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We develop novel algorithms and software on parallel computers for data clustering of large datasets. We are interested in applying our approach, e.g., for analysis of large datasets of microarrays or tiling arrays in molecular biology and for segmentation of high resolution images.

In [doi{10.1109/ICMEW.2014.6890711}], a~graph-based filtering of noisy images is performed by directly computing a projection of the image to be filtered onto a lower dimensional Krylov subspace of the graph Laplacian, constructed using non-negative graph weights determined by distances between image data corresponding to image pixels. We extend the construction of the graph Laplacian to the case, where some graph weights can be negative.

Graph-based spectral denoising is a low-pass filtering using the eigendecomposition of the graph Laplacian matrix of a noisy signal. Polynomial filtering avoids costly computation of the eigendecomposition by projections onto suitable Krylov subspaces. Polynomial filters can be based, e.g., on the bilateral and guided filters. We propose constructing accelerated polynomial filters by running flexible Krylov subspace based linear and eigenvalue solvers such as the Block Locally Optimal Preconditioned Conjugate Gradient (LOBPCG) method.