155 research outputs found
Hypercomplex algebras for dictionary learning
This paper presents an application of hypercomplex algebras combined with dictionary learning for sparse representation of multichannel images. Two main representatives of hypercomplex algebras, Clifford algebras and algebras generated by the Cayley-Dickson procedure are considered. Related works reported quaternion methods (for color images) and octonion methods, which are applicable to images with up to 7 channels. We show that the current constructions cannot be generalized to dimensions above eight
Multimodal Computational Attention for Scene Understanding
Robotic systems have limited computational capacities. Hence, computational attention models are important to focus on specific stimuli and allow for complex cognitive processing. For this purpose, we developed auditory and visual attention models that enable robotic platforms to efficiently explore and analyze natural scenes. To allow for attention guidance in human-robot interaction, we use machine learning to integrate the influence of verbal and non-verbal social signals into our models
A Two-Sided Quaternion Higher-Order Singular Value Decomposition
Higher-order singular value decomposition (HOSVD) is one of the most
celebrated tensor decompositions that generalizes matrix SVD to higher-order
tensors. It was recently extended to the quaternion domain \cite{miao2023quat}
(we refer to it as L-QHOSVD in this work). However, due to the
non-commutativity of quaternion multiplications, L-QHOSVD is not consistent
with matrix SVD when the order of the quaternion tensor reduces to ;
moreover, theoretical guaranteed truncated L-QHOSVD was not investigated. To
derive a more natural higher-order generalization of the quaternion matrix SVD,
we first utilize the feature that left and right multiplications of quaternions
are inconsistent to define left and right quaternion tensor unfoldings and left
and right mode- products. Then, by using these basic tools, we propose a
two-sided quaternion higher-order singular value decomposition (TS-QHOSVD).
TS-QHOSVD has the following two main features: 1) it computes two factor
matrices at a time from SVDs of left and right unfoldings, inheriting certain
parallel properties of the original HOSVD; 2) it is consistent with matrix SVD
when the order of the tensor is . In addition, we study truncated TS-QHOSVD
and establish its error bound measured by the tail energy; correspondingly, we
also present truncated L-QHOSVD and its error bound. Deriving the error bounds
is nontrivial, as the proofs are more complicated than their real counterparts,
again due to the non-commutativity of quaternion multiplications. %Numerical
experiments on synthetic and color video data show the efficacy of the proposed
TS-QHOSVD. Finally, we illustrate the derived properties of TS-QHOSVD and its
efficacy via some numerical examples
Global exponential synchronization of quaternion-valued memristive neural networks with time delays
This paper extends the memristive neural networks (MNNs) to quaternion field, a new class of neural networks named quaternion-valued memristive neural networks (QVMNNs) is then established, and the problem of drive-response global synchronization of this type of networks is investigated in this paper. Two cases are taken into consideration: one is with the conventional differential inclusion assumption, the other without. Criteria for the global synchronization of these two cases are achieved respectively by appropriately choosing the Lyapunov functional and applying some inequality techniques. Finally, corresponding simulation examples are presented to demonstrate the correctness of the proposed results derived in this paper
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