  In the context of cancer, internal "checkerboard" structures are normally
found in the matrices of gene expression data, which correspond to genes that
are significantly up- or down-regulated in patients with specific types of
tumors. In this paper, we propose a novel method, called dual
graph-regularization principal component analysis (DGPCA). The main innovation
of this method is that it simultaneously considers the internal geometric
structures of the condition manifold and the gene manifold. Specifically, we
obtain principal components (PCs) to represent the data and approximate the
cluster membership indicators through Laplacian embedding. This new method is
endowed with internal geometric structures, such as the condition manifold and
gene manifold, which are both suitable for bi-clustering. A closed-form
solution is provided for DGPCA. We apply this new method to simultaneously
cluster genes and conditions (e.g., different samples) with the aim of finding
internal "checkerboard" structures on gene expression data, if they exist.
Then, we use this new method to identify regulatory genes under the particular
conditions and to compare the results with those of other state-of-the-art
PCA-based methods. Promising results on gene expression data have been verified
by extensive experiments
