Talk:Formal concept analysis

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What about unicorns? Concept, yes, but extension, no.

1. Formal concept analysis is about formal concepts in respect to a formal context. The only concept, which may have empty extent is the bottom concept, which always has the entire attribute set as intent.

2. Talking (non-formally) about unicorns leads to a concept in a fantasy setting, which provides imaginary objects to the "real world". So the concept unicorn has a (non-empty) extension. Excluding imaginary objects from "real wolrd" leads to a concept, too, but it is usually not useful to call it unicorn.

WTF is Formal Concept Analysis?

I actually know Lattice Theory out the wazoo, but I still fail to understand what this article is about. Does anyone care to shed any light on the subject? In particular, what is the purpose of this subject? How is it useful? Why is it interesting enough that people have written books and articles on it? It seems vaguely interesting but the current article doesn't really communicate the usefulness or purpose of this subject. Cazort 21:40, 23 October 2007 (UTC)

My naive understanding is that's a principled way of automatically deriving an ontology from a collection of objects and their properties. So it's useful to the extent that ontologies are useful more generally and to the extent that the properties are easier to define and derive than the full ontology. —David Eppstein 22:21, 23 October 2007 (UTC)

Can anyone help fix Sample exclusion dimension? Michael Hardy (talk) 16:55, 28 March 2008 (UTC)

I think the definitions there are unambiguous. What's left out is why you should care; for that I guess you need to refer to the Valiant article (which I haven't yet done). But it has little or nothing to do with formal concept analysis. A concept in that setting is a subset of a given domain; the difficulty of learning a concept is the number of membership queries you have to do to distinguish it from all other concepts in a concept class; and the exclusion dimension is the difficulty of the hardest concept in the class. —David Eppstein (talk) 06:33, 29 March 2008 (UTC)

Recovering the context from the Hasse diagram vs. Example

The first sentence in Recovering ... reads: The Hasse diagram of the concept lattice ... encodes enough information to recover the original context from which it was formed.

Looking at the graphics of the Example (O = {1,2,3,4,5,6,7,8,9,10}, A = {composite,even,odd,prime,square}) and following the description in Recovering I wonder how to recover for example every single of the three numbers 3, 5, 7 from the Hasse diagram since the diagram with O' = {1,2,3,4,6,8,9,10}, A' = A is the same but without the objects 5 and 7 (or the one "ignoring" 6 and 8: O= {1,2,3,4,9,10}, A = A). —Preceding unsigned comment added by 87.184.91.223 (talk) 13:06, 5 August 2008 (UTC)

The example section should be after the formal definition

I would add an extra point to the comment above: it doesn't make much sense to instantiate the example, before stating the formal definitions. The comment above is from 2008, almost 4 years old. In this case I may change the order, and improve both sections if there is no further comments within 2 months Pedro 17:32, 24 February 2012 (UTC) — Preceding unsigned comment added by Pcgomes (talk • contribs)

Gowers disagrees. It can be difficult to read formal definitions without having a clear example in mind first. I think the "intuitive description" provides enough of the framework to understand the example, without getting as abstract as possible as quickly as possible. —David Eppstein (talk) 18:03, 24 February 2012 (UTC)

Recent edits - major revision based on the German article

Today there was some back-and-forth between me and ‎Jwollbold regarding the start of the article. See this diff for Jwollbold's suggested replacement for the start. My take on it is that the new text is far too formal and abstract, giving readers no idea what FCA is good for or why they should care about it, and that we should start more gently and non-technically as the previous introduction did. But I welcome more discussion here. —David Eppstein (talk) 18:31, 22 April 2012 (UTC)

Hi David, fine that a discussion starts, even if initially abrupt - better than few development of the article since 3 years. Nobody had the energy for a profound revision, although several people from the FCA community expressed discontent with missing subjects and unusual presentation and notation. My opinion:

• The article gives readers no idea what FCA is good for ;-), e.g. regarding philosophical background and applications.
• The definition of a concept is far from the formalism based on the Galois connection between O and A.
• Building an ontology (in the stricter sense) is only one amongst many applications.
• "'Natural' object cluster" is non-standard terminology.
• Concept algebra and weak negation are too special subjects and should be shifted to a new article.
• Implicational theory and Attribute exploration are missing completely.
• The layout of the context and lattice are unusual.

