scholarly journals Towards Generalized and Efficient Metric Learning on Riemannian Manifold

2018 ◽  
Author(s):  
Pengfei Zhu ◽  
Hao Cheng ◽  
Qinghua Hu ◽  
Qilong Wang ◽  
Changqing Zhang
Keyword(s):  
Riemannian Manifold ◽  
Visual Recognition ◽  
High Efficiency ◽  
Geodesic Distance ◽  
Metric Learning ◽  
Closed Form Solution ◽  
Form Solution ◽  
Dissimilarity Matrix ◽  
Modeling Data ◽  
Nonlinear Manifolds

Modeling data as points on non-linear Riemannian manifold has attracted increasing attentions in many computer vision tasks, especially visual recognition. Learning an appropriate metric on Riemannian manifold plays a key role in achieving promising performance. For widely used symmetric positive definite (SPD) manifold and Grassmann manifold, most of existing metric learning methods are designed for one manifold, and are not straightforward for the other one. Furthermore, optimizations in previous methods usually rely on computationally expensive iterations. To address above limitations, this paper makes an attempt to propose a generalized and efficient Riemannian manifold metric learning (RMML) method, which can be flexibly adopted to both SPD and Grassmann manifolds. By minimizing the geodesic distance of similar pairs and the interpoint geodesic distance of dissimilar ones on nonlinear manifolds, the proposed RMML is optimized by computing the geodesic mean between inverse of similarity matrix and dissimilarity matrix, benefiting a global closed-form solution and high efficiency. The experiments are conducted on various visual recognition tasks, and the results demonstrate our RMML performs favorably against its counterparts in terms of both accuracy and efficiency.

scholarly journals Extrinsic Least Squares Regression with Closed-Form Solution on Product Grassmann Manifold for Video-Based Recognition

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Yuping Wang ◽  
Lichun Wang ◽  
Dehui Kong ◽  
Baocai Yin
Keyword(s):  
Least Squares ◽  
Closed Form ◽  
Visual Recognition ◽  
Grassmann Manifold ◽  
Geodesic Distance ◽  
Closed Form Solution ◽  
Form Solution ◽  
Multidimensional Data ◽  
Least Squares Regression ◽  
Training Samples

Least squares regression is a fundamental tool in statistical analysis and is more effective than some complicated models with small number of training samples. Representing multidimensional data with product Grassmann manifold has recently led to notable results in various visual recognition tasks. This paper proposes extrinsic least squares regression with Projection Metric on product Grassmann manifold by embedding Grassmann manifold into the space of symmetric matrices via an isometric mapping. The proposed regression has closed-form solution which is more accurate compared with numerical solution of previous least squares regression using geodesic distance. Experiments on several recognition tasks show that the proposed method achieves considerable accuracy in comparison with some state-of-the-art methods.

scholarly journals OPML: A one-pass closed-form solution for online metric learning

2018 ◽  
Vol 75 ◽  
pp. 302-314 ◽  
Author(s):  
Wenbin Li ◽  
Yang Gao ◽  
Lei Wang ◽  
Luping Zhou ◽  
Jing Huo ◽  
...  
Keyword(s):  
Closed Form ◽  
Metric Learning ◽  
Closed Form Solution ◽  
Form Solution ◽  
Online Metric Learning

scholarly journals A Nonlinear Circuit Analysis Technique for Time-Variant Inductor Systems

Sensors ◽  
2019 ◽  
Vol 19 (10) ◽  
pp. 2321 ◽  
Author(s):  
Xinning Wang ◽  
Chong Li ◽  
Dalei Song ◽  
Robert Dean
Keyword(s):  
Closed Form ◽  
Eddy Currents ◽  
High Efficiency ◽  
Nonlinear Differential Equations ◽  
Closed Form Solution ◽  
Form Solution ◽  
Circuit Analysis ◽  
Nonlinear Method ◽  
Sensors And Actuators ◽  
Computation Efficiency

