fix: formatting

This commit is contained in:
Volodymyr Orlov
2020-10-30 15:08:22 -07:00
parent 3a3f904914
commit 81395bcbb7
3 changed files with 40 additions and 40 deletions
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//! # Support Vector Machines
//!
//! Support Vector Machines (SVM) is one of the most performant off-the-shelf machine learning algorithms.
//!
//! Support Vector Machines (SVM) is one of the most performant off-the-shelf machine learning algorithms.
//! SVM is based on the [VapnikChervonenkiy theory](https://en.wikipedia.org/wiki/Vapnik%E2%80%93Chervonenkis_theory) that was developed during 19601990 by Vladimir Vapnik and Alexey Chervonenkiy.
//!
//! SVM splits data into two sets using a maximal-margin decision boundary, \\(f(x)\\). For regression, the algorithm uses a value of the function \\(f(x)\\) to predict a target value.
//!
//! SVM splits data into two sets using a maximal-margin decision boundary, \\(f(x)\\). For regression, the algorithm uses a value of the function \\(f(x)\\) to predict a target value.
//! To classify a new point, algorithm calculates a sign of the decision function to see where the new point is relative to the boundary.
//!
//!
//! SVM is memory efficient since it uses only a subset of training data to find a decision boundary. This subset is called support vectors.
//!
//! In SVM distance between a data point and the support vectors is defined by the kernel function.
//! SmartCore supports multiple kernel functions but you can always define a new kernel function by implementing the `Kernel` trait. Not all functions can be a kernel.
//! Building a new kernel requires a good mathematical understanding of the [Mercer theorem](https://en.wikipedia.org/wiki/Mercer%27s_theorem)
//!
//! In SVM distance between a data point and the support vectors is defined by the kernel function.
//! SmartCore supports multiple kernel functions but you can always define a new kernel function by implementing the `Kernel` trait. Not all functions can be a kernel.
//! Building a new kernel requires a good mathematical understanding of the [Mercer theorem](https://en.wikipedia.org/wiki/Mercer%27s_theorem)
//! that gives necessary and sufficient condition for a function to be a kernel function.
//!
//!
//! Pre-defined kernel functions:
//!
//!
//! * *Linear*, \\( K(x, x') = \langle x, x' \rangle\\)
//! * *Polynomial*, \\( K(x, x') = (\gamma\langle x, x' \rangle + r)^d\\), where \\(d\\) is polynomial degree, \\(\gamma\\) is a kernel coefficient and \\(r\\) is an independent term in the kernel function.
//! * *RBF (Gaussian)*, \\( K(x, x') = e^{-\gamma \lVert x - x' \rVert ^2} \\), where \\(\gamma\\) is kernel coefficient