11.5 Clusters

11.5 Clusters

Earlier, this chapter used the term ?meaningful system states.? What exactly is a meaningful system state? The answer varies, and the question can only be answered within the framework of the problem domain. It might be that some sort of binning (described in Chapter 10 ) assigns continuous measurements to more meaningful labels. At other times, the measurements are meaningfully continuous, limited only by the granularity of the measurement (to the nearest penny, say, or the nearest degree). However, the system may inherently contain some system states that appear, from wholly internal evidence, to be meaningful within the system of variables. (This does not imply that they are necessarily meaningful in the real world.) The system ?prefers? such internally meaningful states.

Recall that at this stage the data set is assumed to represent the population. Chapter 6 discussed the possibility that apparently preferred system states result from sampling bias preferentially sampling some system states over others. The miner needs to take care to eliminate such bias wherever possible. Those preferred system states that remain should tell something about the ?natural? state of the system. But how does the miner find and identify any such states?

Chapter 6 discussed the idea that density of data points across state space varies. If areas that are more dense than average are imagined as points lower than average, and less dense points imagined to be higher, the density manifold can be conceived of as peaks and valleys. Each peak (the locally highest...

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