Methods classification

Cluster analysis is an exploratory data analysis technique aimed at grouping items (e.g. chemicals and their properties) into clusters of similar items according to their position in the multidimensional parameter space. The various clustering methods differ mainly in how they calculate the distance from a point to the cluster it may be to the nearest point, the most distant point or the centroid of the cluster, with the result that the respective clusters will have different shapes. 

The compounds are assigned location coordinates in the n-dimensional space according to their values in the descriptors included in the model and 

Successful discriminant analysis is based on the assumption that the data in each class are normally distributed and all classes have the same covariance matrix (McFarland and Cans, 1990). Discriminant analysis is extremely sensitive to collinearities among descriptors and the ratio of the number of chemicals in the data set to the number of descriptors in the model should exceed 10 1. For the training-set selection, the data quality, the statistical significance, the type of descriptors and the limitations of the model range, the same restrictions apply for discriminant analysis as explained for classical regression analysis (section 3.2.1)  

The compounds are evenly distributed over the different activity classes. 

The data on physico-chemical descriptors cover several orders of magnitude. The descriptor data are evenly distributed over the entire range of the model. The range covered by each parameter exceeds significantly the variability in the parameter for the individual compounds. 

---

CLASSIFICATION METHODS In image processing, it often very interesting to built classes from the data structure. This technique can be partitioned into two categories ... 

Figure 5-30. Second reaction instance of the first cluster for Example 1, obtained by applying the BROAD classification method,...

Alternatives to Multiple Linear Regression Discriminant Analysis, Neural Networks and Classification Methods... 

Although the size separation/classification methods are adequate in some cases to produce a final saleable mineral product, in a vast majority of cases these produce Httle separation of valuable minerals from gangue. Minerals can be separated from one another based on both physical and chemical properties (Fig. 8). Physical properties utilized in concentration include specific gravity, magnetic susceptibility, electrical conductivity, color, surface reflectance, and radioactivity level. Among the chemical properties, those of particle surfaces have been exploited in physico-chemical concentration methods such as flotation and flocculation. The main objective of concentration is to separate the valuable minerals into a small, concentrated mass which can be treated further to produce final mineral products. In some cases, these methods also produce a saleable product, especially in the case of industrial minerals. 

In recent years, several wet milling operations have been initiated with obvious advantages in dust control and potential advantages in the separation of mineral contaminants from the fiber product. On the other hand, large-scale industrial wet classification methods are not in use at present. 

In unsupervised learning, the outcome is usually a hypothesis to then be tested, often usiag classification or prediction methods. If the unsupervised learning process suggests the presence of distinct clusters, the hypothesis can be tested by applyiag a classification method to the data. A low number of misclassified samples would tend to reinforce the hypothesis. 

An example of a classification problem ia which feature weighting and selection was important comes from forensic chemistry (qv). A classification method was needed to determine the paper grade and manufacturer of a paper scrap found at the scene of a crime. In this study, 119 sheets of paper (qv) representing 40 different paper grades and nine manufacturers were obtained (25). The objects were then the paper samples, and the variables consisted of... 

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). 

Ideally, maintenance records should be organized by a classification method compatible with the CCPS Taxonomy in Appendix A and the equipment boundaries in Section 5.5, Generic Failure Rate Data Base. It is important to remember that the taxonomy presented was developed to group equipment into classes that are differentiated by their reliability rather than their design characteristics. Records maintained in this fashion allow the analyst to more easily determine the total pieces of equipment and number failures. 

It is important, especially when consistency has not been designed or built into the maintenance reporting system, to review the data reported to minimize misinterpretation. Clearly defined equipment boundaries for plant hardware are essential for the generation of relevant data. For example, one classification method may define pumps as only the mechanical portions of the pump, whereas another may include the driver (e.g., the motor) and associated controls. Interviews with operating and maintenance personnel as well as review of the maintenance procedures and documents can provide insight into the... 

The lADC Drill Bits Subcommittee began work on a new classification method in 1985. It was determined from the outset that (1) a completely new approach was required, (2) the method must be simple enough to gain widespread acceptance and uniform application, yet provide sufficient detail to be useful, (3) emphasis should be placed on describing the form of the bit, i.e., paint a mental picture of the design , (4) no attempt should be made to describe the function of the bit, i.e., do not link the bit to a particular formation type or drilling technique since relatively little is certain yet about such factors for fixed cutter bits, (5) every bit should have a unique lADC code, and (6) the classification system should be so versatile that it will not be readily obsolete. 

