I was looking at Support Vector machines (SVM) kernels. Looking at Polynomial Kernel and Kernel Perceptron I was curious how they differ?

Work Done

Polynomial Kernel:

$d_{k+1}(x)=d_{k}(\bar{x})+\rho k(\bar{x}_{k}, \bar{x})\; if\bar{x}_k\epsilon\,C_1$

$d_{k+1}(x)=d_{k}(\bar{x})-\rho k(\bar{x}_{k}, \bar{x})\; if\bar{x}_k\epsilon\,C_2$

$where, \; k(\bar{x}_{k}, \bar{x}) = (\bar{x}\cdot \bar{x}_{k}+1)^{q}$

Kernel Perceptron:

This is given by

$g(x)=\sum_{j=1}^{N}a_{j} K(\bar{x},\bar{x}_j)$

So as per my understanding a bias constant is added in former case when compared to later. So how does that impact and what difference does it make? Or am I missing something?

Any insights are appreciated.

I was looking at Support Vector machines (SVM) kernels. Looking at Polynomial Kernel and Kernel Perceptron I was curious how they differ?

Work Done

Polynomial Kernel:

$d_{k+1}(x)=d_{k}(\bar{x})+\rho k(\bar{x}_{k}, \bar{x})\; \mbox{if}\; \bar{x}_k\epsilon\,C_1$

$d_{k+1}(x)=d_{k}(\bar{x})-\rho k(\bar{x}_{k}, \bar{x})\; \mbox{if}\; \bar{x}_k\epsilon\,C_2$

where $k(\bar{x}_{k}, \bar{x}) = (\bar{x}\cdot \bar{x}_{k}+1)^{q}$

Kernel Perceptron:

This is given by

$g(x)=\sum_{j=1}^{N}a_{j} K(\bar{x},\bar{x}_j)$

So as per my understanding a bias constant is added in former case when compared to later. So how does that impact and what difference does it make? Or am I missing something?

Any insights are appreciated.