jensen-Shannon divergence are worse than the distance matrices produced by most other methods, if these matrices are directly compared to the reference distance matrix.
The theoretical results of this study may be useful to find patterns or sets of patterns that minimize the variance of N to further improve our spaced-words approach.
The best method on this dataset was our previously developed spaced-words approach; the tree topology produced by this method precisely coincides with the topology of the reference tree, i.e. the RF distance is zero.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com