627 research outputs found
Tensor Analysis and Fusion of Multimodal Brain Images
Current high-throughput data acquisition technologies probe dynamical systems
with different imaging modalities, generating massive data sets at different
spatial and temporal resolutions posing challenging problems in multimodal data
fusion. A case in point is the attempt to parse out the brain structures and
networks that underpin human cognitive processes by analysis of different
neuroimaging modalities (functional MRI, EEG, NIRS etc.). We emphasize that the
multimodal, multi-scale nature of neuroimaging data is well reflected by a
multi-way (tensor) structure where the underlying processes can be summarized
by a relatively small number of components or "atoms". We introduce
Markov-Penrose diagrams - an integration of Bayesian DAG and tensor network
notation in order to analyze these models. These diagrams not only clarify
matrix and tensor EEG and fMRI time/frequency analysis and inverse problems,
but also help understand multimodal fusion via Multiway Partial Least Squares
and Coupled Matrix-Tensor Factorization. We show here, for the first time, that
Granger causal analysis of brain networks is a tensor regression problem, thus
allowing the atomic decomposition of brain networks. Analysis of EEG and fMRI
recordings shows the potential of the methods and suggests their use in other
scientific domains.Comment: 23 pages, 15 figures, submitted to Proceedings of the IEE
Preconditioning Kernel Matrices
The computational and storage complexity of kernel machines presents the
primary barrier to their scaling to large, modern, datasets. A common way to
tackle the scalability issue is to use the conjugate gradient algorithm, which
relieves the constraints on both storage (the kernel matrix need not be stored)
and computation (both stochastic gradients and parallelization can be used).
Even so, conjugate gradient is not without its own issues: the conditioning of
kernel matrices is often such that conjugate gradients will have poor
convergence in practice. Preconditioning is a common approach to alleviating
this issue. Here we propose preconditioned conjugate gradients for kernel
machines, and develop a broad range of preconditioners particularly useful for
kernel matrices. We describe a scalable approach to both solving kernel
machines and learning their hyperparameters. We show this approach is exact in
the limit of iterations and outperforms state-of-the-art approximations for a
given computational budget
Multipolar Acoustic Source Reconstruction from Sparse Far-Field Data using ALOHA
The reconstruction of multipolar acoustic or electromagnetic sources from
their far-field signature plays a crucial role in numerous applications. Most
of the existing techniques require dense multi-frequency data at the Nyquist
sampling rate. The availability of a sub-sampled grid contributes to the null
space of the inverse source-to-data operator, which causes significant imaging
artifacts. For this purpose, additional knowledge about the source or
regularization is required. In this letter, we propose a novel two-stage
strategy for multipolar source reconstruction from sub-sampled sparse data that
takes advantage of the sparsity of the sources in the physical domain. The data
at the Nyquist sampling rate is recovered from sub-sampled data and then a
conventional inversion algorithm is used to reconstruct sources. The data
recovery problem is linked to a spectrum recovery problem for the signal with
the \textit{finite rate of innovations} (FIR) that is solved using an
annihilating filter-based structured Hankel matrix completion approach (ALOHA).
For an accurate reconstruction, a Fourier inversion algorithm is used. The
suitability of the approach is supported by experiments.Comment: 11 pages, 2 figure
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