Chemometric Methods for Biomedical Raman Spectroscopy and Imaging - Emerging Raman Applications and Techniques in Biomedical and Pharmaceutical Fields - page 191

The ideas behind neural networks are essentially that of nonlinear trans-
formations to provide segmentation. Other methods are based on similar
ideas, including support vector machines (SVM) in which classification is
accomplished by constructing a high-dimensional hyperplane that optimally
separates the data into categories. SVM models can sometimes be related to
neural networks, e.g., a sigmoid kernel function is equivalent to a two-layer,
perceptron neural network. The method is illustrated in Fig. 8.6. The accu-
racy of SVM is largely determined by the selection of parameters to define
the hyperplane. The simplest way to divide two groups is with a straight
line, flat plane, or an N -dimensional hyperplane. If the points are separated
by a nonlinear region, rather than fitting nonlinear curves to the data, SVM
uses a kernel function to map the data into a space where a simple hyper-
plane can be used. For separation of more than two categories, one-against-all
or one-against-one approaches may be used. SVMs are very powerful in that
they can find generalized transformations but are susceptible to over-training,
especially when the numbers of spectra are small compared to the dimension-
ality of the data. Classifications using Raman spectral data and SVM have
been reported for bacteria in a set of studies reported by the Popp group
[101-103], colon histopathology [104], and yeast classification [105]. SVM has
Fig. 8.6. A An example of a two-class system (denoted by light and dark squares )in
which the data can be separated. SVM analysis is used to achieve a one-dimensional
hyperplane (here, a line) that separates the data into two classes. The plane (here,
line) is drawn such that separation is achieved by the segmentation line lying between
the two dashed lines . B The second aspect is to increase the distance between the
dashed lines by optimization (here, rotation angle) such that the distance between
the hyperplane and the data points is highest. The distance between the dashed lines
is called the margin. The vectors (points) that constrain the width of the margin
are the support vectors. C Nonlinear kernels may be useful in segmenting complex
distributions but there is some danger of over-fitting. The circle at the center in
( C )and( D ) becomes critical to definition of the kernel if it is encountered during
training. One possible approach to minimize such errors is to build successively
complex models and evaluate results