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).
References
C.-C. Chang, C.-J. Lin, Libsvm: a library for support vector machines. ACM Trans. Intell. Syst. Technol. 2(3), 27:1–27:27 (2011)
J.D. Hedengren, A.R. Parkinson, KKt conditions with inequality constraints (2013). https://youtu.be/JTTiELgMyuM
J.D. Hedengren, R.A. Shishavan, K.M. Powell, T.F. Edgar, Nonlinear modeling, estimation and predictive control in APMonitor. Comput. Chem. Eng. 70(Manfred Morari Special Issue), 133–148 (2014)
W. Karush, Minima of functions of several variables with inequalities as side conditions, Master’s thesis, Department of Mathematics, University of Chicago, Chicago, IL, 1939
H.W. Kuhn, A.W. Tucker, Nonlinear programming, in Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, CA (University of California Press, Berkeley, 1951), pp. 481–492
W.C. Schefler, Statistics: Concepts and Applications (Benjamin/Cummings Publishing Company, San Francisco, 1988)
B. Scholkopf, A.J. Smola, Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond (MIT Press, Cambridge, 2001)
G. Strang, Introduction to Linear Algebra (Wellesley-Cambridge Press, Wellesley, 2009)
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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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