Learning the Fréchet Mean over the Manifold of Symmetric Positive-Definite Matrices
نویسندگان
چکیده
منابع مشابه
Learning general Gaussian kernel hyperparameters of SVMs using optimization on symmetric positive-definite matrices manifold
We propose a new method for general Gaussian kernel hyperparameter optimization for support vector machines classification. The hyperparameters are constrained to lie on a differentiable manifold. The proposed optimization technique is based on a gradient-like descent algorithm adapted to the geometrical structure of the manifold of symmetric positive-definite matrices. We compare the performan...
متن کاملDeep Manifold Learning of Symmetric Positive Definite Matrices with Application to Face Recognition
In this paper, we aim to construct a deep neural network which embeds high dimensional symmetric positive definite (SPD) matrices into a more discriminative low dimensional SPD manifold. To this end, we develop two types of basic layers: a 2D fully connected layer which reduces the dimensionality of the SPD matrices, and a symmetrically clean layer which achieves non-linear mapping. Specificall...
متن کاملSupervised LogEuclidean Metric Learning for Symmetric Positive Definite Matrices
Metric learning has been shown to be highly effective to improve the performance of nearest neighbor classification. In this paper, we address the problem of metric learning for symmetric positive definite (SPD) matrices such as covariance matrices, which arise in many real-world applications. Naively using standard Mahalanobis metric learning methods under the Euclidean geometry for SPD matric...
متن کاملEmotion Recognition by Body Movement Representation on the Manifold of Symmetric Positive Definite Matrices
Emotion recognition is attracting great interest for its potential application in a multitude of real-life situations. Much of the Computer Vision research in this field has focused on relating emotions to facial expressions, with investigations rarely including more than upper body. In this work, we propose a new scenario, for which emotional states are related to 3D dynamics of the whole body...
متن کاملConic Geometric Optimization on the Manifold of Positive Definite Matrices
We develop geometric optimisation on the manifold of hermitian positive definite (hpd) matrices. In particular, we consider optimising two types of cost functions: (i) geodesically convex (g-convex); and (ii) log-nonexpansive (LN). G-convex functions are nonconvex in the usual euclidean sense, but convex along the manifold and thus allow global optimisation. LN functions may fail to be even g-c...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Cognitive Computation
سال: 2009
ISSN: 1866-9956,1866-9964
DOI: 10.1007/s12559-009-9026-7