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* triadic exploration

* Triadic-Exploration: Added  basic example to doc

* Triadic Exploration: small fix in doc
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maximilian-felde committed Apr 26, 2022
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5. Advanced Topics
1. [pq-cores](doc/pq-cores-in-Formal-Contexts.md)
2. [REST-API Usage](doc/REST-API-usage.md)
3. [triadic-exploration](doc/Triadic-Exploration.org)
6. [API documentation](doc/API.md)
7. [Development](doc/Development.org)

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151 changes: 151 additions & 0 deletions doc/Triadic-Exploration.org
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The triadic-exploration namespace provides a range of functionality to deal with the exploration of triadic contexts.

A tradic context $(G,M,B,Y)$ can be represented as a collection of contexts $\{\mathbb{K}_1,\mathbb{K}_2,\ldots,\mathbb{K}_i\}$ on the same sets of objects $G$ and attributes $M$.

The following example shows the situation of public transport at the train station Bf. Wilhelmshöhe with direction to the city center in Kassel.
This example is part of the paper [[https://arxiv.org/abs/2102.02654][Triadic Exploration and Exploration with Multiple Experts]], see https://arxiv.org/abs/2102.02654.
From Bf. Wilhelmshöhe you can travel by one of four bus lines (52, 55, 100 and 500), four tram lines (1, 3, 4 and 7), one night tram (N3) and one regional tram (RT5) to the city center.
These are the objects of our context.
The buses and trams leave the station at different times throughout each day of the week.
The attributes of our context are the aggregated the leave-times, more specifically, we have split each day in five distinct time slots: early morning from 4:00 to 7:00, working hours from 7:00 to 19:00, evening from 19:00 to 21:00, late evening from 21:00 to 24:00 and night from 0:00 to 4:00.
A bus or tram has a cross the formal context if there is at least one leave-time in the time slot.
Furthermore, we have split the days of the week into Monday to Friday, Saturday and Sunday as conditions.

The respective contexts are part of the triadic-exploration namespace.


First load the respective namespace to deal with triadic contexts and to use the drawing functionality provided by conexp-clj.
#+begin_src clojure :eval never
(use 'conexp.fca.triadic-exploration)
(use 'conexp.gui.draw)
#+end_src


To view the context family from the example use
#+begin_src clojure :eval never
cxt-family-paper
;; =>
;; {:Mo-Fr
;; |:early-morning :evening :late-evening :night :working-hours
;; -----+------------------------------------------------------------
;; :1 |x x x . x
;; :100 |x x x . x
;; :3 |x x x . x
;; :4 |x x x . x
;; :500 |x x x x x
;; :52 |x x x . x
;; :55 |x . . . x
;; :7 |x x . . x
;; :N3 |. . . . .
;; :RT5 |x x x . x
;; ,
;; :Sat
;; |:early-morning :evening :late-evening :night :working-hours
;; -----+------------------------------------------------------------
;; :1 |. x x . x
;; :100 |x x x . x
;; :3 |x x x . x
;; :4 |x x x . x
;; :500 |. x x . x
;; :52 |x . . . x
;; :55 |. . . . .
;; :7 |. . . . x
;; :N3 |. . . x .
;; :RT5 |x x x . x
;; ,
;; :Sun
;; |:early-morning :evening :late-evening :night :working-hours
;; -----+------------------------------------------------------------
;; :1 |. x x . x
;; :100 |x x x . x
;; :3 |x x x . x
;; :4 |x x x . x
;; :500 |. x x . x
;; :52 |. . . . .
;; :55 |. . . . .
;; :7 |. . . . .
;; :N3 |. . . x .
;; :RT5 |. x x . x
;; }
#+end_src

