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?[edit]

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[edit]

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 (talk) 13:06, 5 August 2008 (UTC)

The example section should be after the formal definition[edit]

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 (talkcontribs)

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[edit]

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)