Abstract
This chapter starts by reviewing the basic concepts on Linear Algebra, then we design a simple hyperplane-based classification algorithm. Next, it provides an intuitive and an algebraic formulation to obtain the optimization problem of the Support Vector Machines. At last, hard-margin and soft-margin SVMs are detailed, including the necessary mathematical tools to tackle them both.
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Notes
- 1.
Nonlinear transformations are typical when designing kernels.
- 2.
Remember that λ v = λI v, allowing us the last step.
- 3.
No temporal relation is here assumed.
- 4.
Our notation considers x i to be an identification of some example, without precisely defining its representation (e.g. it might be in a Topological, Hausdorff, Normed, or any other space). However, x i is its vectorial form in some Hilbert space.
- 5.
Distributions are used for illustration purposes. In fact, we remind the reader that the Statistical Learning Theory assumes they are unknown at the time of training.
- 6.
This work as an intercept term, such as θ for the Perceptron and the Multilayer Perceptron algorithms (see Chap. 1).
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Fernandes de Mello, R., Antonelli Ponti, M. (2018). Introduction to Support Vector Machines. In: Machine Learning. Springer, Cham. https://doi.org/10.1007/978-3-319-94989-5_4
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DOI: https://doi.org/10.1007/978-3-319-94989-5_4
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