Such a family of formal contexts can be transformed into a triadic context using
#+begin_src clojure :eval never
(def tcxt-paper (context-family->triadic-context cxt-family-paper))
tcxt-paper
;; {:objects #{:RT5 :52 :500 :4 :100 :7 :55 :1 :3 :N3},
;; :attributes
;; #{:working-hours :late-evening :early-morning :night :evening},
;; :conditions (:Mo-Fr :Sat :Sun),
;; :incidence
;; #{[:1 :early-morning :Mo-Fr] [:100 :evening :Sat]
;; [:RT5 :working-hours :Mo-Fr] [:55 :early-morning :Mo-Fr]
;; [:7 :working-hours :Mo-Fr] [:100 :early-morning :Mo-Fr]
;; [:500 :working-hours :Sun] [:3 :working-hours :Sat]
;; [:500 :evening :Mo-Fr] [:4 :late-evening :Mo-Fr]
;; [:1 :late-evening :Sat] [:3 :evening :Sun]
;; [:500 :late-evening :Mo-Fr] [:RT5 :working-hours :Sat]
;; [:100 :early-morning :Sun] [:100 :working-hours :Sun]
;; [:3 :working-hours :Sun] [:RT5 :late-evening :Sat]
;; [:100 :working-hours :Sat] [:1 :evening :Mo-Fr]
;; [:500 :late-evening :Sun] [:3 :late-evening :Sun]
;; [:100 :evening :Sun] [:4 :evening :Mo-Fr]
;; [:500 :working-hours :Sat] [:1 :evening :Sat]
;; [:100 :early-morning :Sat] [:3 :evening :Sat]
;; [:1 :late-evening :Mo-Fr] [:500 :evening :Sat]
;; [:RT5 :early-morning :Sat] [:500 :night :Mo-Fr]
;; [:500 :evening :Sun] [:52 :working-hours :Mo-Fr]
;; [:RT5 :evening :Sun] [:100 :late-evening :Sat]
;; [:4 :early-morning :Mo-Fr] [:3 :early-morning :Sat]
;; [:4 :working-hours :Mo-Fr] [:1 :evening :Sun]
;; [:52 :early-morning :Sat] [:52 :early-morning :Mo-Fr]
;; [:3 :late-evening :Sat] [:7 :early-morning :Mo-Fr]
;; [:100 :late-evening :Sun] [:4 :evening :Sat]
;; [:4 :working-hours :Sat] [:3 :early-morning :Sun]
;; [:52 :late-evening :Mo-Fr] [:RT5 :working-hours :Sun]
;; [:100 :late-evening :Mo-Fr] [:RT5 :late-evening :Sun]
;; [:55 :working-hours :Mo-Fr] [:7 :evening :Mo-Fr]
;; [:100 :evening :Mo-Fr] [:1 :working-hours :Sun]
;; [:3 :early-morning :Mo-Fr] [:52 :evening :Mo-Fr]
;; [:4 :late-evening :Sun] [:4 :early-morning :Sat] [:N3 :night :Sun]
;; [:1 :late-evening :Sun] [:RT5 :late-evening :Mo-Fr]
;; [:1 :working-hours :Sat] [:3 :evening :Mo-Fr]
;; [:500 :working-hours :Mo-Fr] [:RT5 :evening :Mo-Fr]
;; [:4 :working-hours :Sun] [:4 :late-evening :Sat]
;; [:7 :working-hours :Sat] [:4 :early-morning :Sun]
;; [:RT5 :early-morning :Mo-Fr] [:N3 :night :Sat]
;; [:RT5 :evening :Sat] [:100 :working-hours :Mo-Fr]
;; [:4 :evening :Sun] [:500 :late-evening :Sat]
;; [:500 :early-morning :Mo-Fr] [:3 :working-hours :Mo-Fr]
;; [:3 :late-evening :Mo-Fr] [:52 :working-hours :Sat]
;; [:1 :working-hours :Mo-Fr]}}
#+end_src


To compute all conditional theories use
#+begin_src clojure :eval never
(def all-conditional-implications (compute-all-conditional-theories tcxt-paper))
all-conditional-implications
;; |:Mo-Fr :Sat :Sun
;; -----------------------------------------------------------------------+-----------------
;; (#{:early-morning} ⟶ #{:working-hours}) |x x x
;; (#{:working-hours :night} ⟶ #{:late-evening :early-morning :evening}) |x x x
;; (#{} ⟶ #{:working-hours :late-evening :evening}) |. . .
;; (#{:late-evening} ⟶ #{:working-hours :evening}) |x x x
;; (#{} ⟶ #{:working-hours :late-evening :early-morning :night :evening}) |. . .
;; (#{:working-hours} ⟶ #{:early-morning}) |x . .
;; (#{:night} ⟶ #{:working-hours :late-evening :early-morning :evening}) |x . .
;; (#{:evening} ⟶ #{:working-hours :late-evening}) |. x x
;; (#{:evening} ⟶ #{:working-hours}) |x x x
;; (#{:working-hours :evening} ⟶ #{:early-morning}) |x . .
;; (#{:working-hours :late-evening :early-morning :evening} ⟶ #{:night}) |. . .
;; (#{:working-hours} ⟶ #{:evening}) |. . x
#+end_src


And to draw the corresponding concept lattice to see which implications hold under which conditions use
#+begin_src clojure :eval never
(draw-concept-lattice all-conditional-implications)
#+end_src

[[./images/concept-lattice-conditional-theories.png]]
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1 change: 1 addition & 0 deletions project.clj
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[org.clojure/math.numeric-tower "0.0.4"]
[org.clojure/tools.cli "1.0.194"]
[org.apache.commons/commons-math "2.2"]
[org.clojure/algo.generic "0.1.3"]
[seesaw "1.5.0"]
[reply "0.4.4"
:exclusions [org.clojure/clojure
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