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fix: formatting

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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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src/svm/svr.rs
+11 -11
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@@ -1,21 +1,21 @@
//! # Epsilon-Support Vector Regression.
//!
//! Support Vector Regression (SVR) is a popular algorithm used for regression that uses the same principle as SVM.
//!
//!
//! Support Vector Regression (SVR) is a popular algorithm used for regression that uses the same principle as SVM.
//!
//! Just like [SVC](../svc/index.html) SVR finds optimal decision boundary, \\(f(x)\\) that separates all training instances with the largest margin.
//! Unlike SVC, in \\(\epsilon\\)-SVR regression the goal is to find a function \\(f(x)\\) that has at most \\(\epsilon\\) deviation from the
//! Unlike SVC, in \\(\epsilon\\)-SVR regression the goal is to find a function \\(f(x)\\) that has at most \\(\epsilon\\) deviation from the
//! known targets \\(y_i\\) for all the training data. To find this function, we need to find solution to this optimization problem:
//!
//!
//! \\[\underset{w, \zeta}{minimize} \space \space \frac{1}{2} \lVert \vec{w} \rVert^2 + C\sum_{i=1}^m \zeta_i \\]
//!
//!
//! subject to:
//!
//!
//! \\[\lvert y_i - \langle\vec{w}, \vec{x}_i \rangle - b \rvert \leq \epsilon + \zeta_i \\]
//! \\[\lvert \langle\vec{w}, \vec{x}_i \rangle + b - y_i \rvert \leq \epsilon + \zeta_i \\]
//! \\[\zeta_i \geq 0 for \space any \space i = 1, ... , m\\]
//!
//! Where \\( m \\) is a number of training samples, \\( y_i \\) is a target value and \\(\langle\vec{w}, \vec{x}_i \rangle + b\\) is a decision boundary.
//!
//!
//! Where \\( m \\) is a number of training samples, \\( y_i \\) is a target value and \\(\langle\vec{w}, \vec{x}_i \rangle + b\\) is a decision boundary.
//!
//! The parameter `C` > 0 determines the trade-off between the flatness of \\(f(x)\\) and the amount up to which deviations larger than \\(\epsilon\\) are tolerated
//!
//! Example:
@@ -66,7 +66,7 @@
//! * ["A Fast Algorithm for Training Support Vector Machines", Platt J.C., 1998](https://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/tr-98-14.pdf)
//! * ["Working Set Selection Using Second Order Information for Training Support Vector Machines", Rong-En Fan et al., 2005](https://www.jmlr.org/papers/volume6/fan05a/fan05a.pdf)
//! * ["A tutorial on support vector regression", Smola A.J., Scholkopf B., 2003](https://alex.smola.org/papers/2004/SmoSch04.pdf)
//!
//!
//! <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script>
//! <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>