Page 357 - Computational Statistics Handbook with MATLAB

346 Computational Statistics Handbook with MATLAB

are the left and right child nodes.
t L and t R
{} is the tree containing only the root node.
t 1
is a branch of tree T starting at node t.
T t
)
T is the set of terminal nodes in the tree.
)
T is the number of terminal nodes in tree T.
∗
t k is the node that is the weakest link in tree T k .
n is the total number of observations in the learning set.
is the number of observations in the learning set that belong to the
n j
,
,
j-th class ω j j = 1 …, . J
nt() is the number of observations that fall into node t.
n j t() is the number of observations at node t that belong to class ω j .

.
π j is the prior probability that an observation belongs to class ω j
This can be estimated from the data as

ˆ n j
πj = ---- . (9.11)
n
p ω j t,( ) represents the joint probability that an observation will be in
. It is calculated using
node t and it will belong to class ω j
π j n j t()
(
,
p ω j t) = ---------------- . (9.12)
n j
pt() is the probability that an observation falls into node t and is
given by

J
pt() = ∑ p ω j t,( . ) (9.13)
j = 1

p ω t( ) denotes the probability that an observation is in class ω given
j j
it is in node t. This is calculated from
p ω j t,( )
(
p ω j t) = ------------------ . (9.14)
pt()
rt() represents the resubstitution estimate of the probability of mis-
. This
classification for node t and a given classification into class ω j

© 2002 by Chapman & Hall/CRC