31 research outputs found
Diffusion map for clustering fMRI spatial maps extracted by independent component analysis
Functional magnetic resonance imaging (fMRI) produces data about activity
inside the brain, from which spatial maps can be extracted by independent
component analysis (ICA). In datasets, there are n spatial maps that contain p
voxels. The number of voxels is very high compared to the number of analyzed
spatial maps. Clustering of the spatial maps is usually based on correlation
matrices. This usually works well, although such a similarity matrix inherently
can explain only a certain amount of the total variance contained in the
high-dimensional data where n is relatively small but p is large. For
high-dimensional space, it is reasonable to perform dimensionality reduction
before clustering. In this research, we used the recently developed diffusion
map for dimensionality reduction in conjunction with spectral clustering. This
research revealed that the diffusion map based clustering worked as well as the
more traditional methods, and produced more compact clusters when needed.Comment: 6 pages. 8 figures. Copyright (c) 2013 IEEE. Published at 2013 IEEE
International Workshop on Machine Learning for Signal Processin
Hearing the clusters in a graph: A distributed algorithm
We propose a novel distributed algorithm to cluster graphs. The algorithm
recovers the solution obtained from spectral clustering without the need for
expensive eigenvalue/vector computations. We prove that, by propagating waves
through the graph, a local fast Fourier transform yields the local component of
every eigenvector of the Laplacian matrix, thus providing clustering
information. For large graphs, the proposed algorithm is orders of magnitude
faster than random walk based approaches. We prove the equivalence of the
proposed algorithm to spectral clustering and derive convergence rates. We
demonstrate the benefit of using this decentralized clustering algorithm for
community detection in social graphs, accelerating distributed estimation in
sensor networks and efficient computation of distributed multi-agent search
strategies
Mapping the conformations of biological assemblies
Mapping conformational heterogeneity of macromolecules presents a formidable
challenge to X-ray crystallography and cryo-electron microscopy, which often
presume its absence. This has severely limited our knowledge of the
conformations assumed by biological systems and their role in biological
function, even though they are known to be important. We propose a new approach
to determining to high resolution the three-dimensional conformations of
biological entities such as molecules, macromolecular assemblies, and
ultimately cells, with existing and emerging experimental techniques. This
approach may also enable one to circumvent current limits due to radiation
damage and solution purification.Comment: 14 pages, 6 figure
Estimating View Parameters From Random Projections for Tomography Using Spherical MDS
Background
During the past decade, the computed tomography has been successfully applied to various fields especially in medicine. The estimation of view angles for projections is necessary in some special applications of tomography, for example, the structuring of viruses using electron microscopy and the compensation of the patient\u27s motion over long scanning period. Methods
This work introduces a novel approach, based on the spherical multidimensional scaling (sMDS), which transforms the problem of the angle estimation to a sphere constrained embedding problem. The proposed approach views each projection as a high dimensional vector with dimensionality equal to the number of sampling points on the projection. By using SMDS, then each projection vector is embedded onto a 1D sphere which parameterizes the projection with respect to view angles in a globally consistent manner. The parameterized projections are used for the final reconstruction of the image through the inverse radon transform. The entire reconstruction process is non-iterative and computationally efficient. Results
The effectiveness of the sMDS is verified with various experiments, including the evaluation of the reconstruction quality from different number of projections and resistance to different noise levels. The experimental results demonstrate the efficiency of the proposed method. Conclusion
Our study provides an effective technique for the solution of 2D tomography with unknown acquisition view angles. The proposed method will be extended to three dimensional reconstructions in our future work. All materials, including source code and demos, are available onhttps://engineering.purdue.edu/PRECISE/SMDS