Polynomial Basis Application In Linear Classification
Transformation of dimensions in linear classification is a powerful tool. Normally if we have a dataset such that it’s not possible to linearly classify it , we can do transformation of dimensions i.e. addition of dimensions which causes our dataset to become linearly separable.
I also explained some extent of it yesterday, today I’ll explain some more information about the addition of coefficients to the theta or vector.
Basically, in linear transformation if our data isn’t linearly classifiable then the perceptron algorithm updates the theta vector by addition of more coefficients to it.
For that, you’ll need information of ( general orders ) k values , d values and then adjust the coefficients accordingly . k is the highest possible feature you have included.
- k = 0 , zero order / constant then d = 1.
- k = 1 , first order / linear terms then d = 2 (1,x)
And so on, it continues. What I’m trying to explain is how the polynomial basis allows us to apply the next after the next order so that we can really get our desired transformation and classification possible.
If let’s suppose linear classification isn’t possible then quadratic, if that’s not then cubic and it goes on like such until we get one order desired, on which our data will become linearly classifiable. and during this each iteration if I say ,our theta or vector which includes coefficients gets updated so that we can apply linear classification.
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