IEEE Systems, Man and Cybernetics Magazine - April 2020 - 51

Jim and I were curious about
(radial basis functions, learningthe hybrid approach, but instead
vector quantization, and cascade
Do we need hundreds
of explicitly combining strategies
correlation), discriminant analysis,
of classifiers to
for keeping and discarding protodecision trees other than C5.0,
types, we chose a random, criterule-based classifiers, other bagging
solve real-world
rion-driven technique [20]. Our
and boosting ensembles, 1-NNs,
classification
study was meant to be a proof
Bayesian, generalized linear model,
of concept, and we only played
partial least-squares regression,
problems?
around with the famous iris-data
multivariate adaptive regression
set. We discovered that a random,
splines, etc., are not competitive at
criterion-driven approach [bruteall" (my emphasis). But wait, there
force random search and a basic genetic algorithm (GA)]
is a new kid on the block. The rotation forest [7] beats them
offered the best compromise between classification accuall, according to a more recent study by Bagnall et al. [8].
racy and the reduction rate compared with the classical
(I am quite proud of this, actually, as I have a little contribuexamples of editing and condensing. We subsequently
tion to the rotation-forest ensemble method.)
carried out experimental comparisons [21] and included
I sympathize with all those uncompetitive classifiers.
methods that belonged in the group of prototype replaceBut we all know that there is no single tool for every job. If
ment. In other words, S is no longer a subset of X but of
that were the case, your car, computer, and smartphone
could all be repaired with a hammer. The tool selection
R n, with a cardinality restriction ; S ; # ; X ;. Our random,
depends on the data, of course. And not all is lost. In 2008,
criterion-driven methods were doing okay but not as well
the 1-NN family was included (by experts) among the top
as the prototype-replacement competitors. During those
10 algorithms in data mining [9].
pre-Google times, we were not even aware that our bruteforce random search actually had a name: Monte Carlo 1
Prototype (Instance) Selection
(MC1) [22]. Much as we wanted to, we could not afford to
Observing that the 1-NN philosophy underpins many
run a large experiment. Intel was yet to release the first
seemingly unrelated classifiers, Jim and I set off to unite
Xeon processor, the Pentium II Xeon 400 (1-MB cache,
them under the same umbrella. We called it the general400 MHz).
ized nearest-prototype classifier [10], [11]. We were hoping
A funny story unfolded shortly after the publication of
to pull a rabbit out of the hat; that is, identify niches that
our "apotheosis" of random/GA prototype selection [20].
had not been explored and propose alternative versions of
Our experiments gave a 14-element consistent set for the
the prototype classifier. Alas, Floppy (the rabbit) did not
iris data. The previous record was a 15-element consismaterialize, and instead, Jim and I got properly sucked
tent set, so we beat it by one. Before we published the
into one of the side issues of the 1-NN: instance selection
paper, Jim said, "You know what? I want to be double and
(also known as prototype selection/extraction/generation/
triple sure that we have not made a mistake. Delete your
replacement, data editing for the 1-NN classifier, data con1-NN code, write it again from scratch, and verify the
densing, data reduction, and more).
result. The first thing people will do is stick our winning
We will take prototype selection to mean that we
prototype set in their 1-NN classifier." So I did, and there
choose a subset, S, of the reference set, X, which satiswas no mistake. The paper came out. Almost instantly,
the author of the previous winner (the 15-element consisfies some criteria related to the classification accuracy of
tent prototype set) wrote an indignant email to Jim and
the 1-NN using S as the reference set. Requiring a zero
me claiming that our supposedly consistent set misla(resubstitution) error on X gives rise to the so-called conbeled one object in the iris data. The author suggested
densing methods, of which Hart's condensed 1-NN (CNN)
that we write a retraction and apologize for misleading
[12] is the classic instance. A reference set with a zero
the journal's readership.
resubstitution error is called a consistent subset of X. This
That email exchange didn't do my blood pressure any
approach preserves boundary objects that are likely to be
good, but I knew there was no mistake. It transpired that
misclassified if they are missing from the prototype set.
we had been using slightly different versions of the iris
The alternative approach, called editing, is to select protodata. Jim and I then sourced the original paper by Fisher
types by removing noise. It aims for better generalization
[23] where Anderson's data [24] were published, and it
accuracy with S compared to the result when the whole
turned out that the "real" data set matched Jim's and my
of X is used as the reference set. The pioneering method
version. It could easily have been the other way around. Jim
in this category is due to Wilson (1972) [13]. Through this
was so amused by the situation that he wrote a note but not
approach, border objects that may be misclassified are disto apologize. The title was: "Will the Real Iris Data Please
carded. A third category, called hybrid, includes methods
Stand Up?" [25]. The note included a table with the original
that combine the two ideas. Myriad methods for prototype
iris-data set and warned about the unmatching variants
selection have been proposed in all three categories since
floating around.
those early years [14]-[19].
	

Ap ri l 2020

IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE	

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IEEE Systems, Man and Cybernetics Magazine - April 2020

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