A Bayesian Approach to Geometric
نویسنده
چکیده
| This paper presents a geometric approach to estimating subspaces as elements of complex Grassmann-manifold, with each subspace represented by its unique, complex projection matrix. Variation between the sub-spaces is modeled by rotating their projection matrices via the action of unitary matrices (elements of the unitary group (U(n))). Subspace estimation or tracking then corresponds to the inferences on U(n). Taking a Bayesian approach, a posterior density is derived on U(n) and certain expectations under this posterior are empirically generated. For the choice of Hilbert-Schmidt norm on U(n), to deene estimation errors, an optimal MMSE estimator is derived. It is shown that this estimator achieves a lower bound, deened on the expected squared-errors associated with all possible estimators. The estimator and the bound are computed using (Metropolis-Adjusted) Langevin's-diiusion algorithm for sampling from the posterior. For use in subspace tracking a prior model on subspace rotation, that utilizes New-tonian dynamics, is suggested.
منابع مشابه
A BAYESIAN APPROACH TO COMPUTING MISSING REGRESSOR VALUES
In this article, Lindley's measure of average information is used to measure the information contained in incomplete observations on the vector of unknown regression coefficients [9]. This measure of information may be used to compute the missing regressor values.
متن کاملA Bayesian Networks Approach to Reliability Analysis of a Launch Vehicle Liquid Propellant Engine
This paper presents an extension of Bayesian networks (BN) applied to reliability analysis of an open gas generator cycle Liquid propellant engine (OGLE) of launch vehicles. There are several methods for system reliability analysis such as RBD, FTA, FMEA, Markov Chains, and etc. But for complex systems such as LV, they are not all efficiently applicable due to failure dependencies between compo...
متن کاملA Probabilistic Bayesian Classifier Approach for Breast Cancer Diagnosis and Prognosis
Basically, medical diagnosis problems are the most effective component of treatment policies. Recently, significant advances have been formed in medical diagnosis fields using data mining techniques. Data mining or Knowledge Discovery is searching large databases to discover patterns and evaluate the probability of next occurrences. In this paper, Bayesian Classifier is used as a Non-linear dat...
متن کاملImproving the Performance of Bayesian Estimation Methods in Estimations of Shift Point and Comparison with MLE Approach
A Bayesian analysis is used to detect a change-point in a sequence of independent random variables from exponential distributions. In This paper, we try to estimate change point which occurs in any sequence of independent exponential observations. The Bayes estimators are derived for change point, the rate of exponential distribution before shift and the rate of exponential distribution after s...
متن کاملA Probabilistic Bayesian Classifier Approach for Breast Cancer Diagnosis and Prognosis
Basically, medical diagnosis problems are the most effective component of treatment policies. Recently, significant advances have been formed in medical diagnosis fields using data mining techniques. Data mining or Knowledge Discovery is searching large databases to discover patterns and evaluate the probability of next occurrences. In this paper, Bayesian Classifier is used as a Non-linear dat...
متن کاملRisk Analysis of Operating Room Using the Fuzzy Bayesian Network Model
To enhance Patient’s safety, we need effective methods for risk management. This work aims to propose an integrated approach to risk management for a hospital system. To improve patient’s safety, we should develop flexible methods where different aspects of risk and type of information are taken into consideration. This paper proposes a fuzzy Bayesian network to model and analyze risk in the op...
متن کامل