Tutorial: TM Semantic Visualisation (Part II)
(continued from Part I)
The last time we looked at a map which only contained two topics and where the documents attached to the two topics are completely disjunct:
One additional observation we can make is that the landscape has a rather peculiar structure: If you follow the JJJ mountain southwards towards the HHH ridge, you will see that that continues at the top.
The same holds for the east-west horizon: If you follow the EEE hill westwards, it will have some foothills in the east before you reach the valley of separation.
This Torus topology has not been chosen lightly:
In contrast to a rectangular form, a torus does not have a border. Such borders would distort maps, so that we would loose the property of extensionality, i.e. that the map area one term covers corresponds quantitatively with its contextual importance.
I could also have chosen a globe as surface and then map that onto 2 dimensions, inheriting all the well known projection problems.
So, what happens if we add a few documents to AAA and NNN? Documents which link the words in some documents of AAA to some in NNN?
In that case we would expect the plates to be linked; linked via those terms which appear in these crossboarder documents (attachment 2):
The sitation may now appear to have changed quite drastically. Still, the mountains peaking at JJJ and WWW are clearly visible. And still there is a deep valley between them running from the north to the south.
But now around the EEE ledge there is a pass southwards towards a smaller mountain with a CCC peak. That links further to the east via QQQ and also the south. All these are frequent words in the interlinking documents.