Statistics and Data Analysis for Microarrays Using R and Bioconductor, 2nd Edition

966 Statistics and Data Analysis for Microarrays Using R and Bioconductor

b is the offset from the origin. If b = 0, the hyperplane passes through the

origin.

However, finding such a function is mo re complex in case of nonlinearly

separable data set. The complexity of the target function f(x) depends on the

way input data are represented. A common preprocessing practice in machine

learning is to represent the input data by mapping it to another space as:

x = (x

1

, . . . , x

n

) 7−→ φ(x) = (φ

1

(x), . . . , φ

N

(x)) (29.9)

The new s pace is often referre d to as a feature space in the literature. In

the new feature space, f (x) is represented as:

f(x) = hw · φ(x)i + b =

N

X

q=1

w

q

φ

q

(x) + b (29.10)

It can be shown that Eq. 29.10 can be represented as a linear combination ...