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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{x}_1,\vec{x}_2,...\vec{x}_n \in \mathbb{R}^p</math>, with known class labels for each point <math>y_1, y_2, ..., y_n \in \{+1,-1\}</math>, each <math> \vec{x}_i </math> is a p-dimensional vector. The goal is to find the maximum-margin hyperplane separates the training sample points according to their class labels. The separation hyperplane can be written as | 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{x}_1,\vec{x}_2,...\vec{x}_n \in \mathbb{R}^p</math>, with known class labels for each point <math>y_1, y_2, ..., y_n \in \{+1,-1\}</math>, each <math> \vec{x}_i </math> is a p-dimensional vector. The goal is to find the maximum-margin hyperplane separates the training sample points according to their class labels. The separation hyperplane can be written as | ||
| − | <math> c\ | + | <math> c\cdot y=b </math> |
Revision as of 10:17, 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 discriminant functions
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{x}_1,\vec{x}_2,...\vec{x}_n \in \mathbb{R}^p $, with known class labels for each point $ y_1, y_2, ..., y_n \in \{+1,-1\} $, each $ \vec{x}_i $ is a p-dimensional vector. The goal is to find the maximum-margin hyperplane separates the training sample points according to their class labels. The separation hyperplane can be written as
$ c\cdot y=b $