I participated in Dborchmanns elaboration of a completely new, formally exact German article, for which he still has many ideas. The introduction was meant as an intuitive description - since you don't like it, we should develop a new version together, possibly also move parts to a new section as already tried. Concrete ideas and edits will follow - please respect that I can't be actif in Wikipedia every day. --Jwollbold (talk) 22:17, 22 April 2012 (UTC)

My basic issue with the new version is that phrases like "is the concrete representation of complete lattices and their properties by means of (one-valued) formal contexts" fails to convey any intuition (because there are no intuitive concepts in here, only mathematical abstractions), fails to be readable to people who are not already experts in lattice theory (because otherwise why should they know what a lattice is or why it is important to represent it), uses phrases that even I as someone who has edited this article don't understand (what is one-valued?), and for that matter doesn't even link to the appropriate other Wikipedia articles to explain what these terms mean (note that lattice is a disambiguation page). Basically, you are writing as if the audience is yourself, someone who already knows and appreciates the subject. Per WP:TECHNICAL, we need to start our audiences addressing as broad an audience as possible, and that means saving the technical details for later to the extent possible. —David Eppstein (talk) 23:18, 22 April 2012 (UTC)

I only looked at your contribution after my last edit. You are right, starting with "the concrete representation..." could be difficult to understand. In principle, I tried to make my text more readable - your turn to rewrite it. --Jwollbold (talk) 23:26, 22 April 2012 (UTC)

Your version now seems much more compact and understandable. My text was more suitable for an introduction mentioning important terms, not primarily for an intuitive description. Hence the first sentence and the notion of one-valued (or single-valued, usual) formal context in contrast to many-valued (a relation between objects, attributes and their values). Both terms will be explained later, as well as the philosophical background.

We should revise the lead section and "Overview and history" again, if the mathematical parts are translated from the German article. Do you agree to have extensive formal definitions and the main theorem like there, with additional intuitive explanations? --Jwollbold (talk) 07:37, 23 April 2012 (UTC)

David, you are right with your critism of the introduction, and I think that the introduction in the german article also suffers from too many unexplained phrases. As soon as I have time I'll try to fix this.

However, I would not like to refer to Formal Concept Analysis as a technique of machine learning or of data analysis. It is a mathematical theory with strong philosophical background, which gained attention in those fields. The main motivation of Formal Concept Analysis was to find a correspondance between lattices (in the sense of order theory) and formal contexts. I think that a good introduction should reflect that. I hope that we can find such an introduction together that honors all those facets of FCA. Dborchmann (talk) 07:40, 23 April 2012 (UTC)

To me this statement of motivation makes no sense. The main early results of FCA were to find this correspondence, but before knowing that the coreespondence exists how could it serve as motivation? I was guessing that it was more likely that the early motivation was to provide a mathematical foundation for classifications such as Map of lattices or the standard classifications of quadrilaterals into different types, but that is only a guess. —David Eppstein (talk) 15:35, 23 April 2012 (UTC)

The motivation and aim was restructering lattice theory by relating it to human thinking about reality, i.e. data and concepts. Hence, the "concrete representation of complete lattices". I should translate first "Motivation und philosophischer Hintergrund", then it becomes clearer. --Jwollbold (talk) 16:38, 23 April 2012 (UTC)

I don't understand what you mean by "a principled way of deriving..." Could you explain it so that we can write a clearer sentence? Diego (talk) 13:21, 24 April 2012 (UTC)

Based on mathematical principles rather than ad hoc. —David Eppstein (talk) 15:55, 24 April 2012 (UTC)

Could we then use the word formal instead of "principled" so that we can use a wikilink to explain the concept? Diego (talk) 16:14, 24 April 2012 (UTC)

I think the first sentence is too jargon-ish and abstract anyway. Stating that it's based on mathematical principles could be done in the second sentence, or by saying "based on mathematical principles" instead of "principled". Diego (talk) 16:16, 24 April 2012 (UTC)

Revision of German Article

Line chart of a concept lattice of kinds of bodies of water. Tagged in English language.

