Support Vector Machine

• SVM is a powerful classifier that works both on linearly and non-linearly separable dataLinear Separable
• Finds an optimal hyperplane, that best separates our data so that the distance from nearest points in space to itself(also called margin) is maximized
• These nearest points are called Support Vectors
• For the non-linearly separable case, it uses something called 'Kernel Trick' which will go through in the next part.

A hyperplane is plane of n-1 dimensions in n dimensional feature space, that separates the two classes. For a 2-D feature space, it would be a line and for a 3-D Feature space it would be plane and so on. A hyperplane is able to separate classes if for all points -

w x + b > 0 (For data points in class 1)

w x + b < 0 (For data points in class 0)

Maximum Margin Hyperplane

An optimal hyperplane best separates our data so that the distance/margin from nearest points(called Support Vectors) in space to itself is maximized.

In machine learning, support-vector machines (SVMs, also support-vector networks) are supervised learning models with associated learning algorithms that analyze data used for classification and regression analysis. Given a set of training examples, each marked as belonging to one or the other of two categories, an SVM training algorithm builds a model that assigns new examples to one category or the other, making it a non-probabilistic binary linear classifier (although methods such as Platt scaling exist to use SVM in a probabilistic classification setting). An SVM model is a representation of the examples as points in space, mapped so that the examples of the separate categories are divided by a clear gap that is as wide as possible. New examples are then mapped into that same space and predicted to belong to a category based on the side of the gap on which they fall.

In addition to performing linear classification, SVMs can efficiently perform a non-linear classification using what is called the kernel trick, implicitly mapping their inputs into high-dimensional feature spaces.

When data are unlabelled, supervised learning is not possible, and an unsupervised learning approach is required, which attempts to find natural clustering of the data to groups, and then map new data to these formed groups. The support-vector clustering algorithm, created by Hava Siegelmann and Vladimir Vapnik, applies the statistics of support vectors, developed in the support vector machines algorithm, to categorize unlabeled data, and is one of the most widely used clustering algorithms in industrial applications.

Applications

SVMs can be used to solve various real-world problems:

• SVMs are helpful in text and hypertext categorization, as their application can significantly reduce the need for labeled training instances in both the standard inductive and transductive settings. Some methods for shallow semantic parsing are based on support vector machines.
• Classification of images can also be performed using SVMs. Experimental results show that SVMs achieve significantly higher search accuracy than traditional query refinement schemes after just three to four rounds of relevance feedback. This is also true for image segmentation systems, including those using a modified version SVM that uses the privileged approach as suggested by Vapnik.
• Classification of satellite data like SAR data using supervised SVM.
• Hand-written characters can be recognized using SVM.
• The SVM algorithm has been widely applied in the biological and other sciences. They have been used to classify proteins with up to 90% of the compounds classified correctly. Permutation tests based on SVM weights have been suggested as a mechanism for interpretation of SVM models. Support-vector machine weights have also been used to interpret SVM models in the past. Posthoc interpretation of support-vector machine models in order to identify features used by the model to make predictions is a relatively new area of research with special significance in the biological sciences.

Kernel Based Classifcation in SVM's

Sklearn supports the following types of Kernels, which can be used in many-real life problems.

• Linear Kernel
• RBF Kernel
• Polynomial Kernel
• Sigmoid Kernel

Kernel trick is method of using a linear classifer to solve a non-linear problem. It transforms the linearly in-separable data into linearly separable one.