Supervised SIMCA

Classical supervised pattern recognition methods include /( -nearest neighbor (KNN) and soft independent modeling of class analogies (SIMCA). Both... 

Supervised pattern recognition methods are used for predicting the class of unkno-wm samples given a training set of samples with known class member-sliip. Tvksmethods are discussed in Section 4.3, KNN and SIMCA,... 

Two supervised methods are examined in this chapter, KNN and SIMCA. The KNN models are constructed using the physical closeness of samples in space. It is a simple method that does not rely on many assumptions about the data. SIMCA models are based on more assumptions and define classes using the position and shape of the object formed by the samples in row space. A multidimensional box is constructed for each class using PCA and tlie classification of future samples is perfonned by determining within which box the sample belongs. 

Current methods for supervised pattern recognition are numerous. Typical linear methods are linear discriminant analysis (LDA) based on distance calculation, soft independent modeling of class analogy (SIMCA), which emphasizes similarities within a class, and PLS discriminant analysis (PLS-DA), which performs regression between spectra and class memberships. More advanced methods are based on nonlinear techniques, such as neural networks. Parametric versus nonparametric computations is a further distinction. In parametric techniques such as LDA, statistical parameters of normal sample distribution are used in the decision rules. Such restrictions do not influence nonparametric methods such as SIMCA, which perform more efficiently on NIR data collections. 

Supervised learning methods - multivariate analysis of variance and discriminant analysis (MVDA) - k nearest neighbors (kNN) - linear learning machine (LLM) - BAYES classification - soft independent modeling of class analogy (SIMCA) - UNEQ classification Quantitative demarcation of a priori classes, relationships between class properties and variables... 

SIMCA is a supervised pattern recognition technique, which needs to have the data classrhed manually or done using HCA. SIMCA then performs PCA on each class with a sufficient number of factors retained to account for most of the variation within classes. The number of factors retained is very important. If too few are selected, the information in the model set can become distorted. By using a procedure called cross validation, segments of the data are omitted during PCA, and the omitted data are predicted and compared to the actual value. This is repeated for every data element until each point has been excluded once from the determination. The PCA model that yields the minimum prediction error for the omitted data is retained. 

The aim of supervised classification is to create rules based on a set of training samples belonging to a priori known classes. Then the resulting rules are used to classify new samples in none, one, or several of the classes. Supervised pattern recognition methods can be classified as parametric or nonparametric and linear or nonlinear. The term parametric means that the method makes an assumption about the distribution of the data, for instance, a Gaussian distribution. Frequently used parametric methods are EDA, QDA, PLSDA, and SIMCA. On the contrary, kNN and CART make no assumption about the distribution of the data, so these procedures are considered as nonparametric. Another distinction between the classification techniques concerns the... 

Once the data are prepared, they can be explored chemometrically with techniques as PCA, rPCA, PP, and clustering. These enable visualization of the structure of the data set more specifically, they detect outliers and group similar samples. For several applications, it was confirmed that this approach outperforms the visual comparison of electropherograms. Chemometric techniques can also be apphed to classify samples based on their CE profile. When the classes in the data set are a priori known, supervised classification techniques as EDA, QDA, kNN, CART, PLSDA, SIMCA, and SVM can be used. The choice of techniques will often depend on the preference of the analyst and the complexity of the data. However, when nonlinear classification problems occur, a more complex technique as, for instance, SVM, will be outper-... 

As a final remark it should be realized that when using some Supervised Learning techniques like SIMCA, the scaling of the data set is carried out only over the samples belonging to the same class (separate scaling). This is due because the own fundamentals of the methodology and has a beneficial effect on the classification (Derde et al., 1982). 

If the membership of objects to particular clusters is known in advance, the methods of supervised pattern recognition can be used. In this section, the following methods are explained linear learning machine (LLM), discriminant analysis, A -NN, the soft independent modeling of class analogies (SIMCA) method, and Support Vector Machines (SVMs). 

The first two parts of this section describe supervised learning methods which may be used for the analysis of classified data. One technique, discriminant analysis, is related to regression while the other, SIMCA, has similarities with principal component analysis (PCA). The final part of this section discusses some of the conditions which data should meet when analysed by discriminant techniques. 

The SIMCA method is based on the construction of principal components (PCs) which effectively fit a box (or hyper-box in N dimensions) around each class of samples in a data set. This is an interesting application of PCA, an unsupervised learning method, to different classes of data resulting in a supervised learning technique. The relationship between SIMCA and PLS, another supervized principal components method, can be seen clearly by reference to Section 7.3. 

Mass spectrometry and chemometric methods cover very diverse fields Different origin of enzymes can be disclosed with LC-MS and multivariate analysis [45], Pyrolysis mass spectrometry and chemometrics have been applied for quality control of paints [46] and food analysis [47], Olive oils can be classified by analyzing volatile organic hydrocarbons (of benzene type) with headspace-mass spectrometry and CA as well as PC A [48], Differentiation and classification of wines can similarly be solved with headspace-mass spectrometry using unsupervised and supervised principal component analyses (SIMCA = soft independent modeling of class analogy) [49], Early prediction of wheat quality is possible using mass spectrometry and multivariate data analysis [50],... 

Such a diagnosis is obtained best using supervised or trained algorithms. A number of such predictive algorithms exist, some very similar to that of the principles of PCA (i.e. soft independent modeling of class analogy, SIMCA), linear discriminant analysis (LDA) to more compUcated classifiers such as support vector machines (SVMs), which are based on separating spectral classes by complicated, multidimensional separation planes [30]. At the LSpD, ANNs have been used [52-54] for supervised prediction of class memberships. 

SIMCA soft independent modelling of class analogy—Supervised... 

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