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EnglishThis paper introduces a novel mathematical and computational framework, namely Log-Hilbert-Schmidt metric between positive definite operators on a Hilbert space. This is a generalization of the Log-Euclidean metric on the Rie-mannian manifold of positive definite matrices to the infinite-dimensional setting. The general framework is applied in particular to compute distances between co-variance operators on a Reproducing Kernel Hilbert Space (RKHS), for which we obtain explicit formulas via the corresponding Gram matrices. Empirically, we apply our formulation to the task of multi-category image classification, where each image is represented by an infinite-dimensional RKHS covariance operator. On several challenging datasets, our method significantly outperforms approaches based on covariance matrices computed directly on the original input features, including those using the Log-Euclidean metric, Stein and Jeffreys divergences, achieving new state of the art results.
| Titolo: | Log-Hilbert-Schmidt metric between positive definite operators on Hilbert spaces |
| Autori: | |
| Data di pubblicazione: | 2014 |
| Rivista: | |
| Handle: | http://hdl.handle.net/11562/961554 |
| Appare nelle tipologie: | 04.01 Contributo in atti di convegno |
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