### A Conjugate Property between Loss Functions and Uncertainty Sets in Classification Problems

"... In binary classification problems, mainly two approaches have been proposed; one is loss function approach and the other is minimum distance approach. The loss function approach is applied to major learning algorithms such as support vector machine (SVM) and boosting methods. The loss function repre ..."

Abstract
- Add to MetaCart

(Show Context)
In binary classification problems, mainly two approaches have been proposed; one is loss function approach and the other is minimum distance approach. The loss function approach is applied to major learning algorithms such as support vector machine (SVM) and boosting methods. The loss function represents the penalty of the decision function on the training samples. In the learning algorithm, the empirical mean of the loss function is minimized to obtain the classifier. Against a backdrop of the development of mathematical programming, nowadays learning algorithms based on loss functions are widely applied to real-world data analysis. In addition, statistical properties of such learning algorithms are well-understood based on a lots of theoretical works. On the other hand, some learning methods such as ν-SVM, mini-max probability machine (MPM) can be formulated as minimum distance problems. In the minimum distance approach, firstly, the so-called uncertainty set is defined for each binary label based on the training samples. Then, the best separating hyperplane between the two uncertainty sets is employed as the decision function. This is regarded as an extension of the maximum-margin approach. The minimum distance approach is considered to be useful to construct the statistical models with an intuitive geometric interpretation,

### Convex Optimization for the Design of Learning Machines

"... Abstract. This paper reviews the recent surge of interest in convex optimization in a context of pattern recognition and machine learning. The main thesis of this paper is that the design of task-specific learning machines is aided substantially by using a convex optimization solver as a back-end to ..."

Abstract
- Add to MetaCart

(Show Context)
Abstract. This paper reviews the recent surge of interest in convex optimization in a context of pattern recognition and machine learning. The main thesis of this paper is that the design of task-specific learning machines is aided substantially by using a convex optimization solver as a back-end to implement the task, liberating the designer from the concern of designing and analyzing an ad hoc algorithm. The aim of this paper is twofold: (i) it phrases the contributions of this ESANN 2007 special session in a broader context, and (ii) it provides a road-map to published resultsinthiscontext. 1

### A Multi-Class Support Vector Machine Based on Scatter Criteria

, 2009

"... We re-visit Support Vector Machines (SVMs) and provide a novel interpretation thereof in terms of weighted class means and scatter theory. The gained theoretical insight can be translated into a highly efficient extension to multi-class SVMs: mScatter-SVMs. Numerical simulations reveal that more tha ..."

Abstract
- Add to MetaCart

We re-visit Support Vector Machines (SVMs) and provide a novel interpretation thereof in terms of weighted class means and scatter theory. The gained theoretical insight can be translated into a highly efficient extension to multi-class SVMs: mScatter-SVMs. Numerical simulations reveal that more than an order of magnitude speed-up can be gained while the classification performance remains largely unchanged at the level of the classical one vs. rest and one vs. one implementation of multi-class SVMs.

### SEQUENTIAL MAXIMUM GRADIENT OPTIMIZATION FOR SUPPORT VECTOR DETECTION

"... Support Vector Machines (SVM) are playing an increasing role for detection problems in various engineering domains, notably in statistical signal processing, pattern recognition, image analysis, and communication systems. In this paper, we present a new method for optimizing Support Vector Machines ..."

Abstract
- Add to MetaCart

(Show Context)
Support Vector Machines (SVM) are playing an increasing role for detection problems in various engineering domains, notably in statistical signal processing, pattern recognition, image analysis, and communication systems. In this paper, we present a new method for optimizing Support Vector Machines for classification problems. An implicit reformulation of the optimization problem is proposed. The bias term is added to the primal problem formulation, which leads to eliminating the equality constraint. In order to deal with large data set problems, we propose a decomposition method, Sequential Maximum Gradient Optimization (SMGO), that relies on the selection of the working set via the search of the highest absolute values of the gradient. Furthermore, considering the quadratic nature of the dual problem, the optimum step-size is analytically determined. Moreover the solution, the gradient and the objective function are recursively calculated. The Gram matrix has not to be stored. SMGO is easy to implement and able to perform on large data sets. 1.

### 1Cognitive Radio Network as Wireless Sensor Network (III): Passive Target Intrusion Detection and Experimental Demonstration

"... for radio frequency (RF) passive target intrusion detection. Compared to a cheap WSN, the CRN based WSN is expected to deliver better results due to its strong communication functions and powerful computing ability. Issues addressed in this paper include experimental architecture, waveform design, a ..."

Abstract
- Add to MetaCart

(Show Context)
for radio frequency (RF) passive target intrusion detection. Compared to a cheap WSN, the CRN based WSN is expected to deliver better results due to its strong communication functions and powerful computing ability. Issues addressed in this paper include experimental architecture, waveform design, and machine learning algorithm for classification. In particular, passive target intrusion is experimentally demonstrated using multiple WARP platforms that serve as the cognitive/sensor nodes. In contrast to traditional localization methods relying on radio propagation properties, the technique used in this research is based on machine learning with measured data, considering complicated multipath environment and high dimensional sensing data col-lected by the CRN based WSN. Preliminary experimental results are quite encouraging, suggesting that a large-scale CRN based WSN supported by machine learning techniques has promising potential for passive target intrusion detection in harsh RF environments.