Time-variant inductors exist in many industrial applications, including sensors and actuators. In some applications, this characteristic can be deleterious, for example, resulting in inductive loss through eddy currents in motors designed for high efficiency operation. Therefore, it is important to investigate the electrical dynamics of systems with time-variant inductors. However, circuit analysis with time-variant inductors is nonlinear, resulting in difficulties in obtaining a closed form solution. Typical numerical algorithms used to solve the nonlinear differential equations are time consuming and require powerful processors. This investigation proposes a nonlinear method to analyze a system model consisting of the time-variant inductor with a constraint that the circuit is powered by DC sources and the derivative of the inductor is known. In this method, the Norton equivalent circuit with the time-variant inductor is realized first. Then, an iterative solution using a small signal theorem is employed to obtain an approximate closed form solution. As a case study, a variable inductor, with a time-variant part stimulated by a sinusoidal mechanical excitation, is analyzed using this approach. Compared to conventional nonlinear differential equation solvers, this proposed solution shows both improved computation efficiency and numerical robustness. The results demonstrate that the proposed analysis method can achieve high accuracy.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

Plane Wave Resonance in the Tire Air Cavity as a Vehicle Interior Noise Source

1995 ◽  
Vol 23 (1) ◽  
pp. 2-10 ◽  
Author(s):  
J. K. Thompson
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Interior Noise ◽  
Cavity Resonance ◽  
Test Results ◽  
Vehicle Interior ◽  
Air Cavity ◽  
Vehicle Interior Noise ◽  
Wave Resonance ◽  
Resonance Frequencies

Abstract Vehicle interior noise is the result of numerous sources of excitation. One source involving tire pavement interaction is the tire air cavity resonance and the forcing it provides to the vehicle spindle: This paper applies fundamental principles combined with experimental verification to describe the tire cavity resonance. A closed form solution is developed to predict the resonance frequencies from geometric data. Tire test results are used to examine the accuracy of predictions of undeflected and deflected tire resonances. Errors in predicted and actual frequencies are shown to be less than 2%. The nature of the forcing this resonance as it applies to the vehicle spindle is also examined.

Capacity Analysis for Correlated Multi-Hop MIMO Channels under Colored Noise

2015 ◽  
Vol 1 ◽  
pp. 41
Author(s):  
Nguyen N. Tran ◽  
Ha X. Nguyen
Keyword(s):  
Computational Complexity ◽  
Mutual Information ◽  
Closed Form Solution ◽  
Optimal Solution ◽  
Form Solution ◽  
Maximization Problem ◽  
Capacity Analysis ◽  
Mimo Channels ◽  
Average Mutual Information ◽  
Channel Output

A capacity analysis for generally correlated wireless multi-hop multi-input multi-output (MIMO) channels is presented in this paper. The channel at each hop is spatially correlated, the source symbols are mutually correlated, and the additive Gaussian noises are colored. First, by invoking Karush-Kuhn-Tucker condition for the optimality of convex programming, we derive the optimal source symbol covariance for the maximum mutual information between the channel input and the channel output when having the full knowledge of channel at the transmitter. Secondly, we formulate the average mutual information maximization problem when having only the channel statistics at the transmitter. Since this problem is almost impossible to be solved analytically, the numerical interior-point-method is employed to obtain the optimal solution. Furthermore, to reduce the computational complexity, an asymptotic closed-form solution is derived by maximizing an upper bound of the objective function. Simulation results show that the average mutual information obtained by the asymptotic design is very closed to that obtained by the optimal design, while saving a huge computational complexity.

scholarly journals Geometric Average Asian Option Pricing with Paying Dividend Yield under Non-Extensive Statistical Mechanics for Time-Varying Model

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 828 ◽  
Author(s):  
Jixia Wang ◽  
Yameng Zhang
Keyword(s):  
Statistical Mechanics ◽  
Option Pricing ◽  
Asset Price ◽  
Closed Form Solution ◽  
Real Data ◽  
Form Solution ◽  
Asian Option ◽  
Time Varying ◽  
Dividend Yield ◽  
Geometric Average

This paper is dedicated to the study of the geometric average Asian call option pricing under non-extensive statistical mechanics for a time-varying coefficient diffusion model. We employed the non-extensive Tsallis entropy distribution, which can describe the leptokurtosis and fat-tail characteristics of returns, to model the motion of the underlying asset price. Considering that economic variables change over time, we allowed the drift and diffusion terms in our model to be time-varying functions. We used the I t o ^ formula, Feynman–Kac formula, and P a d e ´ ansatz to obtain a closed-form solution of geometric average Asian option pricing with a paying dividend yield for a time-varying model. Moreover, the simulation study shows that the results obtained by our method fit the simulation data better than that of Zhao et al. From the analysis of real data, we identify the best value for q which can fit the real stock data, and the result shows that investors underestimate the risk using the Black–Scholes model compared to our model.

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