The
margin is the distance between the hyperplane and the nearest samples. These
are called support vector
below, a few references that
I took
Vapnik, V.
Statistical Learning Theory. Wiley-Interscience, New York,
Bernhard
Schölkopf, Alexander J. Smola, Learning
With Kernels: Support Vector Machines, Regularization, Optimization and Beyond,
2002
Positioning:
In this part, I tried to summarize at best what alex smola and bernard scolkopf said in their article about the positioning of the SVM.
The SV algorithm was born thanks to a succession of works developed by Vladimir Vapnik. The latter began in the 1960s in Russia with the generalized portrait algorithm and the theory of Vapnik and Chervonenkis (VC) theory which is a statistical learning theory that characterizes the properties of learning machines that allows them to generalize Well to invisible data. The SVMs were developed mainly in the AT & T laboratories by vladimir vapnik and colleagues. We sitte some of them (Boser, Guyon and Vapnik 1992 and 1993, Cortes and Vapnik 1995, Schololopf, Burges and Vapnik 1995, 1996, Vapnik, Golowich and Smola, 1997).The work and the research on the SVM, are more oriented towards applications of the real world. Focusing on OCR (Optical Character Recognition) and they have become very used and have competed the best systems available in the recognition of objects in a very limited time.
Contribution :
the article is a tuttoriel about SVM, explaning how to use them, their limits and the authors gave us some Current algrithmes to use. so this article contributes
to well understand SVM and this is a way
that summarizes many works that have been made on these subject. the article
should serve as a self contained introduction to Support Vector regression for readers that are new to field of research, and which this rapidly developing one. On the other side, it attempts to give us short overview recent works and rsearchs which are done on it.
Experimentation
I took the following example of algorithm applied to the data from th scikit learn platform, and I reproduced it whith python tool box after that I changed some specifique parameters to the SVM algorithme .
"Comparison of different linear SVM classifiers on a 2D
projection of the iris dataset. We only consider the first 2 features of this
dataset:
·
Sepal length
·
Sepal width
This example shows how to plot the decision surface
for four SVM classifiers with different kernels.
The linear models LinearSVC() and SVC(kernel='linear') yield slightly different decision boundaries. This can be a
consequence of the following differences:
·
LinearSVC minimizes the squared hinge loss while SVC minimizes the
regular hinge loss.
·
LinearSVC uses the One-vs-All (also known as One-vs-Rest)
multiclass reduction while SVC uses the One-vs-One
multiclass reduction.
Both linear models have linear decision boundaries
(intersecting hyperplanes) while the non-linear kernel models (polynomial or
Gaussian RBF) have more flexible non-linear decision boundaries with shapes
that depend on the kind of kernel and its parameters. boundaries with
shapes that depend on the kind of kernel and its parameters."
the following pictures shows th programme proposed