tuning gamma for tslearn.svm.TimeSeriesSVC - Question

[markus-mich]

Hello,

I have a small question about classifying multivariate time series using SVM. In tslearn, there is an option to classify time series or multivariate time series using tslearn.svm.TimeSeriesSVC. Here, according to the documentation, "gak" kernel is used. Now I haven't seen anywhere a detailed explanation how actually the parameter gamma works with this kernel "GAK". Should it always stay in the default value "auto"? Because I have used other gamma parameters like (0.1, 1, 10) but got very bad results compared to "auto". So I wanted to ask how the gamma works with this kernel and I haven't seen a formula anywhere. Or is there a specific article for this ?

Thanks in advance

[felixdivo]

As is stated in the documentation of TimeSeriesSVC, tslearn.metrics.gamma_soft_dtw is used to compute gamma:

gamma : float, optional (default=’auto’) Kernel coefficient for ‘gak’, ‘rbf’, ‘poly’ and ‘sigmoid’. If gamma is ‘auto’ then:

• for ‘gak’ kernel, it is computed based on a sampling of the training set (cf tslearn.metrics.gamma_soft_dtw)
• for other kernels (eg. ‘rbf’), 1/n_features will be used.

The method also references an original paper.

[rtavenar]

Hi,

You can find information on this kernel here, for example: https://marcocuturi.net/GA.html

In tslearn, we use the parameter $\gamma$ in place of $\sigma$ since it is the one used in recent related work by Cuturi and colleagues (softDTW), and the link between $\sigma$ and $\gamma$ is the following:

$\gamma = 2 \sigma^2$

Docs could probably be clearer on this point, any help on this would be welcome.