Problem Classification Category

Distribution of Library Collection by Problem Classification Category ... 

Category—The problem classification assigned from the Center program or system classification guide. 

The methods for solving an optimization task depend on the problem classification. Since the maximum of a function / is the minimum of the function —/, it suffices to deal with minimization. The optimization problem is classified according to the type of independent variables involved (real, integer, mixed), the number of variables (one, few, many), the functional characteristics (linear, least squares, nonlinear, nondifferentiable, separable, etc.), and the problem. statement (unconstrained, subject to equality constraints, subject to simple bounds, linearly constrained, nonlinearly constrained, etc.). For each category, suitable algorithms exist that exploit the problem s structure and formulation. 

We employ the general scheme presented above as a starting point in our discussion of various approaches for handling the R-T effect in triatomic molecules. We And it reasonable to classify these approaches into three categories according to the level of sophistication at which various aspects of the problem are handled. We call them (1) minimal models (2) pragmatic models (3) benchmark treatments. The criterions for such a classification are given in Table I. 

The values of the weights depend on the classification objectives of the problem. Weights can be recalculated as new hypotheses or category assignments are posed during the course of the study. 

Often the goal of a data analysis problem requites more than simple classification of samples into known categories. It is very often desirable to have a means to detect oudiers and to derive an estimate of the level of confidence in a classification result. These ate things that go beyond sttictiy nonparametric pattern recognition procedures. Also of interest is the abiUty to empirically model each category so that it is possible to make quantitative correlations and predictions with external continuous properties. As a result, a modeling and classification method called SIMCA has been developed to provide these capabihties (29—31). 

This kind of statistical consideration is used to detect oudiers, ie, when a sample does not belong to any known group. It is also the basis of a variation of SIMCA called asymmetric classification, where only one category is modelable and distinguished from all others, which spread randomly through hyperspace. This type of problem is commonly encountered in materials science, product quaUty, and stmcture—activity studies. 

Given the intermediate labels from the GPC pattern and sensor interpreters, a KBS is used to map them into the diagnostic labels of interest. However, because the output dimension of the problem is large (at over 300 possible malfunctions), a hierarchical classification system is used to decompose the process into a hierarchical set of malfunction categories that... 

From the structural viewpoint there is much to commend the classification of problems based on the topology of the pipeline network— single branch pipelines, tree networks, and cyclic networks. However, since some methods are applicable to more than one category, rigorous adherence to this classification will lead to unnecessary duplication and overlaps. 

Materials that lie close to or are on a classification boundary may exhibit slugging behavior from either one of the adjoining categories. This could be explained further by the particle size distribution problem or limitation described above. 

E.H. Hurst s overview introduced several themes pursued by other chemical industry speakers. The Dow Chemical Company s E.H. Blair analyzed the problem of setting priorities for testing the 55,000 existing chemicals listed in the TSCA inventory for their effects on health and the environment. Resources for such testing are not unlimited. A systematic classification was made of these substances by production volume. The 9.5% of these substances which account for 99.9% of reported production were divided further into categories such as organic, inorganic, and polymeric. 

Another aspect of polymer informatics, beyond the representation and registration of polymer information and data, is the conversion of data into knowledge and thus into the power to make decisions. To this end, the same tools, which are common in small molecule informatics, have also been used to study polymer data. The work that has been reported so far subdivides into two categories, namely classification and chemometrics problems and property prediction. 

In classification problems the data table is divided horizontally into two or more categories into which objects are grouped. The problem is to make the best use of the variables to classify the objects into categories and, chiefly, to predict the category of objects of unknown category and to evaluate the correctness of this assignment. 

The category correlations can be cancelled only when all the objects of the training set are in the same category, and the method is used as a class modelling technique. However, the bayesian analysis in ARTHUR-BACLASS has b n compared with the usual BA in classification problems about winra and olive oils and about the same classification and prediction abilities were observe for both methods. 

The rule of the K nearest objects, KNN, has been used in classification problems, in connection and comparison with other methods. Usually KNN requires a preliminary standardization and, when the number of objects is large, the computing time becomes very long. So, it appears to be useful in confirmatory/exploratory analysis (to give information about the environment of objects) or when other classification methods fail. This can happen when the distribution of objects is very far from linear, so that the space of one category can penetrate into that of another, as in the two-dimensional example shown in Fig. 28, where the category spares, computed by bayesian analysis or SIMCA, widely overlap. 

In practice, almost all studies on food have some prerecognized categories, and the detection of new categories in an eigenvector plot shows that some factors are unknown or that their importance has been underestimated, so that the classification problem has to be formulated again. 

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