We have considerably revised the German version of this article about a year ago. "We", this is a group, most of us mathematicians at "Ernst Schröder Center for Conceptual Knowledge Processing". Among us, Bernhard Ganter one of the authors of Formal Concept Analysis. Foundations and Applications online-description, Peter Burmeister and Karl Erich Wolff', retired math professors who also were involved in the development of FCA. (see Overview and history and References)

One of our main goals in revising the article was, to write the article in a way, not only comprehensible to mathematicians, as Wikipedia is an encyclopedia for everyone. Not to mention, that Rudolf Wille who can be regarded to be the father of FCA always tried hard to get math out of the ivory tower.

We would like to blend in some of our ideas into this English article. I have tried to translate the introduction of the German article to English: User:MRewald/FBA. We are interested in a cooperation to improve the article.

In the German article we also have replaced the example section by an example, we believe to be more related to practical use. This would be one of the next sections I'd be going to translate. We also have added a list of publications which deal with the practical application of FCA.

I just uploaded a figure in English language with the line chart of the example we used in the German article. Example (de)

Looking forward to productive cooperation --MRewald (talk) 20:32, 23 November 2017 (UTC)

Revision based on the German article

I have started revising the article, based on the work of the German editing group (see the post of MRewald above. A revison seems necessary because the article contains many inaccuracies. Moreover, some parts of it are not really about the topic.

So far I have modified the first two paragraphs. Comments are welcome.

--Bernhard Ganter (talk) 09:49, 8 December 2017 (UTC)

Meanwhile I have also changed the section on Contexts and concepts. However, I need some help from a typography wizard, since I was too stupid to typeset the \mapsto symbol in HTML. Instead, I had to use the math environment, but that looks different. Bernhard Ganter (talk) 10:30, 8 December 2017 (UTC)

And the sections on concept lattices, as well as negation.

Warning: I plan to remove much of the "Algorithms" section. That section is mostly devoted to comparing many algorithms which all solve the same problem: generating all formal concepts. Most of these algorithms are much shorter than this section. My opinion is that such a comparison is not appropriate in this article. If one really believes that all these algorithms deserve to be presented in WP, then I suggest an extra article for that. I am open for discussion.

--Bernhard Ganter (talk) 13:29, 8 December 2017 (UTC)

So I did. --Bernhard Ganter (talk) 06:19, 9 December 2017 (UTC)

Rewrote the "implications" section and integrated the "concept algebras" into a new section called "extensions of the theory". --Bernhard Ganter (talk) 16:13, 8 December 2017 (UTC)

This symbol: "↦"? You can try copying and pasting from here. —David Eppstein (talk) 06:01, 9 December 2017 (UTC)

Great! That works! I am happy! Thank you! --Bernhard Ganter (talk) 06:19, 9 December 2017 (UTC)

Most of the revison is now completed, some work is still to do. Most importantly, the citations need to be tidied up. — Preceding unsigned comment added by Bernhard Ganter (talk • contribs) 16:58, 9 December 2017 (UTC)

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Disambiguation tags removed

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Triadic Concept Analysis

In the section "Extensions of the theory: Triadic concept analysis", Klaus Biedermann should be cited, not only Rudolf Wille. Biedermann did the formalization of the "triadic Galois connection" and other triadic fundamentals. Wille invented the derived trilattice structure and diagram.70.112.90.106 (talk) 11:46, 30 October 2018 (UTC)