# Breaking Down the Support Vector Machine (SVM) Algorithm

So, I was revising machine learning algorithms yesterday; and I observed that SVM is probably a widely used but complicated machine learning algorithm.

So, I was revising machine learning algorithms yesterday; and I observed that SVM is probably a widely used but complicated machine learning algorithm. So, after understanding the intricacies and coding it from scratch; I thought I must write a post to help individuals like me who find it a little bit more complex than its counterparts.

So, SVM basically uses vector space in order to perform the designated tasks. You’d be surprised to know that SVM is actually better than some neural networks when it comes to recognizing handwritten digits and related tasks. Let’s dive into it!

## Basic Intuition

Before we start; you should know that SVM can classify only 2 groups at a single time. But hey; it does not mean it’s limited to binary classifier (more emphasis on the word ‘at a time’). So on an intuitive level; support vector machine separates two categories of data in the dataset with the help of a hyperplane. The perpendicular bisectors from the hyperplane to the datapoints denotes the largest possible distance.

SVM Hyperplane (Decision Boundary) and Perpendicular. Image by Author

In short; even though there can be infinite hyperplanes which can separate the data; the optimum choice is the one with largest separable distances (measure with the perpendicular from the datapoint).

So if a datapoint lies on either side of hyperplane; we can easily tell its category by assuming the hyperplane as a separating wall (just an analogy). But, this can be done with the help of regression too, right? Actually yes, but SVM can handle even more complex separations because it uses vector spaces. Not only this, SVM also does an excellent work in determining the decision boundaries. (That is the best position — max length of perpendicular lines).

Now that we have our basics clear; let’s jump into the technicalities of it.

## Let’s stimulate our brains a bit more

In simple terms, we can say that a vector is a quantity which has a magnitude as well as direction (elementary physics/math). In SVM; the magnitude is the numerical value (which can be calculated either by taking the mod or square root of sums of x and y coordinates; similar to hypotenuse in pythagoras theorum).

Apart from that; another thing to know is the dot product of two vectors, which is simply the multiplication of values in two vectors. It can be understood by the figure attached below.

For example if we have a datapoint ‘u’ (which can be represented with u vector) in a dataset which is seperated by a hyperplane (represented by the red line). Now, we take another vector (w) which is drawn perpendicularly from the hyperplane to the origin. Now the dot product of u and w added with a bias decides the output of our support vector assertion.

Now, if the result of our equation is more than or equal to zero; then we can classify the datapoint on the other side (+ve). In the above example; we can visually see that it is not the case (our datapoint is clearly NOT on the +ve side). But even in complex situations the equation works like magic.

Also, you should note that if u.w+b = 0; then the point comes on the decision boundary (a rare situation).

_“But Satyam, this isn’t complicated. That’s easy to understand.” _Well, I’d love if that was the case. But SVM comes with a few constraints on getting the values of bias and vectors. But yes, once you get past this, I’m sure you will love the SVM.

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