Classification algorithms, statistical

SIMCA is an acronym for Statistical Isolinear Multiple Components Analysis, or Soft Independent Modelling of Class Analogy, or SIMilarographic Computer Analysis, or SIMple Classification Algorithm, or... 

Support vector machine (SVM) is originally a binary supervised classification algorithm, introduced by Vapnik and his co-workers [13, 32], based on statistical learning theory. Instead of traditional empirical risk minimization (ERM), as performed by artificial neural network, SVM algorithm is based on the structural risk minimization (SRM) principle. In its simplest form, linear SVM for a two class problem finds an optimal hyperplane that maximizes the separation between the two classes. The optimal separating hyperplane can be obtained by solving the following quadratic optimization problem ... 

The Bayesian algorithm is a nonclassical statistical method rather than an artificial intelligence approach. Compared to classical statistical methods, it has proved to be very rugged for classification projects not involving bacterial spectra. Therefore an attempt to use it for this application is warranted. 

This leads us to the other hand, which, it should be obvious, is that we feel that Chemometrics should be considered a subfield of Statistics, for the reasons given above. Questions currently plaguing us, such as How many MLR/PCA/PLS factors should I use in my model , Can I transfer my calibration model (or more importantly and fundamentally How can I tell if I can transfer my calibration model ), may never be answered in a completely rigorous and satisfactory fashion, but certainly improvements in the current state of knowledge should be attainable, with attendant improvements in the answers to such questions. New questions may arise which only fundamental statistical/probabilistic considerations may answer one that has recently come to our attention is, What is the best way to create a qualitative (i.e., identification) model, if there may be errors in the classifications of the samples used for training the algorithm ... 

Discriminant Analysis (DA) is a multivariate statistical method that generates a set of classification functions that can be used to predict into which of two or more categories an observation is most likely to fall, based on a certain combination of input variables. DA may be more effective than regression for relating groundwater age to major ion hydrochemistry and well construction because it can account for complex, non-continuous relationships between age and each individual variable used in the algorithm while inherently coping with uncertainty in the age values used for... 

MacKay s textbook [114] offers not only a comprehensive coverage of Shannon s theory of information but also probabilistic data modeling and the mathematical theory of neural networks. Artificial NN can be applied when problems appear with processing and analyzing the data, with their prediction and classification (data mining). The wide range of applications of NN also comprises optimization issues. The information-theoretic capabilities of some neural network algorithms are examined and neural networks are motivated as statistical models [114]. 

These same analysis techniques can be applied to chemical imaging data. Additionally, because of the huge number of spectra contained within a chemical imaging data set, and the power of statistical sampling, the PLS algorithm can also be applied in what is called classification mode as described in Section 8.4.5. When the model is applied to data from the sample, each spectrum is scored relative to its membership to a particular class (i.e. degree of purity relative to a chemical component). Higher scores indicate more similarity to the pure component spectra. While these scores are not indicative of the absolute concentration of a chemical component, the relative abundance between the components is maintained, and can be calculated. If all sample components are accounted for, the scores for each component can be normalized to unity, and a statistical assessment of the relative abundance of the components made. 

Key Words Biological activity chemical descriptors chemical spaces classification methods compound databases decision trees diversity selection partitioning algorithms space transformation statistics statistical medians. 

Fig. 8.11. The classifier development process. Clinical knowledge provides us with a set of classes for supervised classification (top, right). Large numbers of spectra from large sample numbers are reduced to a set of potentially useful features (top, left) or metrics. A modified Bayesian algorithm operates on the metrics to provide predictions that are compared to a gold standard. The end result of the training and validation process is an optimized algorithm, metric set, calibration and validation statistics, and sensitivity analysis of the data...

These same analysis techniques can be applied to chemical imaging data. Additionally, because of the huge number of spectra contained within a chemical imaging data set, and the power of statistical sampling, the PLS algorithm can also be applied in what is called classification mode. In this case, the reference library used to establish the PLS model is... 

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