SVM interpretation in Java and start of Least Similar Spheres (LSS)

Interpretation of SVM

Given that SVM math is difficult to fully implement from scratch, because it uses quadratic optimizers, it was assumed that to create its interpreted version of code, idea, math and logic would be easier to understand. The solution to this difficulty was called plan B and supposed to be used in case author does not manage to implement SVM in Java. It lead to discovery of different interpretation of SVM, which looks easier to understand even at programming the math level.

If we look at SVM hyperplane in 2D, it is a line, which separates two sides. We can imagine that a line can be two parallel lines very close to each other. These lines could be just edges of very large circles, which means that opposite centers have to be very far away from each other. In SVM we use support vectors or closest opposite vectors to support the finding of separating hyperplane, but in interpretation these vectors are used to find anti-support or furthest vectors. In geometry we can measure distances with various formulas, which in SVM are called kernels. The distance between two different vectors is a value. That value can have slightly different name than a measurement of distance, it could be called measurement of how similar or different are the vectors. Author uses these names to further simplify mathematical problem in to more intuitive logical one. That way multidimensional vector space, distances, hyperplanes, hyperspheres can become easier to imagine. Another difficult problem might be to try to imagine hyperplane separating high dimensional space. In previous paragraphs it was mentioned that this high dimensional hyperplane becomes a complex formula with no easy way to imagine its shape. That is where another simplification might help- spheres and hyperspheres. If a circle is simply a set of points which surround a center point always in the same distance, just different direction, so is the sphere. The sphere just has one more dimension, but the idea of the same distance to all directions from center is the same.

Figure 5. Least Similar Sphere LSS or SVM interpretation (Source: Ubaby, 2016)

At first it might seem difficult to imagine hypersphere, but if you look at it just as picking the point in high dimension space and spray the paint same distance in all directions of that space, then that would seem like a sphere. Now if we join all ideas it starts to sound like finding least similar vectors of opposite classes and drawing spheres up to the most similar opposite vectors and then using these spheres to determine how different or how close the new unknown vectors are from these spheres. That is how Least Similar Sphere idea arisen. Author hopes that someone else, somewhere else, some time ago did not already invent this idea and claims that given limited amount of knowledge about the topic and desire to invent, tried to independently and uniquely create something new and unify existing ideas learned from SVM, ANN and clustering.