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.

Previous post:
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.).

New book - Conceptual Structures: Knowledge Visualization and Reasoning

Conceptual Structures: Knowledge Visualization and Reasoning
16th International Conference on Conceptual Structures
ICCS 2008 Toulouse, France, July 7-11, 2008 Proceedings

Eklund, Peter; Haemmerlé, Ollivier (Eds.)

2008, X, 311 p. With online files/update., Softcover

ISBN: 978-3-540-70595-6

48,00 €

About this book

This book constitutes the refereed proceedings of the 16th International Conference on Conceptual Structures, ICCS 2008, held in Toulouse, France, in July 2008.
The 19 revised full papers presented together with 2 invited papers were carefully reviewed and selected from over 70 submissions. The scope of the contributions ranges from theoretical and methodological topics to implementation issues and applications. The papers present a family of Conceptual Structure approaches that build on techniques derived from artificial intelligence, knowledge representation, applied mathematics and lattice theory, computational linguistics, conceptual modeling, intelligent systems and knowledge management.

Bell jars and bell curves

To those who do not know Mathematics it is difficult to get across a real feeling as to the beauty,
the deepest beauty of nature. ... If you want to learn about nature, to appreciate nature,
it is necessary to understand the language that she speaks in.
Richard Feynman. 1918-1988. American physicist.

As those of us who can - work through school, college and those who are gifted (in both senses) take the university detour we identify, refine and utilise our intellectual strengths. This entails that we must also come to recognise our limitations. Looking heaven wards the day dawns that the "way of the astronaut" is a step too far, that's OK others can fly for me. ... At some point and usually much too early in academic careers specific aptitudes, intelligence and abilities crystallise into that form of diamond known as yea or nay. Statistics have it that there are many average scholars out there. Some people are average in maths AND English (languages), a smaller proportion excel in one or the other. So, how is your essay writing? Or should I ask how is your number theory?

The bell curve has its say, but having that bell jar placed over you is just the start of the story. Minds should be constantly enquiring. The result is coming across things you cannot fully comprehend and yet you have this real sense - you know - that "there is a tool here I could use - if only...."

At work we will naturally share many abilities with our peers - including befuddlement when it comes to maths. The nursing literature includes an ongoing parade of titles dedicated to explaining maths and stats to the numerically challenged.

In the mid 80s the dichotomy between the SCIENCES and HUMANITIES was illustrated for me in a working paper from the school of geography at University of Leeds. I still have it, saving it for a rainy day:
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.
Abstract 1985

I came across this like a moth to a flame (thankfully I found an egg-carton to hide under). I began to work through the paper and had a puncture before even leaving the lay-by. My '84 A5 copy is rather basic in terms of print quality. Showing it to a few people at the time they thought perhaps there were some printing errors. They may well be right although may be they were also being kind. It wasn't just a 'NO ENTRY' sign, it was a brick wall I had met before. Some teachers reinforced this wall; while there were many others who did their level best to help me find a way through, or around. The truth is my cognitive wiring just ain't up to it. Referencing a paper is one thing, plumbing its depths and applying it is another.

So the obvious conclusion from this mathematical close encounter (more like a distant approach really) is that I'm challenged when it comes to maths. I've worked my may through (IBM) SPSS descriptive stats and some 'real' stats; implemented BASIC search algorithms. But away from the lecture-IT room the knowledge quickly evaporates. I'm utterly fascinated looking at the world-universe within and around me, but I'm knee deep in a river and dying of thirst. There are millions of people haunted by the spectre of their ineptitude with numbers.

This is one of the main points of Macgill's text. The paper highlights an approach of great potential to social science researchers (including health and social care?) and yet the people most in need of such methods are frequently disadvantaged being unable to fully understand, grasp and apply these tools.

So tantalising, so frustrating - the glass is very frosted for this 'average student' (lifelong learner!).

Is it just about opportunities or opportunities to break the frosted glass?