Properties of Support Vector Machines

Properties of Support Vector Machines

Support vector machines (SVMs) perform pattern recognition between two point classes by finding a decision surface determined by certain points of the training set, termed support vectors (SV). This surface, which in some feature space of possibly infinite dimension can be regarded as a hyperplane, is obtained from the solution of a problem of quadratic programming that depends on a regularizat...

Classiication Properties of Support Vector Machines for Regression Classiication Properties of Support Vector Machines for Regression

In this report we show some consequences of the work done by Pontil et al. in 1]. In particular we show that in the same hypotheses of the theorem proved in their paper, the optimal approximating hyperplane f R found by SVM regression classiies the data. This means that y i f R (x i) > 0 for points which live externally to the margin between the two classes or points which live internally to th...

Properties of Support Vector Machines for Regression Properties of Support Vector Machines for Regression

In this report we show that the-tube size in Support Vector Machine (SVM) for regression is 2= p 1 + jjwjj 2. By using this result we show that, in the case all the data points are inside the-tube, minimizing jjwjj 2 in SVM for regression is equivalent to maximizing the distance between the approximating hyperplane and the farest points in the training set. Moreover, in the most general setting...

STAGE-DISCHARGE MODELING USING SUPPORT VECTOR MACHINES

Establishment of rating curves are often required by the hydrologists for flow estimates in the streams, rivers etc. Measurement of discharge in a river is a time-consuming, expensive, and difficult process and the conventional approach of regression analysis of stage-discharge relation does not provide encouraging results especially during the floods. P

Modeling Nuclear Properties with Support Vector Machines