Data interpretation approaches

S. N. Denting and S. L. Morgan, Experimental Design A Chemometric Approach Elsevier Science Publishing Co., Inc., Amsterdam, The Netherlands, 1987. D. D. Wolff and M. L. Parsons, Pattern Recognition Approach to Data Interpretation Plenum Press, New York, 1983. 

Data Interpretation extends data analysis techniques to label assignment and considers both integrated approaches to feature extraction and feature mapping and approaches with explicit and separable extraction and mapping steps. The approaches in this section focus on those that form numeric-symbolic interpreters to map from numeric data to specific labels of interest. 

This chapter provides a complementary perspective to that provided by Kramer and Mah (1994). Whereas they emphasize the statistical aspects of the three primary process monitoring tasks, data rectification, fault detection, and fault diagnosis, we focus on the theory, development, and performance of approaches that combine data analysis and data interpretation into an automated mechanism via feature extraction and label assignment. 

The front-end and back-end boundaries on each analysis and interpretation component can be defined so that a particular approach or methodology can be determined based on the specific mapping requirements. Practical data interpretation applications often involve the integration of multiple technologies as required by these three distinct forms of data mapping. This... 

By definition, the exemplar patterns used by these algorithms must be representative of the various pattern classes. Performance is tied directly to the choice and distribution of these exemplar patterns. In light of the high dimensionality of the process data interpretation problem, these approaches leave in question how reasonable it is to accurately partition a space such as R6+ (six-dimensional representation space) using a finite set of pattern exemplars. This degradation of interpretation performance as the number of possible labels (classes) increases is an issue of output dimensionality. 

PDF approaches represent a statistically formal way of accomplishing local kernel definition. Although intent and overall results are analogous to defining kernels of PCA features, considerable work currently is required for PDF approaches to be viable in practice. It is presently unrealistic to expect them to adequately recreate the underlying densities. Nevertheless, there are advantages to performing data interpretation based on direct PDF estimation and, as a result, work continues. 

The knowledge required to implement Bayes formula is daunting in that a priori as well as class conditional probabilities must be known. Some reduction in requirements can be accomplished by using joint probability distributions in place of the a priori and class conditional probabilities. Even with this simplification, few interpretation problems are so well posed that the information needed is available. It is possible to employ the Bayesian approach by estimating the unknown probabilities and probability density functions from exemplar patterns that are believed to be representative of the problem under investigation. This approach, however, implies supervised learning where the correct class label for each exemplar is known. The ability to perform data interpretation is determined by the quality of the estimates of the underlying probability distributions. 

To address this situation, a data interpretation system was constructed to monitor and detect changes in the second stage that will significantly affect the product quality. It is here that critical properties are imparted to the process material. Intuitively, if the second stage can be monitored to anticipate shifts in normal process operation or to detect equipment failure, then corrective action can be taken to minimize these effects on the final product. One of the limitations of this approach is that disturbances that may affect the final product may not manifest themselves in the variables used to develop the reference model. The converse is also true—that disturbances in the monitored variables may not affect the final product. However, faced with few choices, the use of a reference model using the process data is a rational approach to monitor and to detect unusual process behavior, to improve process understanding, and to maintain continuous operation. 

In order to obtain for all receptors within all receptor areas (grids), a first good approach is to interpret and extrapolate data by deriving relationships (transfer functions) between the data mentioned before and basic land and climate characteristics, such as land use, soil type, elevation, precipitation, temperature, etc. A summarizing overview of the data acquisition approach is given in Table 7. 

Chemistry (Malinowski and Howery 1980), Chemometrics (Sharaf et al. 1986), Pattern Recognition in Chemistry (Varmuza 1980), and Pattern Recognition Approach to Data Interpretation (Wolff and Parsons 1983). 

Wolff, D. D., Parsons, M. L. Pattern Recognition Approach to Data Interpretation. Plenum Press, New York, 1983. 

The advent of analytical techniques capable of providing data on a large number of analytes in a given specimen had necessitated that better techniques be employed in the assessment of data quality and for data interpretation. In 1983 and 1984, several volumes were published on the application of pattern recognition, cluster analysis, and factor analysis to analytical chemistry. These treatises provided the theoretical basis by which to analyze these environmentally related data. The coupling of multivariate approaches to environmental problems was yet to be accomplished. 

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