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Novel types of convolution operators for quaternion linear canonical transform (QLCT) are proposed. Type one and two are defined in the spatial and QLCT spectral domains, respectively. They are distinct in the quaternion space and are…
The quadratic phase Fourier transform QPFT is a neoteric addition to the class of Fourier transforms and embodies a variety of signal processing tools including the Fourier, fractional Fourier, linear canonical, and special affine Fourier…
Modeling of multidimensional signal using tensor is more convincing than representing it as a collection of matrices. The tensor based approaches can explore the abundant spatial and temporal structures of the mutlidimensional signal. The…
The paper presents a new framework for complex Support Vector Regression as well as Support Vector Machines for quaternary classification. The method exploits the notion of widely linear estimation to model the input-out relation for…
The paper deals with the developing of the methodological backgrounds for the modeling and simulation of complex dynamical objects. Such backgrounds allow us to perform coordinate transformation and formulate the algorithm of its usage for…
Quantum computing is rapidly emerging as a new computing paradigm with the potential to improve decision-making, optimization, and simulation across industries. For industrial engineering (IE) and operations research (OR), this shift…
This paper proposes a novel matrix rank-one decomposition for quaternion Hermitian matrices, which admits a stronger property than the previous results in (sturm2003cones,huang2007complex,ai2011new). The enhanced property can be used to…
Transition amplitudes and transition probabilities are relevant to many areas of physics simulation, including the calculation of response properties and correlation functions. These quantities can also be related to solving linear systems…
Since 2004, researchers have been using the mathematical framework of Quantum Theory (QT) in Information Retrieval (IR). QT offers a generalized probability and logic framework. Such a framework has been shown capable of unifying the…
We construct the quaternion algebra [10] "geometrically" by a three dimensional analogue of the classic two dimensional geometric description of the complex field. The algebraic description of the multiplication operation in three…
Implementing general functions of operators is a powerful tool in quantum computation. It can be used as the basis for a variety of quantum algorithms including matrix inversion, real and imaginary-time evolution, and matrix powers. Quantum…
Scattered data fitting is a frequently encountered problem for reconstructing an unknown function from given scattered data. Radial basis function (RBF) methods have proven to be highly useful to deal with this problem. We describe two…
This Ph.D. thesis provides a comprehensive review of the state-of-the-art in the field of Variational Quantum Algorithms and Quantum Machine Learning, including numerous original contributions. The first chapters are devoted to a brief…
We discuss the relationship between quaternion algebras and quadratic forms with a focus on computational aspects. Our basic motivating problem is to determine if a given algebra of rank 4 over a commutative ring R embeds in the 2x2-matrix…
We show that the core reasons that complex and hypercomplex valued neural networks offer improvements over their real-valued counterparts is the weight sharing mechanism and treating multidimensional data as a single entity. Their algebra…
In this paper we introduce a new algebraic device, which enables us to treat the quaternions as though they were a commutative field. This is of interest both for its own sake, and because it can be applied to develop an "algebraic…
Machine learning algorithms learn a desired input-output relation from examples in order to interpret new inputs. This is important for tasks such as image and speech recognition or strategy optimisation, with growing applications in the IT…
Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process…
Financial forecasting has been an important and active area of machine learning research because of the challenges it presents and the potential rewards that even minor improvements in prediction accuracy or forecasting may entail.…
Artificial intelligence has made great strides in the last decade but still falls short of the human brain, the best-known example of intelligence. Not much is known of the neural processes that allow the brain to make the leap to achieve…