Abstract
We propose a method for unsupervised group matching, which is the task of finding correspondence between groups across different domains without cross-domain similarity measurements or paired data. For example, the proposed method can find matching of topic categories in different languages without alignment information. The proposed method interprets a group as a probability distribution, which enables us to handle uncertainty in a limited amount of data, and to incorporate the high order information on groups. Groups are matched by maximizing the dependence between distributions, in which we use the Hilbert Schmidt independence criterion for measuring the dependence. By using kernel embedding which maps distributions into a reproducing kernel Hilbert space, we can calculate the dependence between distributions without density estimation. In the experiments, we demonstrate the effectiveness of the proposed method using synthetic and real data sets including an application to cross-lingual topic matching.
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Notes
More precisely, kernel k is called characteristic if the map \(\mathcal {P}\rightarrow {\mathcal {H}}_k: \mathbb {P}\rightarrow \mu _\mathbb {P}:= \int k(\cdot ,x) d\mathbb {P}(x)\) is injective. Thus, if we use a characteristic kernel, then the embedding \(\mu _\mathbb {P}\) uniquely identifies the underling distribution \(\mathbb {P}\).
A kernel is called universal if its associated RKHS is dense in the space of bounded continuous functions (Steinwart 2001).
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Iwata, T., Kanagawa, M., Hirao, T. et al. Unsupervised group matching with application to cross-lingual topic matching without alignment information. Data Min Knowl Disc 31, 350–370 (2017). https://doi.org/10.1007/s10618-016-0470-1
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DOI: https://doi.org/10.1007/s10618-016-0470-1