T ESTING THE C OMPLETE D YNAMIC W EATHER

D

The demonstration in the previous section demonstrated, in detail, what occurs within the DynamicWEB hierarchy when an update to a profile occurs. In this section we will extend this to monitoring what occurs at a higher level during an entire run of the Dynamic Weather dataset. Instead of only four objects being examined, this time the full set of twelve, shown in Table 25, will be observed. Across the three updates of each of the twelve instances there are six object drifts that produce a change in the resultant class of the object. Within all of the trees shown in the figures below, each leaf node is pure in class; the highest cutoff value at which this occurs is 0.09.

The first hierarchy, Figure 27, illustrates the structure that is produced after each of the twelve objects have been observed once. The structure is quite broadly spread, largely due to the order of the instances. This portion of the process is identical to

Figure 27. The concept hierarchy after one instance of each object has been observed.

Chapter 6 - Method Verification and Demonstration

Figure 28. The concept hierarchy after each of the objects have had another observation and have all been updated once.

COBWEB and as such can suffer from its order dependency. DynamicWEB, through its updating, is able to largely nullify this as it examines order dependent datasets through multiple updates of each profile. As each profile gets updated, and in that process removed and re-added to the hierarchy, the structure optimises itself by always choosing the best option. This allows the re-addition of a profile to a hierarchy to build upon the knowledge that has been added to the tree since it was previously inserted into the tree. The result of the first twelve updates to the hierarchy is shown in Figure 28. The structure is now not as flat as in Figure 27 with much more depth present, and with some closer matching of sister leaves of the same class. Also four profiles of the positive class are present within the right furthermost leaf node.

Within the updates that occurred between the points in time represented by the two structures above, three objects have drifted from one resultant class to another. The objects for Lahinch and St Andrews have both gone from the negative class to the positive, while County Down drifted from the positive class to the negative. The locations where these profiles are now stored within the tree are with profiles of the same resultant class. This shows DynamicWEB successfully allowing for the object drift and clustering the updated profiles in the correct location. The second round of updates from the third set of observations produced the hierarchy shown in Figure 29. This hierarchy is even simpler in structure than that in Figure 28, and now has

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Figure 29. The concept hierarchy after the second round of updates have been completed.

two leaf nodes, with four or more profiles resident within them. Again, during this round of observations there were three objects which drifted from one concept to another, with Lahinch again drifting, to the negative class along with Gleneagles; while St Davids drifted to the positive class.

The tree structures that were shown within the figures above are quite useful in terms of visualising the knowledge structure produced. They are easily human readable, and do perfectly describe the structure at an exact moment within the timeframe being examined in the dataset. However, their main shortfall is a lack of being able to visually show what drifting has occurred over time. Through comparing two trees it is possible to garner that St Davids was clustered very near to

Dornoch in the update between trees two and three. But knowing how much they changed across all three tree structures or viewing those two objects in comparison to the other objects is not readily apparent. In an effort to illustrate the drifting of objects in relation to one another, Figure 30 displays a category measure for each of the objects within the dataset across the three measurements. These measures allow for direct comparison between the different objects across the time period of the dataset, illustrating the changing similarity of the objects. The measure used is a modified category utility of a singleton node that only contains two object profiles. These profiles are the same as those used within the DynamicWEB knowledge hierarchy and as such the comparison that takes place has a direct link to the current state of the hierarchy. The measure taken compares each object within the dataset to a single object within the dataset, producing a similarity measure between the two

Chapt er 6 - Me thod V er if ic at ion and D em ons tr at ion - 107 - igu re 30. Tr ac k in g th e ob je cts ove rti me in r el ati on to th e oth er ob je cts w ith in th e d atas et

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objects. Figure 30 is built upon comparing all of the object profiles to the Bally Bunion profile. The value of the Y-axis is an un-normalised category utility calculated based upon the two profiles.

In computing this measure as a direct comparison between two objects, we areignoring the existing knowledge within the hierarchy, as it would bias this measure, meaning that it was not a pure direct comparison between the profiles as they currently stand. As we are not using the statistics within the hierarchy, it is only numeric attributes that are used within comparison. If we were to include the nominal attributes within the context of a one to one comparison, they would carry too much extra weight within the similarity measure to produce a useful metric here. This is a short-coming. As such it is shown here purely for a visualisation aid to indicate what is taking place within the Dynamic Weather dataset.