Page 160 - Big Data Analytics for Intelligent Healthcare Management

6.1 INTRODUCTION 153

For this purpose, we will opt with:
1
ð
hθ xðÞ ¼ g θTxÞ ¼ T (6.1)
1+ e θ x
where:
1
gzðÞ ¼ (6.2)
1+ e z
is referred as the logistic or sigmoid function.
g(z) tends towards 1 as z!∞, and g(z) tends towards 0 as z! ∞. Moreover, g(z), and hence also
h(x), is always bounded between 0 and 1. Here we maintain the convention of letting x 0 ¼1, so that:
X n
θ Tx ¼ θ0+ θ j x j (6.3)
i¼1
The classification model has a number of probabilistic assumptions to fit θ for it, and then the param-
eters are fitted using the maximum likelihood.
Let us assume that:
Py ¼ 1 j x; θÞ ¼ hθ xðÞ (6.4)
ð
ð
Py ¼ 0 j x; θÞ ¼ 1 hθ xðÞ (6.5)
This can be presented more efficiently as:
py j x; θÞ ¼ hθ xðÞÞy 1 hθ xðÞÞ1 y (6.6)
ð
ð
ð
SVM is considered to be one of the most important methods for classification and linear kernel [5, 7] is
used for training SVM. The SVM is a generalization of maximal margin classifier and it makes use of a
hyperplane for segregating two types of data. The maximal margin hyperplane outermost from the
training examples is selected. The distance from each training example to a given segregating hyper-
plane can be calculated. The margin is the minimal distance from the examples to the hyperplane.
These two hyperplanes can be represented as given below:
x:y b ¼ 1 and x:y b ¼ 1 (6.7)
Obviously, in order for 2 to be maximized, the value of w should be minimum. The next important
|| w||
step is the feature selection method. The feature selection methods enumerated below are employed
independently and collectively in order to compare performance. All voxels or features present in
the data are used to create sample data which is used for training and testing different learning models.
A training example may have a number of images and each image comprises of thousands of voxels. As
a result, the dimension of the feature vector can be very high.
ROI is a popular method used for selection of features in fMRI image classification [1]. Within
every ROI, the mean activation value referred to as the super voxel is calculated for the voxels.
The feature vectors are the collections of average values [2, 8]. This approach is very useful for data
that is assembled from diverse subjects. Voxels are chosen based on their capability to differentiate
target methods. Here we have used F-ratio based method to find the contribution of each voxel in
the feature set.