Concept Trees: Building Dynamic Concepts from Semi-structured Data Using Nature-Inspired Methods - Complex System Modelling and Control Through Intelligent Soft Computations - page 239

' to an equal or smaller one. This is however the main rule of the

concept tree and there is some mathematical justi

measurement '

cation or foundation to it. Some
of the evidence was found after the creation of the concept tree, more than the
concept tree has been derived from it. However, if it can be used to support the
general model or theory, then why not specify it here. The main point to note is the
fact that base concepts should probably be the most frequently occurring ones
statistically. That is probably a sound enough idea, based on statistics alone. If
trying to compare to a real-world physical law, then if tree branches were allowed to
become larger again, the tree would probably break at that place. This might be an
opportunistic statement, but it is completely the idea behind the triangular counting
rule. Other pieces of evidence that might provide support are listed in the following
sections.

6.1 Problem Decomposition

Any sub-entity must be smaller than the entity it belongs to. This is particularly
relevant to the process of problem decomposition that is used to solve large and
dif cult problems. The larger problem is broken down into smaller ones, until each

smaller problem is simple enough to be solved. So this is another application of the
natural ordering. It is also the case that you cannot be a sub-concept of something
that does not exist. If thinking about Markov models, then one construction of these
will count the number of occurrences, of transitions from one state to another. This
process will necessarily require the first and therefore, if the

model is tree-like without loops, each parent state must have a larger or the same
count value as the following state, as part of the same rule. Similar to concept trees,
Markov models have been used for text classi

' from ' state to exist

cation or prediction, as well as state-

based models.

6.2 Clustering and Energy

Some of the research that has looked at clustering processes, for example, the single
link theory (Sibson 1973 ) might provide support. This original theory proposed that
any node should link to its closest neighbour. These small clusters could then link
to their nearest neighbours in the next iteration, and so on. Therefore, through only
one link from each group, at each iteration, larger clusters can eventually be formed.
It is interesting to note that if there is a certain ordering of the nodes, this process
will work particularly well. A measurement of closeness depends on what is being
measured and also the evaluation criteria. However, suppose that spatial distance is
the metric, where a line of evaluated nodes can only cluster with the node on either
side

necessarily being the closest nodes. Consider the two sets of nodes, repre-
sented by Figs. 4 and 5 . In these

—

figures, each node value is represented by its height