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英文标题
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Probabilistic Riemannian quantification method with log-Euclidean metric learning
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作者英文名
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Zhang Xiaocheng, Tang Fengzhen
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机构英文名
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1.State Key Laboratory of Robotics,Shenyang Institute of Automation,Chinese Academy of Sciences,Shenyang 110016,China;2.Institutes for Robotics & Intelligent Manufacturing,Chinese Academy of Sciences,Shenyang 110169,China;3.University of Chinese Academy of Sciences,Beijing 100049,China
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英文摘要
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In many machine learning applications, the data may be symmetric positive definite(SPD) matrices which are not living in Euclidean space. This paper presented a new probabilistic Riemannian space quantization method based on log-Euclidean metric learning. The proposed method extended the Euclidean probabilistic learning vector quantization(PLVQ) method to deal with SPD matrices by treating them as points on the Riemannian manifold of SPD matrices equipped with log-Euclidean metric, through utilizing a parameterized distance function from log-Euclidean metric learning. On the BCI IV 2a dataset, the proposed method outperformed Euclidean PLVQ by 20% in terms of recognition accuracy. The proposed method also performs better than the first winner of BCI competition IV on this data set. It obtains comparable classification accuracy to PLVQ using affine invariant Riemannian metric, but requires much less computing time, i. e. only needs 1% of the training time, while 10% of the test time. The proposed method also obtains superior performance on the BCI III IIIa and ETH-80 datasets, showing its effectiveness and efficiency.
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英文关键词
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SPD matrix; LVQ; log-Euclidean metric; Riemannian geometry; manifold structure
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