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| − | == Linear | + | == Linear classification Problem Statement== |
| − | In a linear classification problem, the feature space can be divided into different regions by hyperplanes. For a two-catagory case, given training data <math> \vec{ | + | In a linear classification problem, the feature space can be divided into different regions by hyperplanes. For a two-catagory case, given training data <math> \vec{y}_1,\vec{y}_2,...\vec{y}_n \in \mathbb{R}^p</math>, with known class labels for each point <math>w_1, w_2, ..., w_n \in \{+1,-1\}</math>, each <math> \vec{y}_i </math> is a p-dimensional vector. The goal is to find the maximum-margin hyperplane that separates the training sample points according to their class labels. The separation hyperplane can be written as |
| − | + | ||
<math> c\cdot y=b </math> | <math> c\cdot y=b </math> | ||
| + | where <math>\cdot </math> denotes the dot product, c determines the orientation of the hyperplane and | ||
Revision as of 10:22, 1 May 2014
'Support Vector Machine and its Applications in Classification Problems
A slecture by Xing Liu
Partially based on the ECE662 Spring 2014 lecture material of Prof. Mireille Boutin.
Outline of the slecture
- Linear discriminant functions
- Summary
- References
Linear classification Problem Statement
In a linear classification problem, the feature space can be divided into different regions by hyperplanes. For a two-catagory case, given training data $ \vec{y}_1,\vec{y}_2,...\vec{y}_n \in \mathbb{R}^p $, with known class labels for each point $ w_1, w_2, ..., w_n \in \{+1,-1\} $, each $ \vec{y}_i $ is a p-dimensional vector. The goal is to find the maximum-margin hyperplane that separates the training sample points according to their class labels. The separation hyperplane can be written as $ c\cdot y=b $ where $ \cdot $ denotes the dot product, c determines the orientation of the hyperplane and
