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Symmetric nonnegative matrix factorization (NMF), a special but important class of the general NMF, is demonstrated to be useful for data analysis and in particular for various clustering tasks. Unfortunately, designing fast algorithms for…
Nonnegative Matrix Factorization (NMF) is the problem of approximating a nonnegative matrix with the product of two low-rank nonnegative matrices and has been shown to be particularly useful in many applications, e.g., in text mining, image…
In this dissertation, we explore how quantum annealing (QA) and its applications behave in an open system setting. We give derivations and numerical recipes for effective parallel simulation methods for time-dependent open dynamics of…
To increase efficiency in automotive manufacturing, newly produced vehicles can move autonomously from the production line to the distribution area. This requires an optimal placement of sensors to ensure full coverage while minimizing the…
Finding the ground state of the Ising spin-glass is an important and challenging problem (NP-hard, in fact) in condensed matter physics. However, its applications spread far beyond physic due to its deep relation to various combinatorial…
The inversion of extremely high order matrices has been a challenging task because of the limited processing and memory capacity of conventional computers. In a scenario in which the data does not fit in memory, it is worth to consider…
The problem of decomposing a given covariance matrix as the sum of a positive semi-definite matrix of given rank and a positive semi-definite diagonal matrix, is considered. We present a projection-type algorithm to address this problem.…
Boolean matrix factorization (BMF) approximates a given binary input matrix as the product of two smaller binary factors. As opposed to binary matrix factorization which uses standard arithmetic, BMF uses the Boolean OR and Boolean AND…
The quest for real-time dynamic optimization solutions in the process industry represents a formidable computational challenge, particularly within the realm of applications like model-predictive control, where rapid and reliable…
We review here the recent success in quantum annealing, i.e., optimization of the cost or energy functions of complex systems utilizing quantum fluctuations. The concept is introduced in successive steps through the studies of mapping of…
We derive approximation algorithms for the nonnegative matrix factorization problem, i.e. the problem of factorizing a matrix as the product of two matrices with nonnegative coefficients. We form convex approximations of this problem which…
We construct an Ising Hamiltonian with an engineered energy landscape such that it has a local energy minimum which is near to the true global minimum solution, and further away from a false minimum. Using a technique established in…
The symmetric Nonnegative Matrix Factorization (NMF), a special but important class of the general NMF, has found numerous applications in data analysis such as various clustering tasks. Unfortunately, designing fast algorithms for the…
Protein folding is a central challenge in computational biology, with important applications in molecular biology, drug discovery and catalyst design. As a hard combinatorial optimisation problem, it has been studied as a potential target…
Principal component analysis is commonly used for dimensionality reduction, feature extraction, denoising, and visualization. The most commonly used principal component analysis method is based upon optimization of the L2-norm, however, the…
Critical decision-making issues in science, engineering, and industry are based on combinatorial optimization; however, its application is inherently limited by the NP-hard nature of the problem. A specialized paradigm of analogue quantum…
Nonnegative matrix factorization has been widely applied in face recognition, text mining, as well as spectral analysis. This paper proposes an alternating proximal gradient method for solving this problem. With a uniformly positive lower…
Using Quantum Computers to solve problems in Recommender Systems that classical computers cannot address is a worthwhile research topic. In this paper, we use Quantum Annealers to address the feature selection problem in recommendation…
We develop a quantum algorithm to solve combinatorial optimization problems through quantum simulation of a classical annealing process. Our algorithm combines techniques from quantum walks, quantum phase estimation, and quantum Zeno…
We present a matrix factorization algorithm that scales to input matrices that are large in both dimensions (i.e., that contains morethan 1TB of data). The algorithm streams the matrix columns while subsampling them, resulting in low…