Graphics Reference
In-Depth Information
Symmetric and Asymmetric Binary Variables
A binary variable is considered symmetric if both of its states are equally valuable;
that is,there isnopreferenceoverwhichoutcome shouldbecodedas
or
.Abinary
variable isasymmetric iftheoutcomesofthestates arenotequally important, suchas
the positive and negative outcomes of a disease diagnosis. Conventionally, the most
important outcome (the rarer one) is coded
, the other
. hus, asymmetric binary
variables are oten considered “monary” (as if there is only one state).
Sparseness and Dimensionality
Asymmetric binary variables are usually sparse in nature, and it is di
cult to iden-
tify an appropriate association measure that could be used to assess the relationships
among samples and between variables. Dimension reduction techniques also fail in
attempts to summarize high-dimensional data structures in low-dimensional fash-
ions. Listed in Fig.
.
are some similarity measures commonly applied to binary
data. For sparse data, it is common practice to use the Jaccard coe
cient instead of
the simple matching coe
cient.
Figure
.
.
Some similarity measures for binary data
