SIMCA-Method

This concept allows a mathematical description of a single class of patterns. Outliers with deviating features lie outside the box. SIMCA gives for each unknown pattern a probability for each class. Patterns with very low probabilities for all classes probably Indicate a new kind . 

An Interclass distance Is measured as the distance between two hyperboxes relative to their thickness. This measure is used to characterize a classification problem. 

SIMCA Is not only applied to classification of unknowns but also to the prediction of one or several external properties of unknown patterns. 

FIGURE 41. In the SIMCA method a hyperbox is constructed for each class. 

Chemical applications of SINCA have been summarized by Wold et.al. C7, 3493 they include  

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There are many classification methods apart from linear discriminant analysis (Derde et al. [1987] Frank and Friedman [1989] Huberty [1994]). Particularly worth mentioning are the SIMCA method (Soft independent modelling of class analogies) (Wold [1976] Frank [1989]), ALLOC (Coomans et al. [1981]), UNEQ (Derde and Massart [1986]), PRIMA (Juricskay and Veress [1985] Derde and Massart [1988]), DASCO (Frank [1988]), etc. 

Vanden Branden, K., Hubert, M. Chemom. Intell. Lab. Syst. 79, 2005, 10-21. Robust classification in high dimensions based on the SIMCA method. 

To illustrate the problems associated with evaluating such data, we conducted several studies with Aroclor standards and mixtures of these standards in an effort to determine what information could be readily obtained with the SIMCA method of pattern recognition (30-32). The following discussion illustrates some of the features of this approach and describes how the SIMCA method works when applied to Aroclor mixtures. 

The similarity of samples can be evaluated by using geometrical constructs based on the standard deviation of the objects modeled by SIMCA. By enclosing classes in volume elements in descriptor space, the SIMCA method provides information about the existence of similarities among the members of the defined classes. Relations among samples, when visualized in this way, increase one s ability to formulate questions or hypotheses about the data being examined. The selection of variables on the basis of MPOW also provides clues as to how samples within a class are similar, and the derived class model describes how the objects are similar, with regard to the internal variation of these variables. 

In the discussion that follows, the SIMCA method is illustrated by applying it to three problems (1) quality assurance of chromatography data, (2) classification of unknowns, and (3) predicting the composition of unknown samples. This third problem is one of deconvolution of a mixture and calculation of the relative concentration of the constituents (25. 38). 

To illustrate the environmental application of the SIMCA method we examined a set of isomer specific analyses of sediment samples. The data examined were derived from more than 200 sediment samples taken from a study site on the Upper Mississippi River (41). These analytical data were transferred via magnetic tape from the laboratory data base to the Cyber 175 computer where principal component analysis were conducted on the isomer concentration data (ug/g each isomer). 

Unlike the methods discussed above, which strive to find directions in a common space that separate known classes, the SIMCA method [81] works on a quite different principle define a unique space for each class, define class-specific models using each of these spaces, and then apply any unknown sample to all of these models in order to assess class membership. 

Although the development of a SIMCA model can be rather cumbersome, because it involves the development and optimization of J PCA models, the SIMCA method has several distinct advantages over other classification methods. First, it can be more robust in cases where the different classes involve discretely different analytical responses, or where the class responses are not linearly separable. Second, the treatment of each class separately allows SIMCA to better handle cases where the within-class variance structure is... 

Although the SIMCA method is very versatile, and a properly optimized model can be very effective, one must keep in mind that this method does not use, or even calculate, between-class variability. This can be problematic in special cases where there is strong natural clustering of samples that is not relevant to the problem. In such cases, the inherent interclass distance can be rather low compared to the mtraclass variation, thus rendering the classification problem very difficult. Furthermore, from a practical viewpoint, the SIMCA method requires that one must obtain sufficient calibration samples to fully represent each of the J classes. Also, the on-line deployment of a SIMCA model requires a fair amount of overhead, due to the relatively large number of parameters and somewhat complex data processing instructions required. However, there are several current software products that facilitate SIMCA deployment. 

Various methods work in similar ways with regard to some of the steps but the methods may differ in very significant and critical ways in other steps. In some ways the SIMCA method is unique when viewed in the context of these steps. 

Only one class modeling method is conmonly applied to analytical data and this is the SIMCA method ( ) of pattern recognition. In this method the class structure (cluster) is approximated by a point, line, plane, or hyperplane. Distances around these geometric functions can be used to define volumes where the classes are located in variable space, and these volumes are the basis for the classification of unknowns. This method allows the development of information beyond class assignment ( ). 

