Metric Learning for Temporal Sequence Alignment
In this paper, we propose to learn a Mahalanobis distance to perform alignment of multivariate time series. The learning examples for this task are time series for which the true alignment is known. We cast the alignment problem as a structured prediction task, and propose realistic losses between alignments for which the optimization is tractable. We provide experiments on real data in the audio-toaudio context, where we show that the learning of a similarity measure leads to improvements in the performance of the alignment task. We also propose to use this metric learning framework to perform feature selection and, from basic audio features, build a combination of these with better alignment performance.
The paper proposes an approach for learning a Mahalanobis metric for sequence alignment using a structured output prediction framework. It proposes to exploit a symmetrized version of the area loss between two alignments and shows how to make its optimization tractable. The paper is roughly well written but could be improved. Few forward references (e.g. using notations that have not been already defined) make a linear reading difficult. Also few claims that I list below are not so clear would maybe require more comments. -	Page 4 : I am not sure why if one signal is a reference \alpha would be steadily increasing, which is required for the area loss to be linear in Y.-	Page 5 : Second formulation of the symmetrized loss, defined on \bar{Y}(X): The fact that you work on this second formulation of the loss means that you optimize on \bar{Y}(x) rather than on Y(X) ? On page 6 the optimization is indeed performed on \bar{Y}. How to you get a solution in Y at the end? The experimental section show improved results when using your approach (using l_S) enabling the combination of features on the two datasets that you use. I have yet a few comments.On the first dataset you do not provide the results of an approach using uniform loss (i.e. using squared Euclidean distance instead of Mahalanobis), and it seems that you do not provide the best results from [14] either. Maybe because your experiments are not fully comparable with that of [14]? Also it seems you get much different results on this dataset as the ones published in [14] when looking at the accuracies reached with isolated features. You should probably add a discussion on these differences. Also why don’t you provide any comparative results of l_O?On the second dataset, you almost reach the performance of the best single handcrafted feature with the combination of your standard features. I understand it is already a good result but would your approach be able to reach even better results by combining all these handcrafted features?More generally I am not fully convinced by the experiments which miss alternative baselines. Also if one compares such alignment scores to what is learned in Hidden Markov models (HMMs) the learning of the Mahalanobis metric appears as a very narrow topic. Indeed learning a Mahalanobis distance in a Dynamic Time Warping alignment procedure would correspond to using a shared covariance matrix for all Gaussian distribution in a HMM, which is known to be a poor choice. From this viewpoint the topic of the paper, although it is relevant and the proposed method is smart and principled, appears of moderate importance.Minor remarks-	Bottom page 2 : Last term in bottom of the page one guesses what #Y_{t,s} is as well as what s is but it is not introduced.-	Caption of Figure 1. o	Red upper -> red lowero	Blue lower -> blue uppero	\delta_{abs} is undefined at this point.-	Caption of figure 2o	“the most violated constrained” -> “the most violated constraint”o	You say first that “we have represented the most violated constrained at the end of learning, when the training loss is the Hamming one or the symmetrized area loss” where these two cases are indeed much different on the figure. And then you say “Note also that, in terms of Hamming loss the most violated contraint for l_S and the Hamming one are the same, while they differ much for the area loss.” which seems contradictory with the first sentence. -	Equation 6 : missing ^2 for the first norm term -	Page 8 : missing part in the sentence : “Note also that, in terms of Hamming loss the most violated contraint for l_S and the Hamming one are the same, while they differ much for the area loss.”