Data interpretation methods

Data interpretation methods can be categorized in terms of whether the input space is separated into different classes by local or nonlocal boundaries. Nonlocal methods include those based on linear and nonlinear projection, such as PLS and BPN. The class boundary determined by these methods is unbounded in at least one direction. Local methods include probabilistic methods based on the probability distribution of the data and various clustering methods when the distribution is not known a priori. 

The key to decision making systems is the availability of software that can correctly interpret electrochemical data. Data interpretation methods invariably rely on a model that can be used as a basis for comparison. Work in this area has been developing steadily. For example, Olsen and Evans have used simulated theoretical cyclic voltammograms to predict mechanisms from experimental results (35) Harrison and Small have also reported on the use of a library mechanisms (36). 

The total variance Vtot is defined as the sum of the variances of all features and represents an important measure in some data interpretation methods. 

The other parameters used in the calculation of STOMP and GIIP have been discussed in Section 5.4 (Data Interpretation). The formation volume factors (B and Bg) were introduced in Section 5.2 (Reservoir Fluids). We can therefore proceed to the quick and easy deterministic method most frequently used to obtain a volumetric estimate. It can be done on paper or by using available software. The latter is only reliable if the software is constrained by the geological reservoir model. 

Methods for measurement of kp have been reviewed by Stickler,340 41 van Herk Vl and more recently by Beuermann and Buback.343 A largely non critical summary of values of kp and k, obtained by various methods appears in the Polymer Handbook.344 Literature values of kp for a given monomer may span two or more orders of magnitude. The data and methods of measurement have heen critically assessed by IUPAC working parties"45"01 and reliable values for most common monomers are now available. 43 The wide variation in values of kp (and k,) obtained from various studies docs not reflect experimental error but differences in data interpretation and the dependence of kinetic parameters on chain length and polymerization conditions. 

The irrigation method in the period of flooding, e.g., days of holding water in paddy , could be important information for data interpretation. 

Interpretive methods Involve modeling the retention surface (as opposed to the response surface) on the basis of experimental retention time data [478-480,485,525,541]. The model for the retention surface may be graphical or algebraic and based on mathematical or statistical theories. The retention surface is generally much simpler than the response surface and can be describe by an accurate model on the basis of a small number of experiments, typically 7 to 10. Solute recognition in all chromatograms is essential, however, and the accuracy of any predictions is dependent on the quality of the model. 

Fig. 5. Label class decision methods for data interpretation.

More recently, the development of wavelets has allowed the development of fast nonlinear or multiscale filtering methods that can adapt to the nature of the measured data. Multiscale methods are an active area of research and have provided a formal mathematical framework for interpreting existing methods. Additional details about wavelet methods can be found in Strang (1989) and Daubechies (1988). 

The objective functions for both k-means clustering and the F-nearest neighbor heuristic given by Eqs. (20) and (21) use information only from the inputs. Because of this capacity to cluster data, local methods are particularly useful for data interpretation when the clusters can be assigned labels. 

Among nonlocal methods, those based on linear projection are the most widely used for data interpretation. Owing to their limited modeling ability, linear univariate and multivariate methods are used mainly to extract the most relevant features and reduce data dimensionality. Nonlinear methods often are used to directly map the numerical inputs to the symbolic outputs, but require careful attention to avoid arbitrary extrapolation because of their global nature. 

Nonlinear methods based on linear projection also can be used for data interpretation. Since these methods require numeric inputs and outputs, the symbolic class label can be converted into a numeric value for their training. Proposed applications involving numeric to symbolic transformations have a reasonably long history (e.g., Hoskins and Himmel-... 

Local interpretation methods encompass a wide variety of approaches that resolve decisions about input data relative to annotated data or known features that cluster. By characterizing the cluster or grouping, it is possible to use various measures to determine whether an arbitary pattern of data can be assigned the same label as the annotated grouping. All approaches are statistical, but they vary in terms of measures, which include statistical distance, variance, probability of occurrence, and pattern similarity. 

If the probability distribution of the data is or assumed Gaussian, several statistical measures are available for interpreting the data. These measures can be used to interpret the latent variables determined by a selected data analysis method. Those described here are a combination of statistical measures and graphical analysis. Taken together they provide an assessment of the statistical significance of the analysis. 

Our laboratory is interested in the biology of mammalian SGs and PBs, and in understanding their roles in the spatial regulation of mRNA translation and decay. The methods and procedures presented here describe our present knowledge of SG and PB assembly and composition. We indicate some commercially available antibodies useful as SG and PB markers, describe some immunocytochemical protocols that we employ, and offer some caveats regarding data interpretation. 

Rasmussen [82] describes a gas chromatographic analysis and a method for data interpretation that he has successfully used to identify crude oil and bunker fuel spills. Samples were analysed using a Dexsil-300 support coated open tube (SCOT) column and a flame ionisation detector. The high-resolution chromatogram was mathematically treated to give GC patterns that were a characteristic of the oil and were relatively unaffected by moderate weathering. He compiled the GC patterns of 20 crude oils. Rasmussen [82] uses metal and sulfur determinations and infrared spectroscopy to complement the capillary gas chromatographic technique. 

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