492
S. Biswas et al.
two approaches to the analysis of spectral features. In the first, eigenvectors of
the entire spectrum can be considered in some transform space (for example, using principal components analysis or PCA). In this approach, all the information
contained in the spectrum is utilized, making it very powerful. In the opinion of
the authors, this approach also includes all scattering and information dependent
on the sample’s physical characteristics, making its use for classification highly
dependent on the physical characteristics of the data set. In a second approach [48],
spectral knowledge and biochemical insight are used to define spectral features that
may potentially be used for classification. these are named as ‘metrics’. the use
of metrics can easily avoid factors other than chemical differences but may miss
some features useful for classification. An example of a metric can be the ratio of
absorbance of the phosphodiester-specific spectral peak at 1,080 cm
−1
to the amide
II vibration-specific absorbance at 1,545 cm
−1
. this ratio has shown to be useful in
discriminating epithelial cells from stromal cells. Recently, an analysis of variance
on IR imaging data sets [49] revealed that the sample morphology effects on spectra may be large compared to the information bearing metrics for some cases. this
evidence implies that whole spectrum methods to select features, such as PCA, may
be dominated by information that is not chemical in origin. hence, we have strongly
pursued the metric approach in our work. there are two additional goals behind
this process. First, relevant information is contained in a small number of points as
compared to the total number of points in the entire absorption spectrum (dimensionality reduction). Second, information captured by metrics is spectroscopically
understandable since they are selected by studying the biochemically significant
features from the spectra.
the third step of the classification is to use this information to train a classifier
by minimizing the errors or maximizing the detection probability of the classes.
the selected features are used to predict the accuracy of classification using training data. the parameters of the algorithm, quantitative measures of accuracy as
well as the feature set used to classify become apparent at this stage. Supervised
recognition algorithms include several common ones based on Bayes rule, Artificial
Neural Networks (ANN), Linear discriminant Analysis (LdA) or Support vector
machines (Svm). In general, the Bayes rule-based classifiers are most appropriate when a large training set in available while others typically estimate either the
distribution of the data or the complexity of the contour required to separate classes
in the dimensional space of the data. In our experience, the choice of a specific algorithm does not make a tremendous difference in the results obtained, however, the
requirements for data size, speed and insight into classification differ substantially
among the various algorithms. Finally, the validation set is employed to test the
efficacy of the developed algorithm and present its results in an independent test.
Sometimes, a part (1/n) of the training data may be designated as an independent
validation set, the training repeated n times, each time leaving (1/n) part of the data
for validation. this is termed n-fold cross-validation and is often used as a surrogate
for a completely independent data set. We suggest that an independent data set be
used and the n-fold technique be used as a preliminary test for histologic analyses
due to the complexity of biological materials.
S. Biswas et al.
two approaches to the analysis of spectral features. In the first, eigenvectors of
the entire spectrum can be considered in some transform space (for example, using principal components analysis or PCA). In this approach, all the information
contained in the spectrum is utilized, making it very powerful. In the opinion of
the authors, this approach also includes all scattering and information dependent
on the sample’s physical characteristics, making its use for classification highly
dependent on the physical characteristics of the data set. In a second approach [48],
spectral knowledge and biochemical insight are used to define spectral features that
may potentially be used for classification. these are named as ‘metrics’. the use
of metrics can easily avoid factors other than chemical differences but may miss
some features useful for classification. An example of a metric can be the ratio of
absorbance of the phosphodiester-specific spectral peak at 1,080 cm
−1
to the amide
II vibration-specific absorbance at 1,545 cm
−1
. this ratio has shown to be useful in
discriminating epithelial cells from stromal cells. Recently, an analysis of variance
on IR imaging data sets [49] revealed that the sample morphology effects on spectra may be large compared to the information bearing metrics for some cases. this
evidence implies that whole spectrum methods to select features, such as PCA, may
be dominated by information that is not chemical in origin. hence, we have strongly
pursued the metric approach in our work. there are two additional goals behind
this process. First, relevant information is contained in a small number of points as
compared to the total number of points in the entire absorption spectrum (dimensionality reduction). Second, information captured by metrics is spectroscopically
understandable since they are selected by studying the biochemically significant
features from the spectra.
the third step of the classification is to use this information to train a classifier
by minimizing the errors or maximizing the detection probability of the classes.
the selected features are used to predict the accuracy of classification using training data. the parameters of the algorithm, quantitative measures of accuracy as
well as the feature set used to classify become apparent at this stage. Supervised
recognition algorithms include several common ones based on Bayes rule, Artificial
Neural Networks (ANN), Linear discriminant Analysis (LdA) or Support vector
machines (Svm). In general, the Bayes rule-based classifiers are most appropriate when a large training set in available while others typically estimate either the
distribution of the data or the complexity of the contour required to separate classes
in the dimensional space of the data. In our experience, the choice of a specific algorithm does not make a tremendous difference in the results obtained, however, the
requirements for data size, speed and insight into classification differ substantially
among the various algorithms. Finally, the validation set is employed to test the
efficacy of the developed algorithm and present its results in an independent test.
Sometimes, a part (1/n) of the training data may be designated as an independent
validation set, the training repeated n times, each time leaving (1/n) part of the data
for validation. this is termed n-fold cross-validation and is often used as a surrogate
for a completely independent data set. We suggest that an independent data set be
used and the n-fold technique be used as a preliminary test for histologic analyses
due to the complexity of biological materials.