![](bg5.png)
Hence, the learning task in SVM can be formalized
as the following constrained optimization problem:
2
||w||
min
2
w
(5)
n ..., 2, 1,i 1,b)x(wy subject to
ii
(6)
This is also known as a convex optimization
problem, which can be solved by using the standard
Lagrange multiplier method:
N
1i
iii
2
p
1)-b)x(w(y-||w||
2
1
L
(7)
where parameters σ
are called the Lagrange
multipliers. With the Lagrange multipliers, the
decision function can be written as follows:
b)x),K(xysgn(f(x)
ii
n
1i
i
(8)
Additionally, the results of each classifier are
combined by majority voting, and classification of
unknown data is performed based on the class label
to obtain the most frequent votes. The mathematical
function of our ensemble method with k classifiers
can be written as:
))c ,(x)(fmax( argclass(x)
i
k
k
(9)
6 EXPECTED OUTCOME
At the end of this PhD research, a new ensemble
classification method will be available for predicting
prostate cancer from RNA-Seq data. Moreover, a
complete gene expression data simulator will be
developed. The simulator may help to research non-
parametric methods for cancer classification. The
research will lead to new insights for understanding
prostate cancer by identifying candidate genes from
high-dimensional gene expression data. If this is
proven successful, our approach could be applied to
other types of disease.
ACKNOWLEDGEMENT
This work was supported by the National Research
Foundation of Korea (NRF) grant funded by the
Korea government (MSIP) (No. 2008-0062611) and
the Basic Science Research Program through the
National Research Foundation of Korea (NRF)
funded by the Ministry of Science, ICT & Future
Planning (No.2013R1A2A2A01068923).
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