Probabilistic learning vector quantization on manifold of symmetric positive definite matrices

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