After studying these parameters, we will describe and discuss the most important classification methods before suggesting a new quantitative classification method for the fire hazard of a chemical substance. 

The vapour pressure of a liquid provides an essential safety parameter and it is mandatory that safety sheets contain these values (when they are known). This parameter is taken into account in some classification methods of inflammability risk. It enables one to determine the equilibrium vapour concentration of a liquid in air. This concentration can then be used to ascertain whether a working environment presents an inflammability risk (by reference to the inflammability limits) or a toxicity hazard (by comparison with the exposure values). 

This classification system is compulsory throughout Europe, although other classification methods are also used. Like the NFPA code it is based on boiling and flashpoint parameters. It classifies substances into five categories that are defined as follows ... 

The disadvantages of all classification methods so far considered are the same for all qualitative classifications. 

Physical factors favouring inflammability were analysed in paragraph 1.5.4, and the physical factors that apply to unstable compounds were also mentioned. Also underlined was that this classification method was aimed at carrying out quantitative risk analyses. It is precisely for the analysis of dangerous reactions that this method was suggested. It works as follows ... 

Fig. 30.12. Forgy snon-hierarchical classification method. A,. ..,G are objects to be classified 1,..., 4 are successive centroids of clusters.

H. Van der Voet and P.M. Coenegracht, The evaluation of probabilistic classification methods. Part 2. Comparison of SIMCA, ALLOC, CLASSY and LDA. Anal. Chim. Acta, 209 (1988) 1-27. 

H. Van Der Voet, P.M.J. Coenegracht and J.B. Hemel, New probabilistic versions of the Simca and Classy classification methods. Part 1. Theoretical description. Anal. Chim. Acta, 192 (1987) 63-75. 

W. Werther, H. Lohninger, F. Stand and K. Vermuza, Classification of mass spectra. A comparison of yes/no classification methods for the recognition of simple structural properties. Chemom. Intell. Lab. Syst., 22 (1994) 63-67. 

However, not withstanding the above objections, further discussion of the Snyder solvent triangle classification method is justified by its common use in many solvent optimization schemes in liquid chromatography. The polarity index, P, is given by the sum of the logarithms of the polar distribution constants for ethanol, dioxane and nltromethane and the selectivity parameters, X, as the ratio of the polar distribution constant for solute i to... 

The solvent triangle classification method of Snyder Is the most cosDBon approach to solvent characterization used by chromatographers (510,517). The solvent polarity index, P, and solvent selectivity factors, X), which characterize the relative importemce of orientation and proton donor/acceptor interactions to the total polarity, were based on Rohrscbneider s compilation of experimental gas-liquid distribution constants for a number of test solutes in 75 common, volatile solvents. Snyder chose the solutes nitromethane, ethanol and dloxane as probes for a solvent s capacity for orientation, proton acceptor and proton donor capacity, respectively. The influence of solute molecular size, solute/solvent dispersion interactions, and solute/solvent induction interactions as a result of solvent polarizability were subtracted from the experimental distribution constants first multiplying the experimental distribution constant by the solvent molar volume and thm referencing this quantity to the value calculated for a hypothetical n-alkane with a molar volume identical to the test solute. Each value was then corrected empirically to give a value of zero for the polar distribution constant of the test solutes for saturated hydrocarbon solvents. These residual, values were supposed to arise from inductive and... 

Classification methods for leukemia have evolved from simple schemes that were largely phenotypic and considered only age, gender, WBC count, and blast morphology to now-complex methods that include biologic features such as cell-surface receptor features and cytogenetics. 

In the chemical classification method, colorants are grouped according to certain common chemical structural features. The most important... 

Non-hierarchical cluster methods have in common with classification methods that pre-information on the number of classes is needed or desired to start an iteration process. In the course of the clustering a rearrangement of objects between several clusters is possible. 

One of the powerful classification methods is multivariate variance and discriminant analysis (MVDA) (Dillon and Goldstein [1984] Ahrens and Lauter [1974] Danzer et al. [1984]). 

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. 

---