Biomedical Engineering Reference
In-Depth Information
Various examples from technical and non-technical fields of applications can be
found to use MDS as a mapping tool. The MDS has been applied to pilot perfor-
mance data obtained during simulated air-to-air combat [
127
], where an adequate
performance metric was developed to describe the complex interaction between po-
sition advantage and energy management.
Multi-dimensional scaling is also aimed to represent high-dimensional data
in a low-dimensional space with preservation of the similarities between data
points [
47
]. This reduction in dimensionality is crucial for analyzing and reveal-
ing the genuine structure hidden in the data. For noisy data, dimension reduction
can effectively diminish the effect of noise on the embedded structure. For large
data sets, dimension reduction can effectively overcome the information retrieval
complexity. Thus, MDS techniques are used in many applications of data mining
and gene network research [
157
,
160
].
From the field of non-technical applications, the area of medicine seems to suit
most the applicability of MDS, that is, the analysis of biomedical data in general.
For medical image analysis, it is important to take advantage of the full range of
information presented in an image, thus one has to consider distance and shape
attributes [
98
,
166
]. Separation between left and right brain sulci was developed us-
ing MDS for a new geometric representation [
98
]. Topography of functional brain
spaces and cortico-cortical interactions was implemented through MDS [
48
], in or-
der to transform anatomical space so that the distance between cortical areas is
directly related to their functional connectivity. Similarly, MDS has been useful
to provide an automatic method for classification of electroencephalogram (EEG)
waveforms, in order to objectively detect changes in EEG recordings [
60
], with re-
sults in agreement with visual examination by trained physicians. Bearing in mind
the success of previously reported results of MDS in various medical applications,
we propose the use of MDS tools to provide a geometrical mapping of data from
lung function tests in healthy subjects and in patients with respiratory disorders.
There are a manifold of techniques available to cluster data for classification
purposes. These vary in optimization algorithms, speed of convergence, visualiza-
tion technique and complexity. However, the MDS-based algorithms have lower
complexity and faster convergence when compared to other variants [
16
]. If a large
number data points are available, methods for high-dimensional data may be more
suitable than MDS, e.g. self-organizing maps [
89
]. They are based on neural net-
works and rely on feature analysis to reduce dimensionality. In this paper, the di-
mension of our data is relatively low, hence the self-organizing feature maps are not
employed. Moreover, they do not preserve distance information (i.e. only topolog-
ical). The authors of [
89
] showed that a MDS-based tool is preferable for its trade
off between complexity and ability to partition data sets. Moreover, MDS can pro-
cess many types of data: nonnegative or negative, frequencies, correlations, ratings,
etc. [
14
] and can optimally transform the data for better results. The main property
of MDS that will be explored in this paper is that the distances between the points
can be directly interpreted.
MDS is a generic name for a family of algorithms that construct a configuration
of points in a low-dimensional space from information about inter-point distances
