An information geometry approach to shape density Minimum Description Length model selection

Abstract

For advantages such as a richer representation power and inherent robustness to noise, probability density functions are becoming a staple for complex problems in shape analysis. We consider a principled and geometric approach to selecting the model order for a class of shape density models where the square-root of the distribution is expanded in an orthogonal series. The free parameters associated with these estimators can then be rigorously selected using the Minimum Description Length (MDL) criterion for model selection. Under these models, it is shown that the MDL has a closed-form representation, atypical for most applications of MDL in density estimation. We provide a straightforward application of our derivations by using this closed-from MDL criterion to select the optimal multiresolution level(s) for a class of square-root, wavelet density estimators. Experimental evaluation of our technique is conducted on one and two dimensional density estimation problems in shape analysis, with comparative analysis against other popular model selection criteria such as Bayesian and Akaike information criteria.

Target detection for THz radar based on information geometry

“…According to (11), the Riemannian mean R of N co mplex symmetric positive define matrices ( 1, 2,..., )…”

“…In 2011, Arshia Cont, Shlo mo Dubnov, and Gé rard Assayag proposed methods for information processing of audio stream using methods of information geometry and demonstrated on two sample applications for online audio structure discovery and audio matching [10]. Adrian M. Peter and Anand Rangarajan proposed an information geometry approach to shape density minimu m description length model selection [11]. In radar signal processing and data processing fields , Barbaresco studied wake vortex monitoring and Doppler imagin g processing based on information geo metry, his X-band radar experiments in Pairs airport show that information geo metry approach can improve the performance of Doppler detection and Doppler imaging processing.…”

Spherical Minimum Description Length

“…We now have all the ingredients necessary to evaluate Equation (38) for the constrained problem. Substituting Equations (40), (42) and (43) into Equation (38), we get…”

“…Since spherical MDL represents an asymptotic approximation of NML, it is more suitable when applied to large sample data. We refer the reader to [42,43] for more details regarding the issue of misspecification for high-dimensional models. The surface area of a hyperspherical manifold plotted against the cardinality of the parameters.…”