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首页> 外文期刊>Neural Networks and Learning Systems, IEEE Transactions on >Generalized Learning Riemannian Space Quantization: A Case Study on Riemannian Manifold of SPD Matrices
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Generalized Learning Riemannian Space Quantization: A Case Study on Riemannian Manifold of SPD Matrices

机译：广义学习黎曼空间量化：SPD矩阵riemananian歧管的案例研究

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摘要

Learning vector quantization (LVQ) is a simple and efficient classification method, enjoying great popularity. However, in many classification scenarios, such as electroencephalogram (EEG) classification, the input features are represented by symmetric positive-definite (SPD) matrices that live in a curved manifold rather than vectors that live in the flat Euclidean space. In this article, we propose a new classification method for data points that live in the curved Riemannian manifolds in the framework of LVQ. The proposed method alters generalized LVQ (GLVQ) with the Euclidean distance to the one operating under the appropriate Riemannian metric. We instantiate the proposed method for the Riemannian manifold of SPD matrices equipped with the Riemannian natural metric. Empirical investigations on synthetic data and real-world motor imagery EEG data demonstrate that the performance of the proposed generalized learning Riemannian space quantization can significantly outperform the Euclidean GLVQ, generalized relevance LVQ (GRLVQ), and generalized matrix LVQ (GMLVQ). The proposed method also shows competitive performance to the state-of-the-art methods on the EEG classification of motor imagery tasks.
机译：学习矢量量化（LVQ）是一种简单有效的分类方法，享有普及。然而，在许多分类场景中，例如脑电图（EEG）分类，输入特征由相对于弯曲歧管的对称正 - 定向（SPD）矩阵表示，而不是生活在欧氏空间中的载体。在本文中，我们提出了一种新的分类方法，用于生活在LVQ框架中的弯曲riemannian歧管中的数据点。所提出的方法将广义的LVQ（GLVQ）改变为欧几里德距离到适当的黎曼公制下运行的距离。我们实例化了具有riemannian自然度量的SPD矩阵的Riemannian歧管的提出方法。综合数据和现实世界运动图像的经验研究表明，建议的广义学习riemannian空间量化的性能可以显着优于Euclidean GLVQ，广义相关性LVQ（GRLVQ）和广义矩阵LVQ（GMLVQ）。该方法还对电动机图像任务的EEG分类的最先进方法表示竞争性能。

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