Biomedical Engineering Reference
In-Depth Information
5.6.3.2 Clustering
In the case where the user has no prior knowledge of the relationships between groups,
then
k
-means clustering is a simple ML algorithm commonly used in biomechatronics
and medical imaging
k
-means is an evolutionary unsupervised learning algorithm that clusters observations
into
k
groups, where
k
is provided as an input parameter. Each observation is assigned to
a specific cluster based on its proximity to the mean of that cluster. The cluster's mean is
then recomputed and the process is repeated as described:
1.
The algorithm arbitrarily selects
k
points as the initial cluster means.
2.
Each point in the data set is assigned to a cluster based on the Euclidean distance
between that point and each cluster mean.
3.
Each cluster mean is recomputed as the average of the points in that cluster.
4.
Steps 2 and 3 repeat until the clusters converge (typically when no change in the
mean is seen when steps 2 and 3 are repeated).
A disadvantage of
k
-means is that the user specifies the number of clusters as an input to
the algorithm. As designed, the algorithm is not capable of determining the appropriate
number of clusters and depends on the user to identify this in advance. For this reason, it
is a good idea to experiment with different values of
k
to identify the value that best suits
the data.
5.6.3.3 Support Vector Machines
Support vector machines (SVMs) are a set of kernel-based supervised learning methods
that perform their classification by constructing an
N
-dimensional hyperplane that sepa-
rates the measured data into two categories. In most cases the raw data cannot be separated
by a hyperplane, so it must be transformed by the kernel into another “feature” space that
maximizes the separation between the two classes.
In the two-dimensional (2-D) example shown in Figure 5-68, the two different cate-
gories of data are represented by circles and squares. In the original data shown in the
input
space, a complex curve is required to separate the categories. However, the appropriate
kernel transforms the data in such a manner that a straight line separates the two categories
as shown.
FIGURE 5-68
Kernel
transformation for a
2-D SVM.
