Data abstraction and analysis using qualitative scaling.

摘要

Qualitative scaling can provide a framework for pattern recognition and dimensionality reduction which allows flexibility and power to be brought to complex recognition problems in high-dimensional spaces. The scaling approach involves the mapping of data into lower dimensional spaces subject to optimization criteria. These criteria can be formulated in a way which combines a vector space representation with additional qualitative information. A variety of qualitative relations can then be utilized to offer different perspectives on a data set. This formulation also allows various classes of mappings, including nonlinear functions, to be systematically considered through a transformation of the vector space representation. We can also determine the significance of the features and the data objects themselves in the representation of the qualitative relation and their contribution to classification performance. Alternative projections for classifying the data can then be explored, contrasted, and classifier design can thus be organized as a process involving the search and composition of discriminatory scales. The method is shown to be useful for feature extraction, predictive data reduction, visualization and classification, with specific application to problems in biomedical informatics.