IEEE Computational Intelligence Magazine - August 2018 - 15

C. Fitness evaluation in a Population

The fitness function represents how informative the chromosome is to classify the samples. That is, the fitness for an individual is evaluated by measuring the classification accuracy for
interaction of the features. To determine and update the fitness
for each individual, we introduce a gradient descendant rule for
training data D as follows:
w i = w i + h (t j - f ( D j)) v ji,

(7)

where w i is the weight value for i-th feature and t j is the target
class in the j-th training instance D j . h is the learning rate and
v ji is the value of the i-th attribute in the j-th instance. f (D j) is
the predicted output value of the j-th training instance by our
model and determined as follows:

if

n

/ w i $ v ji 2 0,

i=0

(8)

III. Results
a. DNa Methylation Module associated with Breast Cancer

This analysis was carried out based on DNA methylation profiling datasets that experimentally measured the methylation
statuses using DNA Methylation BeadChip [35]. We extracted
data for DNA methylation profiles on chromosome 17 from
breast cancer and normal samples. Then, the data used at our
experiment consist of total 99 samples with 82 cancer and 17
normal samples with 1,587 features. Figure 2 shows the learning curves in the evolutionary process. The fitness value was
improved when the number of generations increased. We introduced a term, in the fitness function, for the number of the
methylation sites to find an individual with a shorter length;

- 1, otherwise.

The difference between the predictions and the target values
specified in the training sequence is used to represent the error
of the current weight vector. The target function is optimized
to minimize the classification error. The weight values are evaluated against a sequence of training samples and are updated to
improve the classification accuracy. The weight update processes
are repeated until they converge after a number of epochs.
Using the learning scheme, we identify the most informative individuals for classification, where the absolute values of
their weights are large. In addition, it is better to find the DNA
methylation module, whose number of features is small. Finally,
the fitness function for the k-th individual X k, Fitness (X k ) is
defined as follows:
Fitness (X k ) = Acc (X k ) - Order (X k ),

1.0
0.9
0.8
Fitness

f ( D j) = *

1,

The DNA methylation levels of the two datasets were represented as beta-values, which were bounded between 0
(unmethylated) and 1 (totally methlyated).

0.7
0.6
0.5
Maximum
Mean
Minimum

0.4
0.3
0

10

20

(9)
1,000

where Acc (X k ) is the classification accuracy for training datasets
and Order (X k ) denotes the number of methylation sites which
are selected in the individual X k.

The high-throughput DNA methylation profiles of large
genomic regions can be produced by both array and NGS
technologies. We applied our approach to these two types of
datasets. The array data were generated by the Illumina Infinium 27 k Human DNA methylation BeadChip, for surveying
genome-wide DNA methylation profiles in breast cancer and
normal samples [35]. We downloaded the dataset from Gene
Expression Omnibus accession number GSE32393, and removed the samples with missing values. Sequence-based datasets
were produced by MethylCap-seq in matched normal and
colorectal cancer samples and collected at GSE39068 [36]. Normalization and preprocessing were carried out using the approaches detailed by Simmer et al. [36].

50

60

Maximum
Mean
Minimum

800

Order

D. Dataset

30
40
Generation
(a)

600
400
200
0
0

10

20

30
40
Generation
(b)

50

60

FIgurE 2 Learning curve using breast cancer datasets. The x-axis is
the number of generations and the y-axis shows (a) fitness values and
(b) the number of methylation sites.

auguSt 2018 | IEEE ComputatIonal IntEllIgEnCE magazInE

15



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