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Saunder September 1, 2015 16:47 K23081˙C008

‘‘Who’’ Entity: Character Identification



101

In LapSVM [15], classifier f is learned by minimizing the following objective

function:

J( f ) =

l



i=1

max(1 − y

i

f (x

i

), 0) +γ

A



f



2

A

+ γ

I



f



2

I

(8.3)

where  f 

2

A

represents the regularization in the corresponding reproducing kernel

Hilbert space (RKHS) to avoid overfitting.



f



2

I

embodies the smoothness

assumption on the underlying manifold; that is, samples with high similarity have

similar classifier responses. Here, we adopt a graph-based manifold regularizer as



f



2

I

=



i, j

( f (x

i

) − f (x

j

))

2

W

ij

.

Bydefining the classifier in theRKHS according to the representertheorem [165],

we have the following classifier representation:

f (·) =

l+u



i=1

α

i

k(x

i

, ·) (8.4)

where k(x

i

,