The support vector machine (SVM) approach represents a data-driven method for solving classification tasks. It has been shown to produce lower prediction error compared to classifiers based on other methods like artificial neural networks, especially when large numbers of features are considered for sample description.
1 Introduction
Support Vector Machines (SVMs) are a technique for supervised machine learning. They can perform
classification tasks by identifying hyperplane boundaries between sets of classes. The original linear SVMs
were developed by Vapnik and Lerner (1963) and were enhanced by Boser, Guyon, and Vapnik (1992) to be
applied to non-linear datasets.
2 Linear models
In the case of linearly separable classes, a maximum margin hyperplane is constructed such that the boundary line stays as far away as possible from each class, as shown in Figure 1a.
The hyperplane is constructed by constructing a linear function:
Each instance has i attributes that define it. The weights, w, are calculated during the training step to build
the linear function. One method of iteratively calculating the weights is the perceptron method.
2 Linear models
In the case of linearly separable classes, a maximum margin hyperplane is constructed such that the boundary line stays as far away as possible from each class, as shown in Figure 1a.
The hyperplane is constructed by constructing a linear function:
Each instance has i attributes that define it. The weights, w, are calculated during the training step to build
the linear function. One method of iteratively calculating the weights is the perceptron method.
In the case that the two classes are not linearly separable, the soft margin optimisation can be performed
(Figure 1b). If instances fall on the “wrong” side of the maximum margin hyperplane, the distance between
the instance and the maximum margin hyperplane, known as the slack is minimised.
In addition to classifying tasks, linear models can be used for regression. Least squares regression can be used to fit a line to a dataset and new numerical values can be predicted for new instances. This technique can also be extended into non-linear space in a similar manner to the non-linear modeling process.
3 Support vectors
Support vectors are instances that are the closest to the linear boundary. There is always at least one support vector per class, often there are more. The support vectors can be chosen by constrained quadratic optimisation. The maximum margin hyperplane can be created using just the support vectors. This means that identifying the support vectors and removing all other instances before creating the linear model results in a computationally cheaper process.
In addition, choosing support vectors reduces the possibility of overfitting the training data. This is because the only time the maximum margin hyperplane will change is if a new instance is introduced into the training set that is a support vectors. All other instances will have no effect on the calculated model.
4 Non-linear data
In many situations classes are not separable by a linear boundary. If this is the case, the input data can be transformed using a nonlinear mapping, φ, into another dimension space. In this new mapping, a linear boundary can be found.
When mapping into a higher dimension space, the computational complexity of the algorithm increases. Because the training process iterates through all instances as it is building its model in order to update the weights for the model, a large number of operations need to be made. It turns out that calculation of the dot product between all instances can be calculated in the lower-dimension space by substituting a kernel function into the equation. The choice of which kernel to use is experimenter-chosen, and the choice can affect the results significantly (Burges 1998).
In addition to classifying tasks, linear models can be used for regression. Least squares regression can be used to fit a line to a dataset and new numerical values can be predicted for new instances. This technique can also be extended into non-linear space in a similar manner to the non-linear modeling process.
3 Support vectors
Support vectors are instances that are the closest to the linear boundary. There is always at least one support vector per class, often there are more. The support vectors can be chosen by constrained quadratic optimisation. The maximum margin hyperplane can be created using just the support vectors. This means that identifying the support vectors and removing all other instances before creating the linear model results in a computationally cheaper process.
In addition, choosing support vectors reduces the possibility of overfitting the training data. This is because the only time the maximum margin hyperplane will change is if a new instance is introduced into the training set that is a support vectors. All other instances will have no effect on the calculated model.
4 Non-linear data
In many situations classes are not separable by a linear boundary. If this is the case, the input data can be transformed using a nonlinear mapping, φ, into another dimension space. In this new mapping, a linear boundary can be found.
When mapping into a higher dimension space, the computational complexity of the algorithm increases. Because the training process iterates through all instances as it is building its model in order to update the weights for the model, a large number of operations need to be made. It turns out that calculation of the dot product between all instances can be calculated in the lower-dimension space by substituting a kernel function into the equation. The choice of which kernel to use is experimenter-chosen, and the choice can affect the results significantly (Burges 1998).
The combination of the so-called kernel trick and the use of support vectors makes SVMs more efficient than regular linear models.
5 Applications
SVMs have been successfully used in classification problems consisting of two or many classes.
Boser, Guyon, and Vapnik (1992) evaluated SVMs for recognising hand-written digits. SVMs have also
been successfully used to classify documents by topic, and the a/b classification of images.
In the music information retrieval area, SVMs are popular for classifying audio features into a set of classes. Mandel and Ellis (2005) use SVMs for performer classification. The technique has also been used to
calculate the mood and style of songs (Mandel, Poliner, and Ellis 2006).
Here is the video of the SVM application with Rapidminer software.
Resources
1.http://www.ncbi.nlm.nih.gov/pubmed/15130823
2.http://www.music.mcgill.ca/~alastair/621/porter11svm-summary.pdf
3.https://www.youtube.com/watch?v=VVQdehQzIOU
2.http://www.music.mcgill.ca/~alastair/621/porter11svm-summary.pdf
3.https://www.youtube.com/watch?v=VVQdehQzIOU
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