27 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
Distributed PARAFAC based DS-CDMA blind receiver for wireless sensor networks
International audienceIn this paper, we consider a collaborative scheme in wireless sensor networks where the multiple access protocol is a DS-CDMA one. When the receiver is equipped with an antenna array, it has been shown that efficient blind receivers can be derived using the PARAFAC tensor model. In general, the parameters of the PARAFAC model are fitted using an alternating least squares algorithm. Herein, we consider the case where each receiver has a single antenna. Therefore, by allowing collaboration in a predefined neighborhood, we derive a distributed alternating least squares algorithm including some average consensus steps
Non-iterative solution for PARAFAC with a Toeplitz matrix factor
International audienceRecently, tensor signal processing has received an increased attention, particularly in the context of wireless communication applications. The so-called PARAllel FACtor (PARAFAC) decomposition is certainly the most used tensor tool. In general, the parameter estimation of a PARAFAC decomposition is carried out by means of the iterative ALS algorithm, which exhibits the following main drawbacks: convergence towards local minima, a high number of iterations for convergence, and difficulty to take, optimally, special matrix structures into account. In this paper, we propose a non-iterative parameter estimation method for a PARAFAC decomposition when one matrix factor has a Toeplitz structure, a situation that is commonly encountered in signal processing applications. We illustrate the proposed method by means of simulation results
Rank-1 Tensor Approximation Methods and Application to Deflation
Because of the attractiveness of the canonical polyadic (CP) tensor
decomposition in various applications, several algorithms have been designed to
compute it, but efficient ones are still lacking. Iterative deflation
algorithms based on successive rank-1 approximations can be used to perform
this task, since the latter are rather easy to compute. We first present an
algebraic rank-1 approximation method that performs better than the standard
higher-order singular value decomposition (HOSVD) for three-way tensors.
Second, we propose a new iterative rank-1 approximation algorithm that improves
any other rank-1 approximation method. Third, we describe a probabilistic
framework allowing to study the convergence of deflation CP decomposition
(DCPD) algorithms based on successive rank-1 approximations. A set of computer
experiments then validates theoretical results and demonstrates the efficiency
of DCPD algorithms compared to other ones