Support Vector Machines in Neuroscience

2008 ◽  
pp. 1283-1293 ◽  
Author(s):  
Onur Seref ◽  
O. Erhun Kundakcioglu ◽  
Michael Bewernitz
Keyword(s):  
Linear Inequality ◽  
Optimization Problem ◽  
Real Life ◽  
Inequality Constraints ◽  
Alternative Methods ◽  
Support Vector ◽  
Classification Problems ◽  
Basic Premise ◽  
Linear Inequality Constraints ◽  
Vector Machines

The underlying optimization problem for the maximal margin classifier is only feasible if the two classes of pattern vectors are linearly separable. However, most of the real life classification problems are not linearly separable. Nevertheless, the maximal margin classifier encompasses the fundamental methods used in standard SVM classifiers. The solution to the optimization problem in the maximal margin classifier minimizes the bound on the generalization error (Vapnik, 1998). The basic premise of this method lies in the minimization of a convex optimization problem with linear inequality constraints, which can be solved efficiently by many alternative methods (Bennett & Campbell, 2000).

scholarly journals A Parallel Mixture of SVMs for Very Large Scale Problems

2002 ◽  
Vol 14 (5) ◽  
pp. 1105-1114 ◽  
Author(s):  
Ronan Collobert ◽  
Samy Bengio ◽  
Yoshua Bengio
Keyword(s):  
Large Scale ◽  
Real Life ◽  
Support Vector ◽  
Small Subset ◽  
Training Algorithm ◽  
Classification Problems ◽  
Data Set ◽  
Large Scale Problems ◽  
Life Problems ◽  
Vector Machines

Support vector machines (SVMs) are the state-of-the-art models for many classification problems, but they suffer from the complexity of their training algorithm, which is at least quadratic with respect to the number of examples. Hence, it is hopeless to try to solve real-life problems having more than a few hundred thousand examples with SVMs. This article proposes a new mixture of SVMs that can be easily implemented in parallel and where each SVM is trained on a small subset of the whole data set. Experiments on a large benchmark data set (Forest) yielded significant time improvement (time complexity appears empirically to locally grow linearly with the number of examples). In addition, and surprisingly, a significant improvement in generalization was observed.

Lp LOSC-Support Vector Machines for Regression Estimation and their Application to Geomatics

2021 ◽  
Author(s):  
Jeff Chak Fu Wong ◽  
Tsz Fung Yu
Keyword(s):  
Undergraduate Students ◽  
Optimization Problem ◽  
Real Life ◽  
Support Vector ◽  
Geoid Model ◽  
Lipschitz Optimization ◽  
Vector Machines ◽  
Vertical Displacements ◽  
Smooth Constraints

<p>The classification of vertical displacements and the estimation of a local geometric geoid model and coordinate transformation were recently solved by the L<sup>2</sup> support vector machine and support vector regression. The L<sup>p</sup> quasi-norm SVM and SVR (0<p<1) is a non-convex and non-Lipschitz optimization problem that has been successfully formulated as an optimization model with a linear objective function and smooth constraints (LOSC) that can be solved by any black-box computing software, e.g., MATLAB, R and Python. The aim of this talk is to show that interior-point based algorithms, when applied correctly, can be effective for handling different LOSC-SVM and LOSC-SVR based models with different p values, in order to obtain better sparsity regularization and feature selection. As a comparative study, some artificial and real-life geoscience datasets are used to test the effectiveness of our proposed methods. Most importantly, the methods presented here can be used in geodetic classroom teaching to benefit our undergraduate students and further bridge the gap between the applications of geomatics and machine learning.</p>

A Review of Machine Learning Techniques for Anomaly Detection in Static Graphs

2020 ◽  
pp. 146-162
Author(s):  
Hesham M. Al-Ammal
Keyword(s):  
Machine Learning ◽  
Neural Networks ◽  
Anomaly Detection ◽  
Real Life ◽  
Machine Learning Techniques ◽  
Support Vector ◽  
Learning Methods ◽  
Data Set ◽  
Learning Techniques ◽  
Vector Machines