### 1Adaptive Kernel-based Image Denoising employing

"... Abstract—The main contribution of this paper is the develop-ment of a novel approach, based on the theory of Reproducing Kernel Hilbert Spaces (RKHS), for the problem of Noise Removal in the spatial domain. The proposed methodology has the advantage that it is able to remove any kind of additive noi ..."

Abstract
- Add to MetaCart

Abstract—The main contribution of this paper is the develop-ment of a novel approach, based on the theory of Reproducing Kernel Hilbert Spaces (RKHS), for the problem of Noise Removal in the spatial domain. The proposed methodology has the advantage that it is able to remove any kind of additive noise (impulse, gaussian, uniform, e.t.c.) from any digital image, in contrast to the most commonly used denoising techniques, which are noise-dependent. The problem is cast as an optimization task in a RKHS, by taking advantage of the celebrated Rep-resenter Theorem in its semi-parametric formulation. The semi-parametric formulation, although known in theory, has so far found limited, to our knowledge, application. However, in the image denoising problem its use is dictated by the nature of the problem itself. The need for edge preservation naturally leads to such a modeling. Examples verify that in the presence of gaussian noise the proposed methodology performs well compared to wavelet based technics and outperforms them significantly in the presence of impulse or mixed noise.

### Data Stream Classication for Structural Health Monitoring via On-line Support Vector Machines

"... Abstract—An important objective of building monitoring is to diagnose the building states and evaluate possible damage. This is a data classication problem. The building states come from many on-line sensors. Normal classication methods, such as support vector machine (SVM), cannot classify this lar ..."

Abstract
- Add to MetaCart

(Show Context)
Abstract—An important objective of building monitoring is to diagnose the building states and evaluate possible damage. This is a data classication problem. The building states come from many on-line sensors. Normal classication methods, such as support vector machine (SVM), cannot classify this large data stream. In this paper, the classical SVM is extended to an on-line classier (OLSVM). This SVM can classify large data stream directly. It is applied for on-line structural health monitoring. The experiment results of a lab scale prototype show the proposed algorithm can detect the damage with the data stream. This method can also be applied to big data classication, when the data set are transformed into a data stream. I.

### Geometric Intuition and Algorithms for Eν–SVM

"... In this work we address the Eν–SVM model proposed by Pérez–Cruz et al. as an extension of the traditional ν support vector classification model (ν–SVM). Through an enhancement of the range of admissible values for the regularization parameter ν, the Eν–SVM has been shown to be able to produce a wid ..."

Abstract
- Add to MetaCart

In this work we address the Eν–SVM model proposed by Pérez–Cruz et al. as an extension of the traditional ν support vector classification model (ν–SVM). Through an enhancement of the range of admissible values for the regularization parameter ν, the Eν–SVM has been shown to be able to produce a wider variety of decision functions, giving rise to a better adaptability to the data. However, while a clear and intuitive geometric interpretation can be given for the ν–SVM model as a nearest–point problem in reduced convex hulls (RCH–NPP), no previous work has been made in developing such intuition for the Eν– SVM model. In this paper we show how Eν–SVM can be reformulated as a geometrical problem that generalizes RCH–NPP, providing new insights into this model. Under this novel point of view, we propose the RapMinos algorithm, able to solve Eν–SVM more efficiently than the current methods. Furthermore, we show how RapMinos is able to address the Eν–SVM model for any choice of regularization norm `p≥1 seamlessly, which further extends the SVM model flexibility beyond the usual Eν–SVM models.

### SOLVING SUPPORT VECTOR MACHINE CLASSIFICATION PROBLEMS AND THEIR APPLICATIONS TO SUPPLIER SELECTION by

"... Recently, interdisciplinary (management, engineering, science, and economics) collaboration research has been growing to achieve the synergy and to reinforce the weakness of each discipline. Along this trend, this research combines three topics: mathematical programming, data mining, and supply chai ..."

Abstract
- Add to MetaCart

Recently, interdisciplinary (management, engineering, science, and economics) collaboration research has been growing to achieve the synergy and to reinforce the weakness of each discipline. Along this trend, this research combines three topics: mathematical programming, data mining, and supply chain management. A new pegging algorithm is developed for solving the continuous nonlinear knapsack problem. An efficient solving approach is proposed for solving the-support vector machine for classification problem in the field of data mining. The new pegging algorithm is used to solve the subproblem of the support vector machine problem. For the supply chain management, this research proposes an efficient integrated solving approach for the supplier selection problem. The support vector machine is applied to solve the problem of selecting potential supplies in the procedure of the integrated solving approach. In the first part of this research, a new pegging algorithm solves the continuous nonlinear knapsack problem with box constraints. The problem is to minimize a convex and differentiable nonlinear function with one equality constraint and box constraints. Pegging algorithm needs to