It is possible to utilize vector machines for both classification and regression.

Hard margin and soft margin comparisons.

Support vector machines with a soft margin.

Support vector machines with a hard margin.

The role of hard and soft margin in support vector machines.

The time required to evaluate a big dataset using this technique makes it unfeasible even for smaller datasets. They’re known as support vectors since they help to stabilize the hyperplane. Support vector machines deal with classification and regression problems.

“Support Vector Machines - Kernels and the Kernel Trick”.Support Vectors are the data points or vectors nearest to the hyperplane and can affect its location. An Introduction to Statistical Learning (Chapter-9). But what if we are getting data from two different source but with similar variables or parameters, in this case, if we draw them in a plane with respect to each other, then the observation two different sources might mix up with each other. We know that each observation has different parameters or variables that define its property and we can draw them on a plane to see where they all lie in respect to each other. And when the new testing features will come, their dot product will be computed with each of the training observations and result will behave like it’s a higher dimensional feature space.ĭot product is one form of kernel, there are many other different type of kernels available depends upon the objective.

The advantage of this kernel is that the complexity of the optimization problem remains dependent only on the dimensionality of input features. This model has high biased but lower variance. Similarly, when C is large it is more tolerant and allowing boundaries to be violated more often. When C is small, the model seeks narrow margins because it want to allow small number of observation to fall on wrong side, and hence the model become highly fit but with high variance. C here is working as a tuning parameter that is chosen via cross-validation. Now comes the trade-off between bias and variance. So, the thing to be consider is that for C > 0 no more than C observation can wrong side of the hyperplane. Be careful that the value of slack variable can be in fraction as well, for example, let’s say C=0.6, then it might the possible that we have three points with slack variable = 0.2 or two points with slack variable = 0.3 or we have C=1.6 with one slack variable =0.6 (wrong side of margin) and another slack variable= 1 (wrong side of the plane). If C=0 it means no observation has violated the margin. Now consider the role of variable C, it is the sum of all the slack variables for all n observations. If slack variable is greater than 1 then “i th” observation is on the wrong side of the hyperplane. If the slack variable is equal to zero then it means that “i th” observation is on correct side of margin and if slack variable is > than 0 then it means “i th” observation is on wrong side of margin. Meaning, if you move vectors, the classifier would change its margin, but if you move all other observations the margin wouldn’t change. Interestingly, this classifier simply depends upon those vectors and not on all other observations available in the training set. Those touching points are called vectors because they are vectors in p-dimensional space. They are defining the length of the margin, farther those points are, farther away those two lines are from the middle hyperplane. Those lines are called margins, and the observations touching those two lines are called vectors. The way maximal margin classifier looks like is that it has one plane that is cutting through the p-dimensional space and dividing it into two pieces, and then it has two lines, each on one and other side of that plane. In simple words, for each testing observation we put all the variables in the equation above and decide which side of the hyperplane that particular observation belongs to, based on the sign of f(x).

Hyperplan vectoriel equation