Probabilistic Learning Vector Quantization on Manifold of Symmetric Positive Definite Matrices

This idea was further extended in (Xie et al., 2017), where Symmetric positive definite (SPD) matrices are widely used sub-manifold learning for dimension reduction is used before data structures in many disciplines, e.g. in medical imaging the tangent space approximation. However, the first-order approximations (Penne et al., 2006) and computer vision as covariance region can lead to undesirable distortion, especially in descriptors (Tuzel et al., 2006; Jayasumana et al., 2015), regions far from the tangent space origin (Tuzel et al., 2008; as well as in brain-computer interface (BCI) (Congedo et al., Jayasumana et al., 2015). The mean of the SPD matrices is a 2017), etc. Endowed with an appropriate metric, SPD matrices frequently used candidate for the tangent space origin, however, form a curved Riemannian manifold. Consequently, many popular no theoretical proof exists to guarantee the mean yields the best machine learning algorithms such as linear discriminant tangent space approximation for the data (Tuzel et al., 2008).