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fix: formatting

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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/svc.rs
+18 -18
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@@ -1,27 +1,27 @@
//! # Support Vector Classifier.
//!
//!
//! Support Vector Classifier (SVC) is a binary classifier that uses an optimal hyperplane to separate the points in the input variable space by their class.
//!
//! During training, SVC chooses a Maximal-Margin hyperplane that can separate all training instances with the largest margin.
//! The margin is calculated as the perpendicular distance from the boundary to only the closest points. Hence, only these points are relevant in defining
//!
//! During training, SVC chooses a Maximal-Margin hyperplane that can separate all training instances with the largest margin.
//! The margin is calculated as the perpendicular distance from the boundary to only the closest points. Hence, only these points are relevant in defining
//! the hyperplane and in the construction of the classifier. These points are called the support vectors.
//!
//! While SVC selects a hyperplane with the largest margin it allows some points in the training data to violate the separating boundary.
//! The parameter `C` > 0 gives you control over how SVC will handle violating points. The bigger the value of this parameter the more we penalize the algorithm
//! for incorrectly classified points. In other words, setting this parameter to a small value will result in a classifier that allows for a big number
//! of misclassified samples. Mathematically, SVC optimization problem can be defined as:
//!
//!
//! While SVC selects a hyperplane with the largest margin it allows some points in the training data to violate the separating boundary.
//! The parameter `C` > 0 gives you control over how SVC will handle violating points. The bigger the value of this parameter the more we penalize the algorithm
//! for incorrectly classified points. In other words, setting this parameter to a small value will result in a classifier that allows for a big number
//! of misclassified samples. Mathematically, SVC optimization problem can be defined as:
//!
//! \\[\underset{w, \zeta}{minimize} \space \space \frac{1}{2} \lVert \vec{w} \rVert^2 + C\sum_{i=1}^m \zeta_i \\]
//!
//!
//! subject to:
//!
//!
//! \\[y_i(\langle\vec{w}, \vec{x}_i \rangle + b) \geq 1 - \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 label value (either 1 or -1) and \\(\langle\vec{w}, \vec{x}_i \rangle + b\\) is a decision boundary.
//!
//! To solve this optimization problem, SmartCore uses an [approximate SVM solver](https://leon.bottou.org/projects/lasvm).
//! The optimizer reaches accuracies similar to that of a real SVM after performing two passes through the training examples. You can choose the number of passes
//!
//! Where \\( m \\) is a number of training samples, \\( y_i \\) is a label value (either 1 or -1) and \\(\langle\vec{w}, \vec{x}_i \rangle + b\\) is a decision boundary.
//!
//! To solve this optimization problem, SmartCore uses an [approximate SVM solver](https://leon.bottou.org/projects/lasvm).
//! The optimizer reaches accuracies similar to that of a real SVM after performing two passes through the training examples. You can choose the number of passes
//! through the data that the algorithm takes by changing the `epoch` parameter of the classifier.
//!
//! Example:
@@ -73,7 +73,7 @@
//!
//! * ["Support Vector Machines", Kowalczyk A., 2017](https://www.svm-tutorial.com/2017/10/support-vector-machines-succinctly-released/)
//! * ["Fast Kernel Classifiers with Online and Active Learning", Bordes A., Ertekin S., Weston J., Bottou L., 2005](https://www.jmlr.org/papers/volume6/bordes05a/bordes05a.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>