Probabilistic learning vector quantization on manifold of symmetric positive definite matrices. (October 2021)

• Record Type: Journal Article
• Authors: Tang, Fengzhen; Feng, Haifeng; Tino, Peter; Si, Bailu; Ji, Daxiong
• Is Part Of: Neural networks. Volume 142(2021)
• Page Start: 105
• Page End: 118
• Publication Date: 2021-10
• Subjects: Probabilistic learning vector quantization -- Learning vector quantization -- Symmetric positive definite matrices -- Riemannian geodesic distances -- Riemannian manifold; Neural computers -- Periodicals; Neural networks (Computer science) -- Periodicals; Neural networks (Neurobiology) -- Periodicals; Nervous System -- Periodicals; Ordinateurs neuronaux -- Périodiques; Réseaux neuronaux (Informatique) -- Périodiques; Réseaux neuronaux (Neurobiologie) -- Périodiques; Neural computers; Neural networks (Computer science); Neural networks (Neurobiology); Periodicals; 006.32
• DOI: 10.1016/j.neunet.2021.04.024
• Languages: English
• ISSNs: 0893-6080

Abstract

Abstract: In this paper, we develop a new classification method for manifold-valued data in the framework of probabilistic learning vector quantization. In many classification scenarios, the data can be naturally represented by symmetric positive definite matrices, which are inherently points that live on a curved Riemannian manifold. Due to the non-Euclidean geometry of Riemannian manifolds, traditional Euclidean machine learning algorithms yield poor results on such data. In this paper, we generalize the probabilistic learning vector quantization algorithm for data points living on the manifold of symmetric positive definite matrices equipped with Riemannian natural metric (affine-invariant metric). By exploiting the induced Riemannian distance, we derive the probabilistic learning Riemannian space quantization algorithm, obtaining the learning rule through Riemannian gradient descent. Empirical investigations on synthetic data, image data, and motor imagery electroencephalogram (EEG) data demonstrate the superior performance of the proposed method.