Biomedical Engineering Reference
In-Depth Information
The weights w
kr
are adjusted using
w
kl
!w
kl
+ "
k
x
l
;
p
l
l
where x
l
=
and where
X
n
"
k
=
k
(1
k
)
jk
j
:
j=1
Before any training sessions begin, the weights
jk
and w
kr
should be
initialized to small random values and should be chosen close enough
to 0 to allow the backpropagation algorithm to converge. In each train-
ing session, the patterns should be randomly permuted to avoid bias, and
training should continue until E is suciently close to 0. The backpropaga-
tion algorithm is well-established and can be found in many textbooks and
monographs. See, for example, Bose and Liang
12
for additional information
about the backpropagation algorithm.
3. Data Mining and Microarrays
Microarrays capture gene expression data for a given state by comparing
mRNA from a population in that state (sample) with mRNA from a pop-
ulation not in that state
1
. If M
l
is the base 2 logarithm of the ratio of the
intensity of the sample to the intensity of the reference for the l
th
gene,
then on average M
l
0 for unregulated genes andjM
l
j>> 0 for regulated
genes.
More generally, if there are N dierent classications for a collection
of training patterns, then for each i = 1; : : : ; N there is a pattern vector
i
=
1
; : : : ;
r
; where
1
if gene l is regulated
l
=
0
otherwise
, i = 1; : : : ; t, where
each q
i
is one of a xed set of output vectors o
1
; : : : ; o
N
and the corre-
sponding p
i
=
p
i
; q
i
Data sets for the classications are of the form
p
1
; : : : ; p
r
are given by
p
l
= R
l
+ M
l
l
where R
l
and M
l
are random variables with
R
l
= 0 and
M
l
>> 0 for
each l2f1; : : : ; rg: Similar to a microarray analysis, the problem is that
of using the training set to predict the pattern
j
for each j = 1; : : : ; N:
For microarray data, there is only one classification (i.e., the \sam-
ple"), which means that classication and feature extraction of microarray
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