4,319 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
A literature survey of low-rank tensor approximation techniques
During the last years, low-rank tensor approximation has been established as
a new tool in scientific computing to address large-scale linear and
multilinear algebra problems, which would be intractable by classical
techniques. This survey attempts to give a literature overview of current
developments in this area, with an emphasis on function-related tensors
Multilinear Time Invariant System Theory
In biological and engineering systems, structure, function and dynamics are
highly coupled. Such interactions can be naturally and compactly captured via
tensor based state space dynamic representations. However, such representations
are not amenable to the standard system and controls framework which requires
the state to be in the form of a vector. In order to address this limitation,
recently a new class of multiway dynamical systems has been introduced in which
the states, inputs and outputs are tensors. We propose a new form of
multilinear time invariant (MLTI) systems based on the Einstein product and
even-order paired tensors. We extend classical linear time invariant (LTI)
system notions including stability, reachability and observability for the new
MLTI system representation by leveraging recent advances in tensor algebra.Comment: 8 pages, SIAM Conference on Control and its Applications 2019,
accepted to appea
- …