Myeloid Leukemia

232 Kohlmann et al.
unsupervised data analyses, a variation filter can be applied. This filter aims at
removing probe sets that demonstrate minimal variation across the complete
data set. Practically, for each gene the standard variance is calculated across all
samples. Then the data matrix is sorted according to the standard variances,
and probes demonstrating a low variance are excluded from the subsequent
analysis. Hierarchical clustering is the method of choice when one has little or
no a priori knowledge of the complete repertoire of expected gene expression
patterns. However, no information about the statistical significance is provided.
In contrast, using hierarchical clustering in a supervised approach helps to visualize
differential gene expression of an already preselected set of genes.
3.4.4. Principal Component Analysis
The need to visualize large amounts of data in many dimensions occurs frequently
in bioinformatics. Commonly, principal component analysis (PCA) is
used in statistics to extract the main relationships in data of high dimensionality
(15). It is a useful tool for categorization of multidimensional data such as
gene expression studies, because it separates the dominating features in the
data set. The background mathematical technique used in PCA is called eigen
analysis. PCA reduces the dimensionality of the data set while retaining most
of the information contained therein via the construction of a linear transformation
matrix. This transformation matrix is composed of the most significant
eigenvectors of the covariance matrix of the input matrix of feature vectors.
The principal components (PC) are the projections of the data on the eigenvectors.
These vectors give the directions in which the data cloud is stretched most.
The significance of an eigenvector is defined by its variance, which is equivalent
to its corresponding eigenvalue. Eigenvalues give an indication of the
amount of information the respective PC represent. PCs corresponding to large
eigenvalues represent much information in the data set, and thus can tell much
about the relations between the data points. Because the original data’s variation
can be retained and explained by a smaller number of transformed variables,
a PCA projects the data into a new two- or three-dimensional space and
may provide valuable insight into the data (Fig. 4).
Fig. 4. (opposite page) Principal component analysis workflow. The multi-dimensional
data are reduced by transformation to a new set of variables, the principle components
(PCs). The traditional approach is to use the first few PCs, because they
capture most of the variation in the original data. In the final graph, data points with
similar characteristics will cluster together. Each patient’s expression pattern is represented
by a color-coded sphere.