Classification-based methods

As discussed, moving from one Pareto optimal solution to another implies trading off. In other words, to move to another Pareto optimal solution where some objective function gets a better value, some other objective function must be allowed to get worse. This is the starting point of classification-based methods where the DM studies a Pareto optimal solution and says what kind of changes in the objective function values would 

Classification is an intuitive way for the DM to direct the solution process because no artificial concepts are used. Objective function values are as such meaningful and understandable for the DM. The DM can express hopes about improved solutions and directly see and compare how well the hopes could be realized. 

To be more specific, when classifying objective functions the DM indicates which function values should improve, which ones are acceptable and which are allowed to get worse. In addition, amounts of improvement or impairments are asked from the DM. There exist several classification-based interactive multi-objective optimization methods. They use different numbers of classes and generate new solutions in different ways. 

Let us point out that expressing preference information as a reference point (Miettinen and Makela, 2002 Miettinen et ai, 2006) is closely related to classification. However, when classification assumes that some objective function must be allowed to get worse, a reference point can be set without considering the current solution. Even though it is not possible to improve all objective function values of a Pareto optimal solution simultaneously, the DM can still express preferences without pa3ung attention to this fact and then see what kind of solutions are feasible. On the other hand, when using classification, the DM is more in control and selects functions to be improved and specifies amounts of impairment for the others. 

we briefly introduce the satisficing trade-off method and then describe the NIMBUS method in some more detail. We pay more attention to NIMBUS (and software implementing it) because we shall refer to it later when discussing applications. 

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The classification-based method uses statistic or other techniques to assign each pixel to the different regions of the image. 

The uses of steel are too diverse to be Hsted completely or to serve as a basis of classification. Inasmuch as grades of steel are produced by more than one process, classification by method of manufacture is not advantageous. The most useful classification is by chemical composition into the large groups of carbon steels, alloy steels, and stainless steels. Within these groups are many subdivisions based on chemical composition, physical or mechanical properties, or uses. 

A classification based first on ion specificity, then on stmctural features has been suggested for the polyethers (7). Another method uses the presence of unsaturation or of aromatic groups in the molecular skeleton (8). In this review the compounds are classified based on the number of carbons in the backbone according to the numbering system proposed in reference 9. The carbon backbone or skeleton refers to the longest chain of contiguous carbons between the carboxyl group and the terminal carbon. 

The classification of methods for studying electrode kinetics is based on the criterion of whether the electrical potential or the current density is controlled. The other variable, which is then a function of time, is determined by the electrode process. Obviously, for a steady-state process, these two quantities are interdependent and further classification is unnecessary. Techniques employing a small periodic perturbation of the system by current or potential oscillations with a small amplitude will be classified separately. 

It should be noted that the above classification system of technetium cluster compounds is not the only possible one. In section 4 another classification is described, which is based on thermal stability and the mechanism of thermal decomposition. Section 2.2 is concerned with the classification based on methods of synthesizing cluster compounds. The classifications based on specific properties of clusters do not at all belittle the advantages of the basic structural classification they broaden the field of application of the latter, because for a better understanding and explanation of any chemical, physico-chemical and physical properties it is necessary to deal directly or indirectly with the molecular and/or electronic structures of the clusters. 

In addition, a method of petroleum classification based on other properties as well as the density of selective fractions has been developed. The method consists of a preliminary examination of the aromatic content of the fraction boiling up to 145°C (295°F), as well as that of the asphaltene content, followed by a more detailed examination of the chemical composition of the naphtha (bp < 200°C < 390°F). For this examination a graph is nsed that is a composite of cnrves expressing the relation among the percentage distillate from the naphtha. 

Compared with non-model-based methods, model-based approaches work better when no adjustment is needed or negative confounding exists. However, success of the algorithm depends on accurate subgroup classification. If random markers are used, then a large number of markers are required for the subgroup classification. 

