Graphics Reference
In-Depth Information
(
) and Slagle et al. (
) related the traveling salesman and shortest spanning
pathproblemstotheclusteringofdataarrays.hecolorhistogramofWegman(
)
wasthefirstcolormatrixvisualization tobereportedinthestatistical literature.Min-
notte and West (
) extended the idea of color histograms to a data image package
that was later used for outlier detection (Marchette and Solka,
).
Some matrix visualization techniques were developed to explore only proximity
matrices: Ling (
) looked for factors of variables by examining relationships us-
ing a shaded correlation matrix; Murdoch and Chow (
) used elliptical glyphs to
represent large correlation matrices; Friendly (
)proposed corrgrams (similar to
the reorderable matrix method) to analyze multivariate structure among the vari-
ables in correlation and covariance matrices. Chen (
,
,and
) integrated
the visualization of a raw data matrix with two proximity matrices (for variables and
samples) into theframeworkofgeneralized association plots(GAP).heCluster and
TreeView packagesofEisen etal.(
)areprobably the mostpopularmatrix visual-
ization packages due to the proliferation of gene expression profiling for microarray
experiments.
he permutation (ordering) of the columns and rows of a data matrix, and prox-
imity matrices for variables and samples, is an essential step in matrix visualization.
Several recent statistical works have touched on the issue of reordering variables and
samples: Chen (
) proposed the concept of the relativity of a statistical graph;
FriendlyandKwan (
)discussedthe ideaofeffect-ordering ofdata displays;Hur-
ley(
)used scatterplot matrices and parallel coordinates plots as examples to ad-
dressthe issueof placing interesting displays inprominent positions. Different terms
(such as the reorderable matrix, the heatmap, the color histogram, the data image
and matrix visualization) have been used in the literature to describe these related
techniques. We use matrix visualization (MV) to refer to them all.
The Basic Principles
of Matrix Visualization
15.3
We use the GAP (Chen,
) approach to illustrate the basic principles of matrix
visualization for continuous data, using the
genes and
microarray exper-
iments collected in the published yeast expression database for visualization and
data mining (Marc et al.,
), which is designated henceforth as Dataset
. De-
tailed descriptions of data preprocessing are given for the yeast Microarray Global
Viewer(http://transcriptome.ens.fr/ymgv/). Forthepurposesofillustration, wehave
selected
samples and
genes across these samples (“Dataset
”), where rows cor-
respond to genes and columns to microarray experiments (arrays). In various gene
expression profile analyses, the roles played by rows and columns are oten inter-
changeable. his interchangeability is well suited to the GAP approach to matrix vi-
sualization, where samples and variables are treated symmetrically and can be inter-
changed directly.
