Dimensionality Reduction of SPD Data Based on Riemannian Manifold Tangent Spaces and Isometry

Symmetric positive definite (SPD) data have become a hot topic in machine learning. Instead of a linear Euclidean space, SPD data generally lie on a nonlinear Riemannian manifold. To get over the problems caused by the high data dimensionality, dimensionality reduction (DR) is a key subject for SPD data, where bilinear transformation plays a vital role. Because linear operations are not supported in nonlinear spaces such as Riemannian manifolds, directly performing Euclidean DR methods on SPD matrices is inadequate and difficult in complex models and optimization. An SPD data DR method based on Riemannian manifold tangent spaces and global isometry (RMTSISOM-SPDDR) is proposed in this research. The main contributions are listed: (1) Any Riemannian manifold tangent space is a Hilbert space isomorphic to a Euclidean space. Particularly for SPD manifolds, tangent spaces consist of symmetric matrices, which can greatly preserve the form and attributes of original SPD data. For this reason, RMTSISOM-SPDDR transfers the bilinear transformation from manifolds to tangent spaces. (2) By log transformation, original SPD data are mapped to the tangent space at the identity matrix under the affine invariant Riemannian metric (AIRM). In this way, the geodesic distance between original data and the identity matrix is equal to the Euclidean distance between corresponding tangent vector and the origin. (3) The bilinear transformation is further determined by the isometric criterion guaranteeing the geodesic distance on high-dimensional SPD manifold as close as possible to the Euclidean distance in the tangent space of low-dimensional SPD manifold. Then, we use it for the DR of original SPD data. Experiments on five commonly used datasets show that RMTSISOM-SPDDR is superior to five advanced SPD data DR algorithms.     

氚增殖剂球床内氦气流动特性的数值模拟

通过计算流体力学(CFD)数值模拟方法,对氚增殖剂球床内部的氦气流动特性进行了初步研究。分析了球床流通长度和流通截面对提氚气体压降的影响,获得了不同入口流速下规则堆积球床和随机堆积球床的压降和阻力系数。      

Millimeter and submillimeter wave measurements of complex optical and dielectric parameters of materials

These two promising millimeter wave materials were found to exhibit one order of magnitude higher absorption coefficient than the common low-loss ceramics such as alumina, fused silica and beryllia. A modular, polarizing, dispersive Fourier transform spectrometer capable of operating over the range 5 mm to 0.004 mm was used to provide a continuous spectrum of the refractive index and absorption coefficient to an accuracy of five decimal places and less than 1 percent, respectively.Partially supported by the U.S. Army Research Office under Contract Number DAAG-29-81-K-0009 and the Office of Fusion Energy, U.S. Department of Energy, under Contract W-7405-eng-26 with Union Carbide Corporation.Supported by the National Science Foundation.     

Directionally differentiable multiobjective optimization involving discrete inclusions

This paper is devoted to multiobjective optimization problems involving discrete inclusions. The objective functions are assumed to be directionally differentiable and the domination structure is defined by a closed convex cone. The directional derivatives are not assumed to be linear or convex. Several concepts of optimal solutions are analyzed, and the corresponding necessary conditions are obtained as well in maximum principle form. As an application of the main results, a maximum principle is also derived for multiobjective optimization with extremalvalue fucctions involving discrete inclusions.The authors are indebted to the referee for detailed comments.The paper was written while the second author was visiting the laboratory of Prof. S. Suzuki, Department of Mechanical Engineering, Sophia University, Tokyo, Japan.     

Optical time-domain reflectometry for distributed sensing of the structural strain and deformation

A unique structure of microbend optical fiber sensor (MOFS) for measuring tensile and compressive strain is described in this paper. The average measuring sensitivity for tensile strain is 35μ using 3 MOFS arrays. The repeatability and stability of MFOS are better than 18μ. The loss sensitivity of single-mode (SM) fiber and multi-mode (MM) fiber used in MOFS, as well as the relationship between the pulse width of diode laser and loss sensitivity are also studied in this paper. From these studies, some conclusions have been obtained. They are (1) the loss sensitivity and repeatability of SM fiber are better when compared to MM fiber in MOFS, and (2) the variation of pulse width of laser would only influent the signal-to-noise ratio and dynamic range, but has no contribution to loss sensitivity. Experimental results also show that loss of SM fiber highly depends on the wavelength of laser, but MM fiber has no such property. The loss of SM fiber between the wavelength of 1550 and 1310 nm is about the ratio of 6.5. Therefore, the experiments reported in this paper used a wavelength of 1310 nm to measure tensile strain and 1550 nm to measure compressive strain based on the above property of SM fiber, without changing the configuration of MOFS.     

Wald意义下的局部π-Bayes最优决策

本文在某些必要的适当条件下,采用一种独特的方式证明Wald意义下的最优决策的存在性.并表明:Wald意义下的最优决策作为一种π-Bayes最优决策实际上是局部的.     

Rejoinder on “Learning from imprecise and fuzzy observations: Data disambiguation through generalized loss minimization”

This is a short note in which I reply to the comments and suggestions made by Luciano Sánchez, Sebastian Destercke and Didier Dubois on my article “Learning from Imprecise and Fuzzy Observations: Data Disambiguation through Generalized Loss Minimization”.     

Optimal portfolio choice for an insurer with loss aversion

The problem of optimal investment for an insurance company attracts more attention in recent years. In general, the investment decision maker of the insurance company is assumed to be rational and risk averse. This is inconsistent with non fully rational decision-making way in the real world. In this paper we investigate an optimal portfolio selection problem for the insurer. The investment decision maker is assumed to be loss averse. The surplus process of the insurer is modeled by a Lévy process. The insurer aims to maximize the expected utility when terminal wealth exceeds his aspiration level. With the help of martingale method, we translate the dynamic maximization problem into an equivalent static optimization problem. By solving the static optimization problem, we derive explicit expressions of the optimal portfolio and the optimal wealth process.     

A study of the effect of the loss function on Bayes Estimate,posterior risk and hazard function for Lindley distribution

In this paper, mathematical properties of Lindley distribution via Bayesian approach are derived under different loss functions. These properties include: Bayes Estimators, posterior risks and failure rate function for simulation scheme. Elicitation of hyperparameters is also discussed. A real life application to waiting time data at the bank is also described for the developed procedures (also using WinBUGS). Results are compared on the basis of posterior risk.     

多维线性模型均值矩阵的线性Minimax估计

本研究多维线性模型中均值矩阵在不同损失函数下的线性Ｍｉｎｉｍａｘ估计,得到了具体的表达式。