Systems, Man & Cybernetics - April 2017 - 23

T

Coclustering of 2-D
and 3-D Data
Coclustering is often called
biclustering for two-dimen-
sional (2-D) data and triclustering for three-dimensional
(3-D) data [1]-[3]. Let us take
the data in Figure 1 as an
example. Our input is a large
matrix in Figure 1(a) that
appears to be just random
data. In fact, a subset of rows
and a subset of columns con-
tain a much smaller coherent
pattern. If we rearrange the
elements in the matrix so
that the rows and columns in
the pattern are placed in a
contiguous region, then we
will see the coherent pat-
tern in Fig ure  1(b). Our task
of co clustering here is to
find the locations or index-
es of these rows and columns
[Figure 1(c)].
This concept of coclus-
tering developed for 2-D
data can be extended to 3-D
and higher-dimensional data,
which are represented as
higher-order tensors. It is use-
ful to explain the terminology
we use here. In pattern recogni-
tion and machine learning, an
input sample represented by a fea-
ture vector is often considered as a
©iStockphoto/grandeduc

he analysis of a
multidimensional
data array is nec-
essary in many
applications. Al-
though a data set can be very
large, it is possible that mean-
ingful and coherent patterns
embedded in the data array
are much smaller in size. For
example, in genomic data, we
may want to find a subset of
genes that coexpress under a
subset of conditions. In this
article, I will explain coclus-
tering algorithms for solving
the coherent pattern-detection
problem. In these methods, a
coherent pattern cor responds
to a low-rank matrix or tensor
and can be represented as an
intersection of hyperplanes in
a high-dimensional space. We
can then extract coherent pat-
terns from the large data array
by detecting hyperplanes.
Examples will be provided to
demonstrate the effectiveness
of the coclustering algorithms
for solving unsupervised pat-
tern classification problems.

Digital Object Identifier 10.1109/MSMC.2017.2664218
Date of publication: 18 April 2017

Coclustering of
Multidimensional
Big Data
A Useful Tool for Genomic, Financial,
and Other Data Analysis
by Hong Yan
2333-942X/17©2017IEEE

Ap ri l 2017

IEEE SyStEmS, man, & CybErnEtICS magazInE

23



Table of Contents for the Digital Edition of Systems, Man & Cybernetics - April 2017

Systems, Man & Cybernetics - April 2017 - Cover1
Systems, Man & Cybernetics - April 2017 - Cover2
Systems, Man & Cybernetics - April 2017 - 1
Systems, Man & Cybernetics - April 2017 - 2
Systems, Man & Cybernetics - April 2017 - 3
Systems, Man & Cybernetics - April 2017 - 4
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Systems, Man & Cybernetics - April 2017 - 7
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Systems, Man & Cybernetics - April 2017 - 12
Systems, Man & Cybernetics - April 2017 - 13
Systems, Man & Cybernetics - April 2017 - 14
Systems, Man & Cybernetics - April 2017 - 15
Systems, Man & Cybernetics - April 2017 - 16
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Systems, Man & Cybernetics - April 2017 - 18
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Systems, Man & Cybernetics - April 2017 - 20
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Systems, Man & Cybernetics - April 2017 - 22
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Systems, Man & Cybernetics - April 2017 - 27
Systems, Man & Cybernetics - April 2017 - 28
Systems, Man & Cybernetics - April 2017 - 29
Systems, Man & Cybernetics - April 2017 - 30
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Systems, Man & Cybernetics - April 2017 - 40
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Systems, Man & Cybernetics - April 2017 - 42
Systems, Man & Cybernetics - April 2017 - 43
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Systems, Man & Cybernetics - April 2017 - Cover3
Systems, Man & Cybernetics - April 2017 - Cover4
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