Probabilistic Learning Vector Quantization on Manifold of Symmetric Positive Definite Matrices
Shenyang Institute of Automation, Chinese Academy of Sciences（中国科学院沈阳自动化研究所）；Institutes for Robotics and Intelligent Manufacturing, Chinese Academy of Sciences（中国科学院机器人与智能制造创新研究院）；University of Chinese Academy of Sciences（中国科学院大学）；University of Birmingham（伯明翰大学）；Beijing Normal University（北京师范大学）；Zhejiang University（浙江大学）
Fengzhen Tang, Haifeng Feng, Peter Tino, Bailu Si, Daxiong Ji
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 EEG data demonstrate the superior performance of the proposed method.
We propose a novel algorithm for quantizing continuous latent representations in trained models. Our approach applies to deep probabilistic models, such as variational autoencoders (VAEs), and enables both data and model compression. Unlike current end-to-end neural compression methods that cater the model to a fixed quantization scheme, our algorithm separates model design and training from quantization. Consequently, our algorithm enables "plug-and-play" compression with variable rate-distortion trade-off, using a single trained model. Our algorithm can be seen as a novel extension of arithm…
Wrapped Gaussian on the manifold of Symmetric Positive Definite Matrices
LAMSADE, CNRS, PSL Univ. Paris-Dauphine, France（巴黎-萨克雷大学巴黎-达菲学院、国家科学研究中心、巴黎-达菲大学）；Inria center at the University of Bordeaux / LaBRI, France（波尔多大学/LaBRI与Inria中心）；TAU, LISN, University Paris-Saclay, France（巴黎-萨克雷大学、LISN、TAU）
