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**1 - 7**of**7**### A geometric approach to support vector machine (svm) classification

- IEEE Transactions on Neural Networks

"... Classification ..."

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### SVM-Geom-IEEE_rev1c.doc

"... Abstract-The geometric framework for the SVM classification problem provides an intuitive ground for the understanding and the application of geometric optimization algorithms, leading to practical solutions of real world classification problems. In this work, the notion of "reduced convex hul ..."

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Abstract-The geometric framework for the SVM classification problem provides an intuitive ground for the understanding and the application of geometric optimization algorithms, leading to practical solutions of real world classification problems. In this work, the notion of "reduced convex hull" is employed and supported by a set of new theoretical results. These results allow existing geometric algorithms to be directly and practically applied to solve not only separable, but also non-separable classification problems both accurately and efficiently. As a practical application of the new theoretical results, a known geometric algorithm has been employed and transformed accordingly to solve non-separable problems successfully.

### STRICT MAXIMUM SEPARABILITY OF TWO FINITE SETS: AN ALGORITHMIC APPROACH

"... The paper presents a recursive algorithm for the investigation of a strict, linear separation in the Euclidean space. In the case when sets are linearly separable, it allows us to determine the coefficients of the hyperplanes. An example of using this algorithm as well as its drawbacks are shown. Th ..."

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The paper presents a recursive algorithm for the investigation of a strict, linear separation in the Euclidean space. In the case when sets are linearly separable, it allows us to determine the coefficients of the hyperplanes. An example of using this algorithm as well as its drawbacks are shown. Then the algorithm of determining an optimal separation (in the sense of maximizing the distance between the two sets) is presented.

### SUPPORT VECTOR MACHINE (SVM) CLASSIFICATION THROUGH GEOMETRY

"... Support Vector Machines is a very attractive and useful tool for classification and regression; however, since they rely on subtle and complex algebraic notions of optimization theory, lose their elegance and simplicity when implementation is concerned. It has been shown that the SVM solution, for t ..."

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Support Vector Machines is a very attractive and useful tool for classification and regression; however, since they rely on subtle and complex algebraic notions of optimization theory, lose their elegance and simplicity when implementation is concerned. It has been shown that the SVM solution, for the case of separate classes, corresponds to the minimum distance between the respective convex hulls. For the nonseparable case, this is true for the Reduced Convex Hulls (RCH). In this paper a new geometric algorithm is presented, applied and compared with other non-geometric algorithms for the non-separable case. 1.

### An Accelerated MDM Algorithm for SVM Training

"... Abstract. In this work we will propose an acceleration procedure for the Mitchell–Demyanov–Malozemov (MDM) algorithm (a fast geometric algorithm for SVM construction) that may yield quite large training savings. While decomposition algorithms such as SVMLight or SMO are usually the SVM methods of ch ..."

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Abstract. In this work we will propose an acceleration procedure for the Mitchell–Demyanov–Malozemov (MDM) algorithm (a fast geometric algorithm for SVM construction) that may yield quite large training savings. While decomposition algorithms such as SVMLight or SMO are usually the SVM methods of choice, we shall show that there is a relationship between SMO and MDM that suggests that, at least in their simplest implementations, they should have similar training speeds. Thus, and although we will not discuss it here, the proposed MDM acceleration might be used as a starting point to new ways of accelerating SMO. 1

### 5 Statistical Pattern Recognition

, 2004

"... 1.1 What is the Statistical Pattern Recognition Toolbox and how it has been developed?.................................. 3 1.2 The STPRtool purpose and its potential users.............. 3 ..."

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1.1 What is the Statistical Pattern Recognition Toolbox and how it has been developed?.................................. 3 1.2 The STPRtool purpose and its potential users.............. 3