On robust estimation of the location parameter

This text, drawn from the author's lectures at the University of California at Berkeley, is intended as a textbook for a one-term course in basic ring theory. The material covered includes the Wedderburn-Artin theory of semi-simple rings, Jacobson's theory of the radical representation theory of groups and algebras, prime and semi-prime rings, primitive and semi-primitive rings, division rings, ordered rings, local and semi-local rings, and perfect and semi-perfect rings. By aiming the level of writing at the novice rather than at the expert, and by stressing the role of examples and motivation, the author has produced a text which is suitable not only for use in a graduate course, but also for self-study by other interested graduate students. Numerous exercises are also included. This graduate textbook on rings, fields and algebras is intended for graduate students in mathematics.

A first course in noncommutative rings, by T. Y. Lam. Pp. 385. £37 (pb), £62.50 (hb). 2001. ISBN 0 387 95325 6 (pb), 0 387 95183 0 (hb) (Springer-Verlag).

A comprehensive survey on support vector machine classification: Applications, challenges and trends

The problem of discriminating between two finite point sets in n-dimensional feature space by a separating plane that utilizes as few of the features as possible is formulated as a mathematical program with a parametric objective function and linear constraints. The step function that appears in the objective function can be approximated by a sigmoid or by a concave exponential on the nonnegative real line, or it can be treated exactly by considering the equivalent linear program with equilibrium constraints. Computational tests of these three approaches on publicly available real-world databases have been carried out and compared with an adaptation of the optimal brain damage method for reducing neural network complexity. One feature selection algorithm via concave minimization reduced cross-validation error on a cancer prognosis database by 35.4% while reducing problem features from 32 to 4.

Feature Selection via Mathematic Programming

With the fast expansion of renewable energy system installed capacity in recent years, the availability, stability, and quality of smart grids have become increasingly important. The renewable energy output forecasting applications have also been developing rapidly in recent years, and such techniques have particularly been applied in the fields of wind and solar photovoltaic (PV). In the case of solar PV output forecasting, many applications have been performed with machine learning and hybrid techniques. In this paper, we propose a high-precision deep neural network model named PVPNet to forecast PV system output power. The methodology behind the proposed model is based on deep neural networks, and the model is able to generate a 24-h probabilistic and deterministic forecasting of PV power output based on meteorological information, such as temperature, solar radiation, and historical PV system output data. The forecasting accuracy of PVPNet is determined by the mean absolute error (MAE) and root mean square error (RMSE) values. The results from the experiments show that the MAE and RMSE of the proposed algorithm are 109.4845 and 163.1513, respectively. The results prove that the prediction accuracy of the PVPNet outperforms other benchmark models, and the algorithm also effectively predicts complex time series with a high degree of volatility and irregularity.

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Multiple-Input Deep Convolutional Neural Network Model for Short-Term Photovoltaic Power Forecasting

MLTSVM: A novel twin support vector machine to multi-label learning

Robust L1-norm two-dimensional linear discriminant analysis

In this paper, we formulate a twin-type support vector machine for large-scale classification problems, called weighted linear loss twin support vector machine (WLTSVM). By introducing the weighted linear loss, our WLTSVM only needs to solve simple linear equations with lower computational cost, and meanwhile, maintains the generalization ability. So, it is able to deal with large-scale problems efficiently without any extra external optimizers. The experimental results on several benchmark datasets indicate that, comparing to TWSVM, our WLTSVM has comparable classification accuracy but with less computational time.

Weighted linear loss twin support vector machine for large-scale classification

In this paper, we propose a robust linear discriminant analysis (RLDA) through Bhattacharyya error bound optimization. RLDA considers a nonconvex problem with the $L_{1}$ -norm operation that makes it less sensitive to outliers and noise than the $L_{2}$ -norm linear discriminant analysis (LDA). In addition, we extend our RLDA to a sparse model (RSLDA). Both RLDA and RSLDA can extract unbounded numbers of features and avoid the small sample size (SSS) problem, and an alternating direction method of multipliers (ADMM) is used to cope with the nonconvexity in the proposed formulations. Compared with the traditional LDA, our RLDA and RSLDA are more robust to outliers and noise, and RSLDA can obtain sparse discriminant directions. These findings are supported by experiments on artificial data sets as well as human face databases.

Robust and Sparse Linear Discriminant Analysis via an Alternating Direction Method of Multipliers

In this paper, we propose a robust L1-norm non-parallel proximal support vector machine (L1-NPSVM), which aims at giving a robust performance for binary classification in contrast to GEPSVM, especially for the problem with outliers. There are three mainly properties of the proposed L1-NPSVM. Firstly, different from the traditional GEPSVM which solves two generalized eigenvalue problems, our L1-NPSVM solves a pair of L1-norm optimal problems by using a simple justifiable iterative technique. Secondly, by introducing the L1-norm, our L1-NPSVM is more robust to outliers than GEPSVM to a great extent. Thirdly, compared with GEPSVM, no parameters need to be regularized in our L1-NPSVM. The effectiveness of the proposed method is demonstrated by tests on a simple artificial example as well as on some UCI datasets, which shows the improvements of GEPSVM.

Chun-Na Li

Papers

MLTSVM: A novel twin support vector machine to multi-label learning

Robust L1-norm two-dimensional linear discriminant analysis

Weighted linear loss twin support vector machine for large-scale classification

Robust and Sparse Linear Discriminant Analysis via an Alternating Direction Method of Multipliers

Robust L1-norm non-parallel proximal support vector machine