IEEE Systems, Man and Cybernetics Magazine - April 2020 - 50

There are three classes in this
I was gradually losing faith in the
data set: 1) background (black), 2)
fuzzy side of fuzzy-pattern recogniI treasure that time
top and tail (green), and 3) face
tion. You might ask what I was
as the most valuable
and bottom (blue). The only two
doing, then, visiting the editor-infeatures of data point x are its x 1
chief (EiC) of IEEE Transactions on
and enlightening
Fuzzy Systems (the founding EiC, at
and x 2 coordinates. The Bayes
experience of
that). Good question. It turned out
error for this data set is zero
that Jim and I had a soft spot for the
because there are no overlapmy career.
nearest-neighbor (1-NN) classifier
pi ng points with different class
and its variants, which was the sublabels. But the configuration of
ject of our COBASE grant. This artithe classes is beautifully bizarre.
cle tells the story of our collaboration on prototype selection
Figure 1(b) shows the data set sampled randomly from the
and what has happened since.
full data. The classification regions of the 1-NN classifier
using the sampled data as the reference set are shown in
Prototype Classifiers
Figure  1(c). George looks a bit disheveled but, actually,
more than 93% of the labels match the original ones.
The data were prepared from an image of 391 rows #
Definition
769
columns of pixels and contain 300,679 points. Our ranIn prototype classification, the data live in some metric
domly sampled data contain 1,000 points. The question in
space R n equipped with a distance. Depending on which
this article is: Can we use a reference set of fewer than
discipline or school (or continent) you come from, you may
1,000 points and achieve similar (or better) accuracy in
have a different name for the elements of R n. In pattern
recognizing George?
recognition, we call those objects, data points, or even patterns. In machine learning, you are more likely to call them
instances or examples. In statistics, we talk about observaWho Cares About Prototype Classifiers?
tions and (the dubious singular-plural) samples. These are
Who cares about prototype classifiers today? Hello, we have
all names for the same thing: x ! R n.
deep-learning neural networks. I hear this old question
n
repeated over and over. During the 1980s, we were ready to
X
1
R
.
We have a labeled reference set of prototypes,
dismiss the decision-tree classifier since we were building
Each prototype is an element of R n and labeled in one of
expert systems. Soon, we didn't care much about expert
c classes. A new data point x ) is labeled as its nearest
systems, either, because the almighty multilayer perceptron
prototype from the reference set X. This is the 1-NN
came to power. By the 1990s, we hailed the new king: the
classifier [2], [3], where the points in the reference set are
support-vector machine (SVM). And today? Today, we have
called prototypes.
deep-learning neural networks, and nothing else will do.
Delgado et al. [4] carried out a massive experimental
My Example Data
comparison
of classifiers in an attempt to answer the proI can hear Jim saying, "Pictures, Lucy. I like pictures!
vocative question: Do we need hundreds of classifiers to
Where are the pictures?" I like pictures, too, and here they
solve real-world classification problems? A staggering 179
come. Have you ever seen a picture of Jim when he wasn't
classifiers from 17 families were compared on 121 data
clutching, cuddling, or dangling a 5-kg-plus fish? You have?
sets. And the authors' answer was no. We don't need hunReally? Take another look; I bet there is a piranha printed
dreds of classifiers. The current favorites are the random
on his cap or T-shirt. Jim and fish ... it's something else. So,
forest [5] and SVM [6]. Long live the winners! The message
for my examples, I am choosing a 2D data set to suit the
from the conclusion of the paper is clear: "The remaining
theme [Figure 1 (a)]. Unusual, eh? Wherever did the good
families of classifiers, including other neural networks
old Gaussians go? Just for fun, I will call the fish George.

(a)

(b)

(c)

Figure 1. The George data set. The (a) full set, (b) sampled data, X (the prototypes), and (c) 1-NN regions using

X (6.68% error).

50	

IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE Apri l 2020



IEEE Systems, Man and Cybernetics Magazine - April 2020

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