A comment on "A fast L_p spike alignment metric" by A. J. Dubbs, B. A. Seiler and M. O. Magnasco [arXiv:0907.3137]

Measuring the transmitted information in metric-based clustering has become something of a standard test for the performance of a spike train metric. In this comment, the recently proposed L_p Victor-Purpura metric is used to cluster spiking responses to zebra finch songs, recorded from field L of anesthetized zebra finch. It is found that for these data the L_p metrics with p>1 modestly outperform the standard, p=1, Victor-Purpura metric. It is argued that this is because for larger values of p, the metric comes closer to performing windowed coincidence detection.Comment: 9 pages, 3 figures included as late

Sequence alignment, mutual information, and dissimilarity measures for constructing phylogenies

Existing sequence alignment algorithms use heuristic scoring schemes which cannot be used as objective distance metrics. Therefore one relies on measures like the p- or log-det distances, or makes explicit, and often simplistic, assumptions about sequence evolution. Information theory provides an alternative, in the form of mutual information (MI) which is, in principle, an objective and model independent similarity measure. MI can be estimated by concatenating and zipping sequences, yielding thereby the "normalized compression distance". So far this has produced promising results, but with uncontrolled errors. We describe a simple approach to get robust estimates of MI from global pairwise alignments. Using standard alignment algorithms, this gives for animal mitochondrial DNA estimates that are strikingly close to estimates obtained from the alignment free methods mentioned above. Our main result uses algorithmic (Kolmogorov) information theory, but we show that similar results can also be obtained from Shannon theory. Due to the fact that it is not additive, normalized compression distance is not an optimal metric for phylogenetics, but we propose a simple modification that overcomes the issue of additivity. We test several versions of our MI based distance measures on a large number of randomly chosen quartets and demonstrate that they all perform better than traditional measures like the Kimura or log-det (resp. paralinear) distances. Even a simplified version based on single letter Shannon entropies, which can be easily incorporated in existing software packages, gave superior results throughout the entire animal kingdom. But we see the main virtue of our approach in a more general way. For example, it can also help to judge the relative merits of different alignment algorithms, by estimating the significance of specific alignments.Comment: 19 pages + 16 pages of supplementary materia