In this example, two principal components are arbitrarily selected. More or fewer may be necessary, and this is a function of a predetermined stopping rule for extraction of principal components from X. In SIMCA method, a cross validation technique (2) is used. 

After the feature selection process has been carried out once by the SIMCA method, it is necessary to refine the model because the iK>del may shift slightly. This refining of the model leads to an ( timal set of descriptors with optimal mathematical structure. 

The SIMCA method of pattern recognition is in a comprehensive set of programs for classification, and we have discussed how it works in this regard. Classification problems represent only a few of types of problems that can be solved with this approach. 

A method successfully used for chromatographic data and capable to answer this and related questions is the SIMCA method (Statistical Isolinear Multiple Component Analysis). It has been constructed and developed by Svante Wold and his group at the University of Umea, Sweden. 

The SIMCA method and the principal components (PC) analysis, a common method for obtaining a view of multivariate data, have been described in detail elsewhere (4,5) thus only a short presentation will be given here. 

SIMCA (each class described by a PC model). The basic idea of the SIMCA method is that multivariate data measured on a group of similar objects, a proper class are well approximated by a simple PC model. 

Moreover, because the Mahalanobis distance is a chi-square function, as is the SIMCA distance used to define the class space in the SIMCA method (Sect. 4.3), it is possible to use Coomans diagrams (Sect. 4.3) both to visualize the results of modelling and classification (distance from two category centroids) and to compare two different methods (Mahalanobis distance from the centroids versus SIMCA distance). 

The basic steps involved in identifying a sample using NIR will be illustrated using the SIMCA method, which is one of the popular methods for product ID. The... 

SIMCA method relies on a pattern-recognition technique called principal component analysis (PCA). 

The SIMCA method has been developed to overcome some of these limitations. The SIMCA model consists of a collection of PCA models with one for each class in the dataset. This is shown graphically in Figure 10. The four graphs show one model for each excipient. Note that these score plots have their origin at the center of the dataset, and the blue dashed line marks the 95% confidence limit calculated based upon the variability of the data. To use the SIMCA method, a PCA model is built for each class. These class models are built to optimize the description of a particular excipient. Thus, each model contains all the usual parts of a PCA model mean vector, scaling information, data preprocessing, etc., and they can have a different number of PCs, i.e., the number of PCs should be appropriate for the class dataset. In other words, each model is a fully independent PCA model. 

For the SIMCA method, calibration is done by constructing a set of Z class-specific PCA models. Each PCA model is built using only the calibration samples from a single class. Consequently, one obtains a set of PCA model parameters for each of the Z classes... 

When the SIMCA method is applied to the polyurethane data, it is found that two PCs are optimal for each of the four local PCA class models. When this SIMCA model is applied to the prediction sample A, it correctly assigns it to class 2. When the model is applied to prediction sample B, it is stated that this sample does not belong to any class,... 

Dunn III, WJ. and Wold, S., An assessment of carcinogenicity of N-nitroso compounds by the SIMCA method of pattern recognition, J. Chem. Inf. Comput, Sci., 21, 8-13, 1981. 

When data are high dimensional, the approach of the previous section can no longer be applied because the MCD becomes uncomputable. In the previous example (Section 6.8.1.3), this was solved by applying a dimension-reduction procedure (PC A) on the whole set of observations. Instead, one can also apply a PC A method on each group separately. This is the idea behind the SIMCA method (soft independent modeling of class analogy) [77],... 

The SIMCA method, first advocated by the S. Wold in tire early 1970s, is regarded by many as a form of soft modelling used in chemical pattern recognition. Although there are some differences with linear discriminant analysis as employed in traditional statistics, the distinction is not as radical as many would believe. However, SIMCA has an important role in the history of chemometrics so it is important to understand the main steps of the method. 

The SIMCA method defines a factorial model with a,- principal components for each of the k groups, starting with the corresponding matrix of standardised data. 

Dunn III, W.J. and Wold, S. (1978). A Structure-Carcinogenicity Study of 4-Nitroquinoline 1-Oxides Using the SIMCA Method of Pattern Recognition. J.Med.Chem.,21,1001. 

A far better way to achieve a classification is to use the SIMCA method which is briefly discussed in Chapter IS. 

Objects The score plots describe the large and systematic variation between the objects. Often, clear groupings can be discerned in the score plots. This indicates that there are subgroups in the set of objects and that objects which belong to such a subgroup are more similar to each other than to members of other subgroups. Such groupings can then be used for classification of new objects by the SIMCA method, see below. 

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