What is support vector machine/SVM

Last updated on:8 days ago

SVM is usually mentioned in Machine Learning. But sometimes I still get confused that how it relates to ML.

Definition

In machine learning, support vector machines/SVMs are supervised learning models with associated learning algorithms that analyse data for classification and regression analysis.

Also, the neural network is a learning model of machine learning. Different learning models with a different cost function, characteristics, application.

Support vector machine is a large margin classifier.

A Support Vector Machine (SVM) performs classification by finding the hyperplane that maximizes the margin between the two classes. The vectors (cases) that define the hyperplane are the support vectors.

SVM hypothesis

$$\min_\theta C \sum^{m}_{i=1} [y^{(i)} cost_1 (\theta^T x^{(i)}) + $$

$$(1 - y^{(i)}) cost_0( \theta^T x^{(i)})] + \frac{1}{2} \sum^{n}_{i=1} \theta_j^2$$

Need to specify

  • Choice of parameter C
  • Choice of kernel (similarity function)

For C, remember, C is larger, then theta or omega is larger, then the model is going to overfit

Kernels

Adapt SVM to develop complex nonlinear classifier

$$f_i = similarity(x, l^{(i)}) = exp ( - \frac{|| x - l^{(i)}|| ^2}{2 \sigma ^2})$$

Superscript is still the level of layer.

Kernel types

Linear kernel
$$\theta_0 + \theta_1 x_1 + … + \theta_n x_n \ge 0$$

Polynomial kernel

$ k(x,l) = (x^T l)^2, (x^T l)^3, (x^T l+1)^2,$$

$$(x^T l + constant)^{degree}$
More esoteric

string k, chi-square k, histogram intersection k

Logistic regression vs SVM

  • If n is larger than m, use logistic regression or SVM without a kernel
    With so many features, linear functions can fit very complicated non-linear function
  • If n is small, m is intermediate
    Use SVM with Gaussian kernel
  • If n is small, m is large
    Create/add more features, then use logistic regression or SVM without a kernel

Neural network likely to work well for most of these settings, but maybe slower to train.

Reference

[1] Andrew NG, Machine learning

[2] Support-vector machine

[3] Support Vector Machine - Classification (SVM)