Distance-based methods possess a superior discriminating power and allow highly similar compounds (e.g. substances with different particle sizes or purity grades, products from different manufacturers) to be distinguished. One other choice for classification purposes is the residual variance, which is a variant of soft independent modeling of class analogy (SIMCA). 

An ROC curve plots the true positives against the false positives for different classifications of the same set of objects this corresponds to plotting a against n - a using the notation of Table 1, and thus the shape of an ROC curve tends to the shape of a cumulative recall plot when n a. An example of the use of ROC plots in chemoinformatics is provided by the work of Cuissart et al. on similarity-based methods for the prediction of biodegradability (24). 

Data from HTS often has a relatively high error or noise content and provides a very low precision activity measure, often binary ( pass-fail ). This effectively makes linear activity modeling impossible and classification-based QSAR methods must be employed. The database of 455 compounds, each active against one... 

There are many advantages in using this approach to feature selection. First, chance classification is not a serious problem because the bulk of the variance or information content of the feature subset selected is about the classification problem of interest. Second, features that contain discriminatory information about a particular classification problem are usually correlated, which is why feature selection methods using principal component analysis or other variance-based methods are generally preferred. Third, the principal component plot... 

A second fundamental classification of quantum chemistry calculations can be made according to the quantity that is being calculated. Our introduction to DFT in the previous sections has emphasized that in DFT the aim is to compute the electron density, not the electron wave function. There are many methods, however, where the object of the calculation is to compute the full electron wave function. These wave-function-based methods hold a crucial advantage over DFT calculations in that there is a well-defined hierarchy of methods that, given infinite computer time, can converge to the exact solution of the Schrodinger equation. We cannot do justice to the breadth of this field in just a few paragraphs, but several excellent introductory texts are available... 

To classify a new sample, fc-NN computes its distances (usually, the multivariate Euclidean distances, see Eq. 7) from each of the samples of a training set, whose class membership is known. The k nearest samples are then taken into consideration to perform the classification generally, a majority vote is employed, meaning that the new object is classified into the class mostly represented within the k selected objects. Being a distance-based method, it is sensitive to the measurement units and to the scaling procedures applied. 

Fig. 4. Application of bioinformatics tools to 2D-DIGE data analysis. Proteome data consisting of the normalized spot intensity values are exported from the image analysis software and their correlation with clinicopathological data examined. Using informatics tools including clustering algorithms and machine-learning methods, a novel cancer classification based on proteome data is established, and key proteomic features and proteins corresponding to biomarker candidates are identified.

The SCOP database is curated manually, with the objective of placing proteins in the correct evolutionary framework based on conserved structural features. Two similar enterprises, the CATH (class, architecture, topology, and homologous superfamily) and FSSP (/old classification based on structure-structure alignment of proteins) databases, make use of more automated methods and can provide additional information. 

Several methods of viral classification are in use. Classification based upon epidemiological criteria, such as enteric or respiratory viruses, is useful, but of more significance are schemes based upon the morphology of the virion (symmetry, envelope, etc.) and lype of nucleic acid (DNA, RNA, number of strands, polarity, etc.)... 

Subramanian, A., Harper, W. J., and Rodriguez-Saona, L. E. (2009a). Cheddar cheese classification based on flavor quality using a novel extraction method and Fourier transform infrared spectroscopy. J. Dairy Sci. 92, 87-94. 

It is easily understood that if the aseptic operation is performed in a separated small space from which personnel have been completely excluded, the necessity for room classification based on particulate and environmental microbiological monitoring requirements may be significantly reduced. In other words, critical operations in an aseptic area should be performed in the smallest space, and intervention by personnel should be minimized by indirect means through the use of protective glove ports and/or half suits. Application of these methods can minimize the chance of contamination. Following are such systems currently in place to reduce the contamination rate in aseptic processing. 

Segmentation can be performed according to four different approaches thresholding based, region based, gradient based, and classification based. In current applications, the first two methods are generally preferred (Du and Sun, 2004). 

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