We review the existing alternatives for defining model-based distances for clustering sequences and propose a new one based on the Kullback-Leibler divergence. This distance is shown to be especially useful in combination with spectral clustering. For improved performance in real-world scenarios, a model selection scheme is also proposed.
Csiszár's f-divergence is a way to measure the similarity of two probability distributions. We study the extension of f-divergence to more than two distributions to measure their joint similarity. By exploiting classical results from the comparison of experiments literature we prove the resulting divergence satisfies all the same properties as the… (More)
We derive a generalized notion of f-divergences, called (f, l)-divergences. We show that this generalization enjoys many of the nice properties of f-divergences, although it is a richer family. It also provides alternative definitions of standard divergences in terms of surrogate risks. As a first practical application of this theory, we derive a new… (More)
This paper proposes a novel similarity measure for clustering sequential data. We first construct a common state space by training a single probabilistic model with all the sequences in order to get a unified representation for the dataset. Then, distances are obtained attending to the transition matrices induced by each sequence in that state space. This… (More)
We show that the variational representations for f-divergences currently used in the literature can be tightened. This has implications to a number of methods recently proposed based on this representation. As an example application we use our tighter representation to derive a general f-divergence esti-mator based on two i.i.d. samples and derive the dual… (More)