Comparison of dimension reduction methods for DEA under big data via Monte Carlo simulation

Data with large dimensions will bring various problems to the application of data envelopment analysis(DEA).In this study,we focus on a“big data”problem related to the considerably large dimensions of the input-output data.The four most widely used approaches to guide dimension reduction in DEA are compared via Monte Carlo simulation,including principal component analysis(PCA-DEA),which is based on the idea of aggregating input and output,efficiency contribution measurement(ECM),average efficiency measure(AEC),and regression-based detection(RB),which is based on the idea of variable selection.We compare the performance of these methods under different scenarios and a brand-new comparison benchmark for the simulation test.In addition,we discuss the effect of initial variable selection in RB for the first time.Based on the results,we offer guidelines that are more reliable on how to choose an appropriate method.

Motion Planning for Robots with Topological Dimension Reduction Method

This paper explores the realization of robotic motion planning, especially Findpath problem, which is a basic motion planning problem that arises in the development of robotics. Findpath means: Give the initial and desired final configurations of a robotic arm in 3-dimensionnl space, and give descriptions of the obstacles in the space, determine whether there is a continuous collision-free motion of the robotic arm from one configure- tion to the other and find such a motion if it exists. There are several branches of approach in motion planning area, but in reality the important things are feasibility, efficiency and accuracy of the method. In this paper ac- cording to the concepts of Configuration Space (C-Space) and Rotation Mapping Graph (RMG) discussed in [1], a topological method named Dimension Reduction Method (DRM) for investigating the connectivity of the RMG (or the topologic structure of the RMG )is presented by using topologic technique. Based on this ap- proach the Findpath problem is thus transformed to that of finding a connected way in a finite Characteristic Network (CN). The method has shown great potentiality in practice. Here a simulation system is designed to embody DRM and it is in sight that DRM can he adopted in the first overall planning of real robot sys- tem in the near future.

Decision Bayes Criteria for Optimal Classifier Based on Probabilistic Measures

This paper addresses the high dimension sample problem in discriminate analysis under nonparametric and supervised assumptions. Since there is a kind of equivalence between the probabilistic dependence measure and the Bayes classification error probability, we propose to use an iterative algorithm to optimize the dimension reduction for classification with a probabilistic approach to achieve the Bayes classifier. The estimated probabilities of different errors encountered along the different phases of the system are realized by the Kernel estimate which is adjusted in a means of the smoothing parameter. Experiment results suggest that the proposed approach performs well.

THE PERTURBATION PROBLEM OF AN ELLIPTIC SYSTEM WITH SOBOLEV CRITICAL GROWTH

In this paper,we study the following perturbation problem with Sobolev critical exponen t:{-Δu=(1+εK(x))u^2*-1+α/2*u^a-1v^3+εh(x)u^pP,x∈R^N,-Δu=(1+εQ(x))v^2*-1+β/2*u^B-1+εl(x)u^q,x∈R^N,u>0,v>0,x∈R^N where 0<p,q<1,α+β=2*:=2N/N-2,α,β≥3,4.Using a perturbation argument and a finite dimensional reduc tion met hod,we get the exis tence of positive solutions to problem(0.1)and the asymptotic property of the solutions.

Approximate contact solutions for non-axisymmetric homogeneous and power-law graded elastic bodies:A practical tool for design engineers and tribologists

In two recent papers,approximate solutions for compact non-axisymmetric contact problems of homogeneous and power-law graded elastic bodies have been suggested,which provide explicit analytical relations for the force–approach relation,the size and the shape of the contact area,as well as for the pressure distribution therein.These solutions were derived for profiles,which only slightly deviate from the axisymmetric shape.In the present paper,they undergo an extensive testing and validation by comparison of solutions with a great variety of profile shapes with numerical solutions obtained by the fast Fourier transform(FFT)-assisted boundary element method(BEM).Examples are given with quite significant deviations from axial symmetry and show surprisingly good agreement with numerical solutions.

A Topological Implementation for Motion Planning of a Robotic Arm

An efficient path planning algorithm based on topologic method is presented in this paper.The colli- sion free path planning for three-joint robotic arm consists of three parts:partition of C-space,construc- tion of CN and search for a path in CN.We mainly solved the problems of partitioning the C-space and judging the connectivity between connected blocks,etc.For the motion planning of a robotic arm with a gripper,we developed the concepts of global planning and local planning,and discussed the basic fac- tors for constructing the planning system.In the paper,some evaluation and analysis of the complexity and reliability of the algorithm are given,together with some ideas to improve the efficiency and increase the reliability.At last,some experimental results are presented to show the efficiency and accuracy of the nigorithm.

PCA for predicting quaternary structure of protein

The number and arrangement of subunits that form a protein are referred to as quaternary structure.Knowing the quaternary structure of an uncharacterized protein provides clues to finding its biological function and interaction process with other molecules in a biological system.With the explosion of protein sequences generated in the Post-Genomic Age,it is vital to develop an automated method to deal with such a challenge.To explore this prob-lem,we adopted an approach based on the pseudo position-specific score matrix(Pse-PSSM)descriptor,proposed by Chou and Shen,representing a protein sample.The Pse-PSSM descriptor is advantageous in that it can combine the evolution information and sequence-correlated informa-tion.However,incorporating all these effects into a descriptor may cause‘high dimension disaster’.To over-come such a problem,the fusion approach was adopted by Chou and Shen.A completely different approach,linear dimensionality reduction algorithm principal component analysis(PCA)is introduced to extract key features from the high-dimensional Pse-PSSM space.The obtained dimension-reduced descriptor vector is a compact repre-sentation of the original high dimensional vector.The jack-knife test results indicate that the dimensionality reduction approach is efficient in coping with complicated problems in biological systems,such as predicting the quaternary struc-ture of proteins.