Detection of anomalies in a given data set is a vital step in several applications in cybersecurity; including intrusion detection, fraud, and social network analysis. Many of these techniques detect anomalies by examining graph-based data. Analyzing graphs makes it possible to capture relationships, communities, as well as anomalies. The advantage of using graphs is that many real-life situations can be easily modeled by a graph that captures their structure and inter-dependencies. Although anomaly detection in graphs dates back to the 1990s, recent advances in research utilized machine learning methods for anomaly detection over graphs. This chapter will concentrate on static graphs (both labeled and unlabeled), and the chapter summarizes some of these recent studies in machine learning for anomaly detection in graphs. This includes methods such as support vector machines, neural networks, generative neural networks, and deep learning methods. The chapter will reflect the success and challenges of using these methods in the context of graph-based anomaly detection.

scholarly journals Mathematical model for determining rational machining conditions for flat grinding with the wheel periphery on machines with a rectangular table

2018 ◽  
Vol 224 ◽  
pp. 01112
Author(s):  
Dmitriy L. Skuratov ◽  
Dmitriy G. Fedorov ◽  
Dmitriy V. Evdokimov
Keyword(s):  
Mathematical Model ◽  
Objective Function ◽  
Linear Inequality ◽  
Inequality Constraints ◽  
Machining Time ◽  
Functional Parameters ◽  
Linear Inequality Constraints ◽  
Machining Quality ◽  
Machining Conditions ◽  
Grinding Operations

A mathematical model is presented for determining the rational machining conditions for flat grinding operations by the rim of a wheel on machines with a rectangular table consisting of a linear objective function and linear inequality constraints. As the objective function, the equation, determining the main machining time, was used. And constraints which are related to the functional parameters and parameters determining the machining quality and the kinematic capabilities of the machine were used as inequality constraints.

A Reference Governor for Nonlinear Systems Based on Quadratic Programming

2016 ◽  
Author(s):  
Nan I. Li ◽  
Ilya Kolmanovsky ◽  
Anouck Girard
Keyword(s):  
Nonlinear Systems ◽  
Quadratic Programming ◽  
Optimization Problem ◽  
Inequality Constraints ◽  
Closed Loop System ◽  
Linear Inequality Constraints ◽  
And Control ◽  
Bounded Disturbance ◽  
State And Control Constraints ◽  
Reference Governor

The reference governor modifies set-point commands to a closed-loop system in order to enforce state and control constraints. In this paper, we describe an approach to reference governor implementation for nonlinear systems, which is based on bounding (covering) the response of a nonlinear system by the response of a linear model with a set-bounded disturbance input. Such a design strategy is of interest as it reduces the online optimization problem to a convex quadratic programming (QP) problem with linear inequality constraints, thereby permitting standard QP solvers to be used. A numerical example is reported.

scholarly journals Correlation Kernels for Support Vector Machines Classification with Applications in Cancer Data

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Hao Jiang ◽  
Wai-Ki Ching
Keyword(s):  
Support Vector Machines ◽  
Positive Semidefinite ◽  
Superior Performance ◽  
Support Vector ◽  
Svm Classifier ◽  
Classification Problems ◽  
Correlation Kernel ◽  
Cancer Data ◽  
Tumor Tissues ◽  
Vector Machines

High dimensional bioinformatics data sets provide an excellent and challenging research problem in machine learning area. In particular, DNA microarrays generated gene expression data are of high dimension with significant level of noise. Supervised kernel learning with an SVM classifier was successfully applied in biomedical diagnosis such as discriminating different kinds of tumor tissues. Correlation Kernel has been recently applied to classification problems with Support Vector Machines (SVMs). In this paper, we develop a novel and parsimonious positive semidefinite kernel. The proposed kernel is shown experimentally to have better performance when compared to the usual correlation kernel. In addition, we propose a new kernel based on the correlation matrix incorporating techniques dealing with indefinite kernel. The resulting kernel is shown to be positive semidefinite and it exhibits superior performance to the two kernels mentioned above. We then apply the proposed method to some cancer data in discriminating different tumor tissues, providing information for diagnosis of diseases. Numerical experiments indicate that our method outperforms the existing methods such as the decision tree method and KNN method.

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