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Concepts is a simple Python implementation of Formal Concept Analysis (FCA_).
FCA provides a mathematical model for describing a set of objects (e.g. King Arthur, Sir Robin, and the holy grail) with a set of properties (e.g. human, knight, king, and mysterious) which each of the objects either has or not. A table called formal context defines which objects have a given property and vice versa which properties a given object has.
This package runs under Python 2.7 and 3.5+, use pip_ to install:
.. code:: bash
$ pip install concepts
This will also install the bitsets_ and graphviz_ packages from PyPI as required dependencies.
Rendering lattice graphs depends on the Graphviz software_. Make sure its
dot executable is on your systems' path.
Create a formal context defining which object has which property, e.g. from a simple ASCII-art style cross-table with object rows and property columns (alternatively load a CXT or CSV file):
.. code:: python
>>> from concepts import Context
>>> c = Context.fromstring('''
... |human|knight|king |mysterious|
... King Arthur| X | X | X | |
... Sir Robin | X | X | | |
... holy grail | | | | X |
... ''')
>>> c # doctest: +ELLIPSIS
<Context object mapping 3 objects to 4 properties [dae7402a] at 0x...>
Query common properties of objects or common objects of properties (derivation):
.. code:: python
>>> c.intension(['King Arthur', 'Sir Robin'])
('human', 'knight')
>>> c.extension(['knight', 'mysterious'])
()
Get the closest matching objects-properties pair of objects or properties (formal concepts):
.. code:: python
>>> c['Sir Robin', 'holy grail']
(('King Arthur', 'Sir Robin', 'holy grail'), ())
>>> c['king',]
(('King Arthur',), ('human', 'knight', 'king'))
Iterate over the concept lattice of all objects-properties pairs:
.. code:: python
>>> for extent, intent in c.lattice:
... print('%r %r' % (extent, intent))
() ('human', 'knight', 'king', 'mysterious')
('King Arthur',) ('human', 'knight', 'king')
('holy grail',) ('mysterious',)
('King Arthur', 'Sir Robin') ('human', 'knight')
('King Arthur', 'Sir Robin', 'holy grail') ()
Make a Graphviz visualization of the lattice (use .graphviz(view=True) to
directly render it and display the resulting PDF):
.. code:: python
>>> c.lattice.graphviz() # doctest: +ELLIPSIS
<graphviz.dot.Digraph object at 0x...>
.. image:: https://raw.github.com/xflr6/concepts/master/docs/holy-grail.png :align: center
The generation of the concept lattice is based on the algorithm from C. Lindig.
Fast Concept Analysis_. In Gerhard Stumme, editors, Working with Conceptual
Structures - Contributions to ICCS 2000, Shaker Verlag, Aachen, Germany, 2000.
The included example CXT files are taken from Uta Priss' FCA homepage_
The implementation is based on these Python packages:
The following package is build on top of concepts:
If you want to apply FCA to bigger data sets, you might want to consider other implementations_ based on more sophisticated algorithms_ like In-Close_
or Fcbo_.
Concepts is distributed under the MIT license_.
.. _FCA: https://en.wikipedia.org/wiki/Formal_concept_analysis .. _Fast Concept Analysis: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.143.948 .. _FCA homepage: http://www.upriss.org.uk/fca/examples.html
.. _pip: https://pip.readthedocs.io .. _Graphviz software: http://www.graphviz.org
.. _bitsets: https://pypi.org/project/bitsets/ .. _graphviz: https://pypi.org/project/graphviz/ .. _features: https://pypi.org/project/features/
.. _other implementations: http://www.upriss.org.uk/fca/fcasoftware.html .. _more sophisticated algorithms: http://www.upriss.org.uk/fca/fcaalgorithms.html .. _In-Close: https://sourceforge.net/projects/inclose/ .. _Fcbo: http://fcalgs.sourceforge.net
.. _MIT license: https://opensource.org/licenses/MIT
.. |--| unicode:: U+2013
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FAQs
Formal Concept Analysis with Python
We found that concepts demonstrated a healthy version release cadence and project activity because the last version was released less than a year ago. It has 2 open source maintainers collaborating on the project.
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