| In the not too distant past, data based decision-making was frequently hampered by the lack or scarcity of data. Today, we are largely faced with the other extreme. Over the years, government agencies and private entities alike have come to realize the value of historical information to sound decision making and, over time, have established and refined elaborate policies for the collection of information and its storage in data depositories; some of it for immediate analytical purposes and some of it for potential future uses. Operations and success of most regulatory agencies are based on data and sound data inference, some of which play an essential role to the well-being of the nation. Data in general has become a valuable commodity and the acquisition, compilation, and marketing of data has become a profitable business model.; Consequently, an analyst's focus has shifted from acquiring data to elimination of redundant data and noise. In most practical settings, there exists a dire need for data reduction with its necessity arising from either computational complexity, resource leverage, or structural complexity. Much work in this area has been done on reduction methods for metric data, with primary focus on linear models. However, fewer results are available for non-linear or categorical data models.; The research presented here presents an approach that combines correspondence-analytic, information theoretic, and approximation-theoretic concepts to derive a fast reduction procedure suitable for categorical data. The procedure can also be applied to metric data where it proves to perform as well as linear regression on multi-normal data and superior otherwise. All types of monotone relationships, linear or non-linear, are handled well. In addition, the procedure is robust to outliers, which makes it more desirable than l2 methods, especially for exploratory and control purposes. The procedure also has a very limited data requirement, which distinguishes it from other information-theoretic procedures whose data requirement increases exponentially with the number of variables and which, in turn, are numerically highly unstable.; Structural data models are developed, feasibility lemmas and methods of efficient parameter estimation are derived. Effectiveness and application of the methodology are demonstrated on synthetic and real datasets. |
