Feature Extraction and Inner Product Representation in Tree Structures - Prof. Dan Roth, Study notes of Computer Science

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Features

A “feature” is a function on a structure, e.g.,

h( x) (^) = (^) Number of times

B C A

is seen in

(^) x

1 T

A

d DE B e fg FG C

2 T

A

de DE B

C

h F b BC A c

h(

1 T

h(

2 T

Feature Vectors

A set of functions

1 h (^) : (^) : (^) : (^) h d (^) define a

(^) feature vector

x) (^) =

hh

(^1) (x ); (^) h (^2) (x ) (^) : : (^) : dh (^) (x

)i

1 T

A

d DE B e fg FG C

2 T

A

de DE B

C

h F b BC A c



(T

h 1

i



(T

h 2

i

All Sub-fragments for Tagged Sequences

Given: State symbols

fS

(^) ; (^) C ; (^) N

g

Terminal symbols

fa;

(^) b; c; : (^) : (^) :

g

An infinite set of sub-fragments

S

a j S

S — C

S — C

b j

An infinite set of features, e.g.,

3 h (^) (x ) (^) = (^) Number of times

S — b j C

is seen in

(^) x

Inner Products

x) (^) =

hh

(^1) (x ); (^) h (^2) (x ) (^) : : (^) : dh (^) (x

)i

Inner product (“

Kernel

”) between two structures

1 T (^) and 2 T (^) :

1 T

(^)  (T (^2) ) =

i=1 X d

i h( 1 T (^) )h i (^) (T (^2) )

1 T A

de DE B

fg FG C

2 T

A

de DE B

C

h F b BC A c

1 T (^) ) (^) =

h 1

i

2 T (^) ) (^) =

h 2

i

1 T

(^)  (T (^2) ) =

All Subtrees Representation



is now huge

But

inner product

(^) 

(T



(T

can be computed

efficiently using dynamic programming.