From differential to information geometry

Target detection for THz radar based on information geometry

“…It is important to compute Riemannian mean in the framework of information geo metry. This problem can be solved by a new gradient descent algorithm [6,7]. The N normal distributions ( ) , 1,..., In order to compute Riemannian mean, direct taking advantage of the geodesic equation [6], we could identify the tangent vector v with the opposite of the gradient of the objective function 12 ( , , .... , ) N J R R R .…”

“…This problem can be solved by a new gradient descent algorithm [6,7]. The N normal distributions ( ) , 1,..., In order to compute Riemannian mean, direct taking advantage of the geodesic equation [6], we could identify the tangent vector v with the opposite of the gradient of the objective function 12 ( , , .... , ) N J R R R . In this case, the result of computing Riemannian mean by gradient descent algorithm is accordance with that based on Jacobi field and exponential map [8].…”

“…Pennec constructed statistical tools on n-dimension Riemannian manifold and defined Karcher mean [5]. Felix Opitz discussed the analogy between differential and informat ion geometry [6].Those concepts on statistical manifold greatly extend the application scope of statistical manifo ld and develop information geometry. In the past two decades, information geometry has been applied to a variety of fields : statistical This work is supported by the Fundamental Research Funds for the Central Universities under Projects ZYGX2012J029 inference [3], control theory, neural network [3], medical imaging [7], signal processing [8], statistical physics, high level computational vision [9] and so on.…”