Graphics Reference
In-Depth Information
Introduction
15.1
he graphical exploration of quantitative/qualitative data is an initial but essential
stepinmodernstatistical data analysis. Matrixvisualization (Chen,
;Chenetal.,
) is a graphical technique that can simultaneously explore the associations be-
tween thousands of subjects, variables, and their interactions, without needing to
first reduce the dimensions of the data. Matrix visualization involves permuting the
rows and columns of the raw data matrix using suitable seriation (reordering) algo-
rithms, together with the corresponding proximity matrices. he permuted rawdata
matrix and two proximity matrices are then displayed as matrix maps via suitable
color spectra, and the subject clusters, variable groups, and interactions embedded
in the dataset can be extracted visually.
Since the introduction of exploratory data analysis (EDA, Tukey,
), boxplots
andscatterplots, aidedbyinteractive functionality, haveprovidedthe statistical com-
munity with important graphical tools.hesetools,together with various techniques
forreducingdimensions, areusefulforexploring thestructureofthedata whenthere
areamoderatenumber ofvariables andwhenthestructureisnottoocomplex. How-
ever, with the recent rapid advances in computing, communications technology, and
high-throughput biomedical instruments, the number of variables associated with
the dataset can easily reach tens of thousands, but the need for practical data anal-
ysis remains. Dimension reduction tools oten become less effective when applied
to the visual exploration of information structures embedded in high-dimensional
datasets. On the other hand, matrix visualization, when integrated with computing,
memory, and display technologies, has the potential to enable us to visually explore
the structures that underlie massive and complex datasets.
his chapter on matrix visualization unfolds as follows. We briefly review studies
in this field in the next section. he foundation of matrix visualization, under the
framework of generalized association plots (GAP, Chen,
), is then discussed in
Sect.
.
,alongwithsomerelatedissues.hisisfollowed,inSect.
.
,bysomegener-
alization. Section
provides a matrix visualization examples involving
variables
(arrays) and
samples (genes). A comparison of matrix visualization with other
popular graphical tools in terms of e
ciency versus number of dimensions is then
given in Sect.
.
. Section
.
illustrates matrix visualization for binary data, while
Sect.
.
discusses generalizations and extensions. We conclude this chapter with
some perspectives on matrix visualization in Sect.
.
.
Related Works
15.2
he concept of matrix visualization was introduced by Bertin (
)as a reorderable
matrix for systematically presenting data structures and relationships. Carmichael
andSneath (
)developedtaxometric mapsforclassifying OUTs (operational tax-
onomy units) in numerical phenetics analysis. Hartigan (
) introduced the direct
clusteringofadatamatrix,laterknownasblockclustering(Tibshirani,
).Lenstra
