Systems, Man & Cybernetics - January 2015 - 27

A related problem is cluster validity for big data-once we approximate
literal clusters in big data, how do we
verify their quality and utility? Since
it's basically an insoluble problem for
little data, I don't anticipate anything
beyond a bunch of newly minted "big
data validation methods" papers that
basically do the same thing as their
small data cousins. What is that? Not
much. But that won't stop any of us
from writing them-after all, that's
what we do. Is this too cynical? I don't
think so, but if you do, fine with me.
And finally, there is the question of
tendency assessment for big data-
how do we even know where there are
clusters in big data? Visual methods
are promising for little data, but how
to extend them to big data is a real
challenge. Many people are currently
working on a variety of approaches
to each of these problems for all four
types of clustering (crisp, fuzzy, probabilistic, and possibilistic). I expect to
see many new algorithms for big data
at our fingertips in the next decade.
I don't expect to see any progress
here, but, certainly, we will see tons of
papers anyway. Will they work better
than clustering in small data? No. But
that's life in cluster analysis-mostly
an art, with just enough science to
make it respectable.
ER: Fuzzy clustering has now
been around for 45 years. Since its
beginnings, we have continuously
improved our understanding of the
nature of classification problems.
New, challenging problems have
led to the development of new techniques, while leading to a general
perspective of those problems. This
viewpoint regards generalized clustering problems as the process of discovering interesting structures in a
data set. As conceived in the context
of qualitative representation methods, this process is governed by a
catalog of prototypical data models
[28]. The data mining processes are
optimization methods that search
for data subsets that approximately
match one of those models. Measures
of approximation quality permit us to
determine the extent to which a data

subset matches a prototypical structure. Recently, this methodology has
been successfully applied in several
fields, notably to problems arising in
bioinformatics. I strongly believe that
this approach will open new vistas
and greatly expand the scope of application of fuzzy clustering methods.
About the Author
Rudolf Seising obtained his Ph.D.
degree in philosophy of science and
his German Habilitation degree in
history of science from the LudwigMaximilians-University in Munich
after studying mathematics, physics,
and philosophy at the Ruhr-University
of Bochum, Germany. He was with
the University of the Armed Forces in
Munich from 1988 to 2002. From 2002
to 2008, he was with the University of
Vienna Medical School. Since 2005,
he has been a college lecturer at the
Faculty of History and Arts at the Ludwig-Maximilians-University Munich.
From April to September 2008, he was
acting as professor for the history
of science at the Friedrich-SchillerUniversity Jena, Germany, and from
September 2009 to March 2010 at
the Ludwig-Maximilians-University,
Munich. He was visiting researcher
(2008-2010) and an adjunct researcher (2010-2014) at the European Centre
for Soft Computing in Mieres (Asturias), Spain, and he has been a visiting
scholar at the University of California,
Berkeley. Recently, he has returned
as a professor to the Friedrich-Schiller-University Jena. Since 2004, he
has been the chair of the IFSA History Special Interest Group and, since
2007, of the EUSFLAT Working Group
Philosophical Foundations. He is also
a member of the IEEE Computational Intelligence Society (CIS) History
Committee and the IEEE CIS Fuzzy
Technical Committee. In 2013, he
cofounded the online journal Archives
for the Philosophy and History of
Soft Computing. His main areas of
research comprise historical and
philosophical foundations of science
and technology. Among other books,
he edited Views on Fuzzy Sets and
Systems from Different Perspectives
Ja nu a r y 2015

(Springer, 2009), Soft Computing in
Humanities and Social Sciences (with
V. Sanz, Springer, 2012), On Fuzziness:
A Homage to Lotfi A. Zadeh-Volumes
I and II (with E. Trillas, S. Termini,
and C. Moraga, Springer, 2013), and
Fuzziness and Medicine: Philosophical Reflections and Application Systems in Health Care: A Companion
Volume to Sadegh-Zadeh's "Handbook
on Analytical Philosophy of Medicine"
(with M.E. Tabacchi, Springer, 2013).
References
[1] E. H. Ruspini, "A theory of mathematical classification, Dissertation," Ph.D. dissertation, Univ. California,
Los Angeles, CA, 1977.
[2] J. C. Bezdek, "Fuzzy mathematics in pattern classification," Ph.D. dissertation, Graduate School, Cornell
Univ., Ithaca, NY, 1973.
[3] R. R. Sokal and P. H. A. Sneath, Principles of Numerical Taxonomy. San Francisco, CA: Freeman, 1963.
[4] P. H. A. Sneath and R. R. Sokal, Numerical Taxonomy: The Principles and Practice of Numerical
Classification. San Francisco, CA: Freeman, 1973.
[5] L. A. Zadeh, "Fuzzy sets," Inform. Control, vol. 8,
no. 3, pp. 338−353, 1965.
[6] L. A. Zadeh, "Fuzzy sets and systems," in System
Theory (Microwave Research Institute Symposia Series
XV), J. Fox Ed. Brooklyn, New York: Polytechnic Press,
1965, pp. 29-37.
[7] R. Seising, "The Fuzzification of Systems," in The
Genesis of Fuzzy Set Theory and Its Initial Applications-Developments up to the 1970s (Studies in Fuzziness and Soft Computing, vol. 216). Berlin, Germany;
New York: Springer, 2007.
[8] E. H. Ruspini, "A new approach to clustering,"
Inform. Control, vol. 15, no. 1, pp. 22-32, 1969.
[9] M. Minsky and S. Papert, Perceptrons. Cambridge,
MA: MIT Press, 1969.
[10] F. Rosenblatt, "The perceptron: A probabilistic
model for information storage and organization in the
brain," Psychol. Rev., vol. 65, no. 6, pp. 386-408, 1958.
[11] A. Novikoff, "On convergence proofs for perceptions," in Proc. Symp. Mathematical Theory Automata, Apr. 1962, vol. 12, pp. 615-622.
[12] R. O. Duda and P. E. Hart, Pattern Classification
and Scene Analysis. New York: Wiley, 1973.
[13] R. Krishnapuram and J. Keller, "A possibilistic
approach to clustering," IEEE Trans. Fuzzy Syst., vol.
1, no. 2, pp. 98-110, 1993.
[14] J. A. Hartigan, Clustering Algorithms. New York:
Wiley, 1975.

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