Biology Reference
In-Depth Information
where k is the number of clusters, n
i
is the number of members in the i-th
clust
e
r, y
imj
is the j-th coordinate of the m-th member of the i-th cluster,
and y
ij
is the j-th coordinate of the center of the i-th cluster. In general,
smaller values of D
AV
and S indicate more strongly expressed clustering
within groups.
A variation of the classical K-Means algorithm uses the quantity from
Eq. (12-8) to reassign data points to clusters in ways that decrease the
value of S. The algorithm terminates when two different iterations return
essentially the same value for S within a small tolerance. Another
variation applies the K-Means method multiple times with different
randomly selected initial cluster centers from the data. The final
clustering is chosen to have the smallest within-cluster sum of
squares, S.
Clustering procedures are included in a variety of commercial and
noncommercial computer software packages. We encourage you to use
Michael Eisen's Cluster and Tree View programs (Eisen et al. [1998]) to
examine the diffuse large B-cell lymphoma (DLBCL) data (available on
his Web site; see Internet Resources at the end of this chapter). This
should allow you to duplicate the result reported in Alizadeh et al.
(2000), identifying two types of B-cell lymphoma: germinal center B-like
DLBCL and activated B-like DLBCL. In Figure 12-13, we reproduce one
of the diagrams reported in the paper that includes both row and
column clustering.
VI. MICROARRAYS AND CIRCADIAN RHYTHMS
A. Introduction
In Chapter 11, we discussed some of the genetic mechanisms of
circadian rhythms that are expressed at the level of the whole organism
and in diverse organs, tissues, and cells. Some of the genes involved
have been identified, but we would like to discover what other genes are
expressed in a circadian manner. With microarray technologies, we no
longer need to confine our molecular investigations to the period gene or
the other known genes, such as tim, clock, or cycle. Now we can look at
the gene expression patterning of many hundreds or thousands of genes
simultaneously and explore in greater detail an organism's system of
temporal regulation and control of circadian patterns.
Many gene expression studies
6
have contributed to our current
understanding of the molecular basis of circadian clocks and how the
oscillators in different tissues and organs may be coordinated. The
eventual goals of such studies are to develop an accurate systems-level
6. Reviewed in Reppert and Weaver (2002), Richter et al. (2004), and
Bell-Pedersen et al. (2005).
