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First inspection of data-driven partially ordered sets.

- 1. Path to „Idagrotte“, Sächsische Schweiz Tutorial: Spyout • Rainer Bruggemann • Peter Koppatz
- 2. Imagine, you have a wonderful data matrix. The data matrix has no gaps, objects are a, b, c,…, two indicators q1, q2. The file is called chaindivlength3.txt. These two buttons make your data file available for PyHasse. I like more the „sets“-Button at the top, but the other can be used as well.
- 3. Press „Sets“ and a window pops up, asking you where the file chaindivlength3.txt can be found. We check first „list of sets“. Perhaps this file is already in the internal data base?
- 4. Indeed it is already in the internal data base! If not, select „Load CSV (or txt) data from file. In this case you have to 1) Browse through your system of folders to identify the location of the file ; German: „Durchsuchen“ 2) „submit“
- 5. The next step: You may check, whether you have uploaded the correct file. In „General Info“ you‘ll find many interesting items; however for the moment: Just select „data“, then you‘ll see: Ah, not all data are shown here, because of the limited area within this presentation. However, we think: You are happy. These data are those you have gathered.
- 6. „General Info“ is module independent: •Show: Hasse diagram •Matrix data: matrix specifications •Calculations: Order theoretical information
- 7. Other items in „Calculations“ (2) Order theoetical information – Zeta matrix: adjacency matrix of the directed graph resulting from object‘s comparison based on their data – Cover matrix: The transitive reduction of the zeta matrix – Levels: A weak order of the objects – Equivalence classes: Due to the fact that objects may be equivalent to each other with respect to the actually considered indicators
- 8. We suppose that you will be mostly interested in the Hasse diagram… Press Calculations, select „Hasse diagram“:
- 9. You didn‘t get the same graph??? Your result looks like that one? With the mouse drag and draw function the graph can be edited by just move the vertices in horizontal directions (taking into regard the invariance of order relations)! Many other tools are available. However, here we concentrate us on the next steps.
- 10. Sorry! You don‘t like the color of the Hasse diagram?? Here we are (Select: Home, Setting):
- 11. Background color for nodes as well as the two backgroundcolors were changed: If this setting is not your favourate one, select yourself the parameters of drawing.
- 12. Try by yourself what can be done ….
- 13. Here „posetic coordinates“ are shown: For example object b has 2 elements in its principal down set, 4 elements in its principal up set and b is incomparable with 6 other objects.
- 14. When you are interested in ranking then chains are of special interest: Any chain allows you a unique ranking of a subset of objects, without any additional assumption such as weight parameters. After selecting objects a and d and pressing „Calc“ The following list of chains, ordered for decreasing lengths is obtained.
- 15. Chain 0 is the longest one, it includes 6 objects out of 11, then 4 chains (chain 1 - chain 4) appear with only 4 objects, finally there are two short chains with only 3 objects.
- 16. • Chains are important, because they allow an unambiguous ranking of some objects, although there are more than one attributes. • Are all these chains similar? For example chain 5 and 6 differ only by one element. What can be said about the four chains with four objects? A similarity study of chains is the task of another module, namely chain. • Six objects out of 11: Perhaps not that good result. You want an order, where all 11 objects are included, without taking care for weights? Then look to the module lpom of PyHasse. Perhaps this module makes you happy. • You want to apply another procedure to get a linear order of your objects? Ok, in our point of view the Copeland index could do a good job. See module copeland • Let us finally try another object pair: Some remarks are now in order…
- 17. Let us try for instance „b“ and „i“. Here is the reponse of the PyHasse program! When you look at the Hasse diagram, you see the reason: These two objects are incomparable. Therefore either you select another pair, or you detect, why these two objects are incomparable:
- 18. Pressing „Calc“ gives: Ok, ok! This result is not too interesting, as we have only two attributes. The response of spyout tells you q1 for the first object (object b) has value 10, for the second object (object i) 4, but for attribute q2 the relation is turned around: Object b has value 10, but object i has by far a larger value in q2, namely 53. Finally the last column shows what is the general range of the attribute Values supporting you with some ideas whether the data differences are important or not.
- 19. • Usually many attribute pairs can be considered, where each single pair can but contribute to the incomparability found. • Furthermore the data differences can be very different. Both aspects must be shown to the user. He may draw his own conclusions. • Often one wants to see incomparability in the context of the whole data matrix. If yes, then PyHasse offers another module namely acm for a deepened analysis. • The user may think that sometimes data differences are not really important. An analysis based on fuzzy concepts may then be helpful. PyHasse has a module, called fuzzy, which can be helpful. Once again, some remarks are in order:
- 20. • See www.pyhasse.org and references and links therein • Demo: http://spyout.pyhasse.org • You want to contact us: The email address: spyout@pyhasse.org • You want to call us? – R.Bruggemann (+49) 30 6496676 – P.Koppatz (+49) 331 20029708