805 research outputs found
Overview of Constrained PARAFAC Models
In this paper, we present an overview of constrained PARAFAC models where the
constraints model linear dependencies among columns of the factor matrices of
the tensor decomposition, or alternatively, the pattern of interactions between
different modes of the tensor which are captured by the equivalent core tensor.
Some tensor prerequisites with a particular emphasis on mode combination using
Kronecker products of canonical vectors that makes easier matricization
operations, are first introduced. This Kronecker product based approach is also
formulated in terms of the index notation, which provides an original and
concise formalism for both matricizing tensors and writing tensor models. Then,
after a brief reminder of PARAFAC and Tucker models, two families of
constrained tensor models, the co-called PARALIND/CONFAC and PARATUCK models,
are described in a unified framework, for order tensors. New tensor
models, called nested Tucker models and block PARALIND/CONFAC models, are also
introduced. A link between PARATUCK models and constrained PARAFAC models is
then established. Finally, new uniqueness properties of PARATUCK models are
deduced from sufficient conditions for essential uniqueness of their associated
constrained PARAFAC models
60 GHz Blockage Study Using Phased Arrays
The millimeter wave (mmWave) frequencies offer the potential for enormous
capacity wireless links. However, designing robust communication systems at
these frequencies requires that we understand the channel dynamics over both
time and space: mmWave signals are extremely vulnerable to blocking and the
channel can thus rapidly appear and disappear with small movement of obstacles
and reflectors. In rich scattering environments, different paths may experience
different blocking trajectories and understanding these multi-path blocking
dynamics is essential for developing and assessing beamforming and
beam-tracking algorithms. This paper presents the design and experimental
results of a novel measurement system which uses phased arrays to perform
mmWave dynamic channel measurements. Specifically, human blockage and its
effects across multiple paths are investigated with only several microseconds
between successive measurements. From these measurements we develop a modeling
technique which uses low-rank tensor factorization to separate the available
paths so that their joint statistics can be understood.Comment: To appear in the Proceedings of the 51st Asilomar Conference on
Signals, Systems, and Computers, 201
Blind Multiclass Ensemble Classification
The rising interest in pattern recognition and data analytics has spurred the
development of innovative machine learning algorithms and tools. However, as
each algorithm has its strengths and limitations, one is motivated to
judiciously fuse multiple algorithms in order to find the "best" performing
one, for a given dataset. Ensemble learning aims at such high-performance
meta-algorithm, by combining the outputs from multiple algorithms. The present
work introduces a blind scheme for learning from ensembles of classifiers,
using a moment matching method that leverages joint tensor and matrix
factorization. Blind refers to the combiner who has no knowledge of the
ground-truth labels that each classifier has been trained on. A rigorous
performance analysis is derived and the proposed scheme is evaluated on
synthetic and real datasets.Comment: To appear in IEEE Transactions in Signal Processin
Joint Tensor Factorization and Outlying Slab Suppression with Applications
We consider factoring low-rank tensors in the presence of outlying slabs.
This problem is important in practice, because data collected in many
real-world applications, such as speech, fluorescence, and some social network
data, fit this paradigm. Prior work tackles this problem by iteratively
selecting a fixed number of slabs and fitting, a procedure which may not
converge. We formulate this problem from a group-sparsity promoting point of
view, and propose an alternating optimization framework to handle the
corresponding () minimization-based low-rank tensor
factorization problem. The proposed algorithm features a similar per-iteration
complexity as the plain trilinear alternating least squares (TALS) algorithm.
Convergence of the proposed algorithm is also easy to analyze under the
framework of alternating optimization and its variants. In addition,
regularization and constraints can be easily incorporated to make use of
\emph{a priori} information on the latent loading factors. Simulations and real
data experiments on blind speech separation, fluorescence data analysis, and
social network mining are used to showcase the effectiveness of the proposed
algorithm
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
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