Path to „Idagrotte“, Sächsische Schweiz

Tutorial: Chain

• Rainer Bruggemann• Peter Koppatz

Rauschenstein,Elbsandsteingebirge

As usual you have to select your set of interest.

A list of object sets pops up. The blue button at the left side: Selection of subsets.Usually the Hasse diagram of the selected object set, i.e. „chain-pollution.csv“Is of most interest: Select „General Info“

General Info provides information about the partially ordered set (here „chain-pollution.csv“) which are not module specific.Here we want to see the Hasse diagram.

An important information can be deduced by inspecting the Hasse diagram:For example the sequence 30 < 6 < 22 < 14 < 57 shows that for some objectsthe attribute values are simultaneously increasing (including equality).Subsets of objects with no mutual incomparability are called chains.Do we have more than one chain? Are chains different from each other?For these two questions you will find answers in the menu „Module Specific“.

Selection: Chain statistics

Here you are informed about chains between the maximal and minimal elements ofthe poset, having a height a certain internally calculated average value.For instance between 18 and 30 there is no chain with a height 4.556, whereasbetween 57 and 30 five chains can be found having a sufficient large height.

Usually you want to find more conclusions examining pretty long chains.1) Most often dissimilar chains are of interest, two chains are the dissimilar the less coinciding objects they contain.2) Sometimes one is interested in exceptions where the synchroneous increase of attribute values leads to conflicting object profiles (see spyout).

The menu „Similarity as table“ calculates the Tanimoto-coefficient of pairs of chains having the same height. Whereas the menu „Similarity as bar diagrams“ represents the Tanimoto values as horizontal bars for each pair of chain.

The first part informs about potential candidates. For example of interestis the object pair 57 and 30 because here 5 chains appear. Selecting the startvertex 57 and thesinkvertex 30 the following results appear:

Note that startvertex, sinkvertex and maxch have to be carefully be selected.After the selection, the button „Calc“ is to be pressed.The probable common chain height is indicated in „Number of levels = number of elements in a maximum chain“ which is 5 in the poset selected (red ellipse).The entries are the Tanimoto coefficients of each of the pairs of the five chains.Chain 1 is similar with chain 2 (0.667), whereas chain 5 differs considerably from chain 1 (0.25).

„Similarity as bardiagram“

The presentation in a table as in the slide before contains redundant information, because similarity is a symmetric property. Hence the presentation as a bar diagram may be more appropriate.

The menu „chain selection“ aims at a information about any single chains the user want to examine:

After selection of startvertex, sinkvertex and maxch (whereby the chain statistics could give valuable information) one of the possible chains is to be selected. We know, between 30 and 57 there are 5 chains, so the user has first to select theChain he is mostly interested. For example chain no 5.

Pressing the button „Show chain as Hasse diagram“ generates a Hasse diagramwhere the special chain, selected by the user, is marked (next slide):

Chain 5 in the Hasse diagram, visualizing the poset of the dataset „chain-pollution.csv“.

By crossing with the mouse, a little window pops up,Informing the user about equivalent elements and about the profiles. In the chain 5 a simultaneous increasefrom profile (0,0,0,0) of object 30 to (2,1,0,1) of object 57can be observed.A chain 30,6,45,14,57 would have the height 5 too and wouldbe very similar to chain no 5. Tanimoto-coefficient = 4/6 = 0.667.Object 14 has the profile (1,1,0,1) , whereas object 38 has theprofile (2,1,0,0). Although object 14 does not contradict the simultaneous increase of the attribute values from 30 to 57it is in conflict with 38. Coincidence in the 2nd and third attribute,but differences in the first and fourth attribute.

• See also:• https://www.pyhasse.org, • http://de.slideshare.net/pyhasse/tutorial-spyout• http://chain.pyhasse.org (Demo)• You want to contact us: The email address:

chain@pyhasse.org• You want to call us? – R.Bruggemann (+49) 30 6496676– P.Koppatz (+49) 331 20029708