Systems, Man & Cybernetics - January 2015 - 25

broad procedural characteristics while
avoiding discussion of underlying concepts and ideas. Many of the proposed
algorithms produced different results
depending on the order in which the
sample points were processed.
The evolving theory of optimization, which was then widely applied
in areas such as operations research
and systems control, provided a sound
basis to characterize the aims of clustering algorithms as the optimization
of a functional defined over the set
of partitions of the sample set. Finding optimal partitions into conventional subsets was a hard problem,
essentially requiring the solution of
integer-programming problems. Fuzzy
partitions, on the other hand, could
be treated with the powerful tools of
modern mathematical analysis.
RS: Maybe I am wrong, but it seems
that you both discussed very early
the applicability of fuzzy clustering
in medical diagnosis. I think that
you, Enrique, published a paper in
Spanish on medical diagnosis some
years before your paper on the "new
approach" appeared-and I guess that
you were in Argentina at that time.
Jim, you presented "Feature Selection
for Binary Data-Medical Diagnosis
with Fuzzy Sets" [15] at the National
Computer Conference in 1976. Can you
explain the background and the reasons for this link to medical diagnosis?
JB: The appearance of the stomach disease data in the 1976 and 1977
papers was not related to any specific interest I had in medical diagnosis. Nor was it related to my belief
that fuzzy clustering was a special
tool for medical diagnosis. I needed
a labeled data set that had binaryvalued features to test my idea about
feature selection using the cluster
centers generated by fuzzy c-means,
and this data set happened to be the
one I stumbled upon that satisfied
those criteria. A more accessible reference than the one you have listed
is "Prototype Classification and Feature Selection with Fuzzy Sets." [16].
ER: The initial motivation for
fuzzy clustering was the need of

mathematical economists in Argentina to find structures on the output
of their models, primarily for summarization purposes.
My original paper on fuzzy clustering, however, was written when I was
in the United States and treated the
problem in general, application-independent terms. Although I was, by then,
working at the University of Southern
California as part of a pioneering project on applications of computers to
medicine, our efforts were concerned
mainly with the application of dynamic
programming and invariant imbedding
techniques to other areas of applied science. A notable exception was the application of system identification techniques to models of drug metabolism.
None of these efforts, as far as I can
recall, involved cluster analysis.
By the time my original paper was
published, however, I was working at
the UCLA Brain Research Institute.
It was then that I started to deal with
problems posed by neurophysiologists
who, at the time, relied mainly on EEG
recordings as their main source of experimental data. The main application
of my techniques in this field was a
paper that appeared in Brain Research
in 1972 [17]. The purpose of the paper
was to answer basic questions about
the nature of sleep from the application
of fuzzy clustering techniques to EEG
data. Its introduction stressed that
sleep staging had been confined to the
development of recognition algorithms
that assigned EEG signals to previously defined classes. Our study, however,
was concerned mainly with the question: "What are the stages of sleep?" In
other words, we were concerned with
the discovery of significant structures
in EEG data that shed light on the nature of sleep. Multiple epochs of EEG
sleep were first subjected to spectral
analysis. These spectra were then reduced by principal component analysis, and a distance was defined between the normalized representations.
The resulting distance matrix was then
subject to fuzzy cluster analysis.
RS: Jim, you wrote in "Numerical Taxonomy with Fuzzy Sets" in 1974 [18]
Ja nu a r y 2015

that "Pattern classification has provided great impetus for the theory of
fuzzy sets, the basic reference to which
is the original work by Zadeh (1965).
In particular, the papers of Bellman,
Kalaba, and Zadeh (1966); Wee (1967);
Flake and Turner (1968); Gitman and
Levine (1970); Ruspini (1969, 1970); and
Dunn (1973a, 1973b) trace the evolution of fuzzy sets as a theoretical basis
for cluster analysis" [8], [19]-[26].
In my historical research, I found a
memorandum [26] for the RAND Corporation officially listed as written
in October 1964 by Bellman, Kalaba,
and Zadeh that has the same title and
text as the later journal article of 1966
[19]. This memo was written by Zadeh
alone (as he said to me in an interview)
when he returned from a journey to
Dayton, Ohio, where he was supposed
to give a talk on pattern recognition
at Wright-Patterson Air Force Base.
I never found any papers, programs,
or the title of this talk in his private
archive, maybe because it was a talk
for the U.S. military.
However, it is my considered opinion that during this travel he started
thinking about pattern recognition
problems and grades of membership of an object to be an element
of a class. In the memo (and also in
the later article of 1966), he wrote:
"For example, suppose that we are
concerned with devising a test for
differentiating between handwritten
letters O and D. One approach to
this problem would be to give a set
of handwritten letters and indicate
their grades of membership in the
fuzzy sets O and D. On performing
abstraction on these samples, one
obtains the estimates n O and nu D of
n O and n D, respectively. Then given
a letter x which is not one of the given
samples, one can calculate its grades
of membership in O and D, and, if O
and D have no overlap, classify x in
O or D." [6]. (See Figure 5.)
Also, you, Enrique, referred in
your first article "A New Approach
to Clustering" in 1969 to the 1966
article of Lotfi Zadeh, but you wrote:
"However, our fuzzy sets have a strong
probabilistic meaning, and our rules

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Table of Contents for the Digital Edition of Systems, Man & Cybernetics - January 2015

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Systems, Man & Cybernetics - January 2015 - Cover3
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