11.3 Mapping Using Entropy

11.3 Mapping Using Entropy

Entropic measurements are the foundation for evaluating and comparing information content in various aspects of a data set. Recall that entropy measures levels of certainty and uncertainty. Every data set has some theoretical maximum entropy when it is in a state of maximum uncertainty. That is when all of the meaningful outcomes are equally likely. The survey uses this measure to examine several aspects of the data set.

As an example of what entropy measurements can tell the miner about a data set, the following discussion uses two data sets similar to those first described in Chapter 6 as an example. Chapter 6 discussed, in part, relationships that were, and those that were not, describable by a function. Two data sets were illustrated (Figures 6.1 and 6.2 ). The graphs in these two figures show similar manifolds except that, due to their orientation, one can be described by a function and the other cannot. Almost all real-world data sets are noisy, so the example data sets used here comprise noisy data approximating the two curves. Data set F (functional) contains the data for the curve that can be described by a function, and data set NF (nonfunctional) contains data for the curve not describable by a function.

While simplified for the example, both of these data sets contain all the elements of real-world data sets and illustrate what entropy can tell the miner. The example data is both simplified and small. In practice, the...

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11.3 Mapping Using Entropy

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