Robust least squares projection twin SVM and its sparse solution

Least squares projection twin support vector machine(LSPTSVM)has faster computing speed than classical least squares support vector machine(LSSVM).However,LSPTSVM is sensitive to outliers and its solution lacks sparsity.Therefore,it is difficult for LSPTSVM to process large-scale datasets with outliers.In this paper,we propose a robust LSPTSVM model(called R-LSPTSVM)by applying truncated least squares loss function.The robustness of R-LSPTSVM is proved from a weighted perspective.Furthermore,we obtain the sparse solution of R-LSPTSVM by using the pivoting Cholesky factorization method in primal space.Finally,the sparse R-LSPTSVM algorithm(SR-LSPTSVM)is proposed.Experimental results show that SR-LSPTSVM is insensitive to outliers and can deal with large-scale datasets fastly.

DOA ESTIMATION USING A SPARSE LINEAR MODEL BASED ON EIGENVECTORS

To reduce high computational cost of existing Direction-Of-Arrival(DOA) estimation techniques within a sparse representation framework,a novel method with low computational com-plexity is proposed.Firstly,a sparse linear model constructed from the eigenvectors of covariance matrix of array received signals is built.Then based on the FOCal Underdetermined System Solver(FOCUSS) algorithm,a sparse solution finding algorithm to solve the model is developed.Compared with other state-of-the-art methods using a sparse representation,our approach also can resolve closely and highly correlated sources without a priori knowledge of the number of sources.However,our method has lower computational complexity and performs better in low Signal-to-Noise Ratio(SNR).Lastly,the performance of the proposed method is illustrated by computer simulations.

Sparse approximate solution of fitting surface to scattered points by MLASSO model

The goal of this paper is to achieve a computational model and corresponding efficient algorithm for obtaining a sparse representation of the fitting surface to the given scattered data. The basic idea of the model is to utilize the principal shift invariant(PSI) space and the l_1 norm minimization. In order to obtain different sparsity of the approximation solution, the problem is represented as a multilevel LASSO(MLASSO)model with different regularization parameters. The MLASSO model can be solved efficiently by the alternating direction method of multipliers. Numerical experiments indicate that compared to the AGLASSO model and the basic MBA algorithm, the MLASSO model can provide an acceptable compromise between the minimization of the data mismatch term and the sparsity of the solution. Moreover, the solution by the MLASSO model can reflect the regions of the underlying surface where high gradients occur.

I_(ϵ+)LGEA:A Learning-Guided Evolutionary Algorithm Based on I_(ϵ+) Indicator for Portfolio Optimization

Portfolio optimization is a classical and important problem in the field of asset management,which aims to achieve a trade-off between profit and risk.Previous portfolio optimization models use traditional risk measurements such as variance,which symmetrically delineate both positive and negative sides and are not practical and stable.In this paper,a new model with cardinality constraints is first proposed,in which the idiosyncratic volatility factor is used to replace traditional risk measurements and can capture the risks of the portfolio in a more accurate way.The new model has practical constraints which involve the sparsity and irregularity of variables and make it challenging to be solved by traditional Multi-Objective Evolutionary Algorithms(MOEAs).To solve the model,a Learning-Guided Evolutionary Algorithm based on I_(ϵ+)indicator(I_(ϵ+)LGEA)is developed.In I_(ϵ+)LGEA,the I_(ϵ+)indicator is incorporated into the initialization and genetic operators to guarantee the sparsity of solutions and can help improve the convergence of the algorithm.And a new constraint-handling method based on I_(ϵ+)indicator is also adopted to ensure the feasibility of solutions.The experimental results on five portfolio trading datasets including up to 1226 assets show that I_(ϵ+)LGEA outperforms some state-of-the-art MOEAs in most cases.