c/o JAN: Formal Concept Analysis ... and an encouraging footnote

My source:

Fuzzy cognitive mapping: an old tool with new uses in nursing research #phdchat https://t.co/mAYNxsTcpl

— Journal of Advanced Nursing (@jadvnursing) September 19, 2019

Andersson, N, Silver, H. Fuzzy cognitive mapping: An old tool with new uses in nursing research. J Adv Nurs. 2019; 00: 1– 8. https://doi.org/10.1111/jan.14192

This tweet prompted a reply and further reflection, as I've been aware of FCA for quite a while. A math disability (but remote fascination?) precludes me really 'getting to grips' with this. As noted before on W2tQ, visualization in the humanities (social sciences) has still not realised its potential. Those researchers, professional workers ... who could benefit from its application, being in the 'humanities', often do not understand the underlying mathematics. Even though they are not necessarily that advanced (sixth-form - undergraduate?).

Over the years I have built up a small library of related papers and books. The Macgill (1984) paper referenced below, I started to 'read' and work through and got a short way. The print quality is rather poor and obviously dated, but that is not the problem. I will try again. Since the 1980s software has changed beyond the proprietary packages of MathCad, MathLab, Maple and Mathematica and collectively they should (must?) make these methods more accessible. Of course, I thought this with regards to the use of content management system for a website (yes, that one!). Again though it's not the tools, but my choice, time and focus.

I write this and it might only be intuition, but I'm not just sure, I know there is something here.

Seeing FCA in JAN's tweet I thought of a certain footnote even though on my copy the reference seems incomplete:

Kwong, C. P. A Topological Framework for Formal Concept Analysis, The Chinese University of Hong Kong.

On the first page the footnote reads:

"The adjective "formal" is used to emphasize the mathematical substance of the objects being studied, which may be left out when such a formality is superfluous."

As you can imagine this is quite a gift for me. In a way it suggests the following from a 2x2 matrix with keywords (concepts), to an arbitrary array:

individual

|

INTERPERSONAL : SCIENCES

humanistic ----------------------------------------------- mechanistic

SOCIOLOGY : POLITICAL

|

group - population

1 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1	1 1 0 1 0 1 0 0 1 0 1 0 0 0 1 1
1 1 1 1 0 0 1 1 0 0 1 1 0 1 1 0	0 1 1 0 1 1 1 1 0 0 0 0 0 1 1 0

There is a worry here. When your formative nurse education and training stressed the need to shift from a task-oriented approach to individualised, then filling the domains of Hodges' model with '1's and '0's is a bona fide task-checklist - even if a binary one.

There is a response to that concern for another post; but before that there is another source c/o:

Johana Ramírez Gaviria (2015) Aspectos topológicos en el Análisis deConceptos FormalesTopological aspects in Formal Concept Analysis, Universidad Nacional de Colombia Facultad de Ciencias Exactas y Naturales Departamento de Matemáticas y Estadística Manizales, Colombia. p.6.

c/o Google, Spanish – detected, English

En [26] se plantean nuevos modelos para el FCA usando nociones de la topología algebraica. El contexto formal convencional es reemplazado por una matriz con entradas ”1” ó ”0” denominada matriz contexto, para construir una familia simplicial (familia concepto), de ahi se desprenden propiedades que relacionan la teoría de la topología algebraica con el FCA.

Cabe resaltar que hasta el momento no se ha trabajado en dotar de estructura topológica los contextos formales en el FCA generalizado, donde los datos de las tablas toman valores difusos en lugar de valores binarios como se tiene para el FCA clásico.

In [26] new models for the FCA are proposed using notions of the topology algebraic The conventional formal context is replaced by a matrix with “1” or "0" called context matrix, to build a simplicial family (concept family), from there properties that relate the theory of algebraic topology with the FCA.

It should be noted that so far no work has been done to provide a topological structure the formal contexts in the generalized FCA, where the data in the tables take values diffuse instead of binary values ​​as you have for the classic FCA. 

[26, reference is Kwong]

  The whole thesis would need translating, but I have a sense that this too is useful.

Working through papers, files, journals, books getting rid of, sorting, re-filing ... I'll see if I can add to the reading below.

Atkin, R. (1974). Mathematical Structure in Human Affairs. London, Heinemann.

Macgill, S.M. (1984). Structural Analysis of Social Data, A Guide to Ho's Galois Lattice Approach and A Partial Re-Specification of QAnalysis, Working Paper 416, School of Geography, University of Leeds.

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Bell jars and bell curves


Thanks to @jadvnursing for this tweet in-particular and for RTs.
(Paper e-copy received with thanks c/o Neil Andersson, 25 Oct 2019.).