Relative Pairwise Relationship Constrained Non-negative Matrix Factorisation

Non-negative Matrix Factorisation (NMF) has been extensively used in machine learning and data analytics applications. Most existing variations of NMF only consider how each row/column vector of factorised matrices should be shaped, and ignore the relationship among pairwise rows or columns. In many cases, such pairwise relationship enables better factorisation, for example, image clustering and recommender systems. In this paper, we propose an algorithm named, Relative Pairwise Relationship constrained Non-negative Matrix Factorisation (RPR-NMF), which places constraints over relative pairwise distances amongst features by imposing penalties in a triplet form. Two distance measures, squared Euclidean distance and Symmetric divergence, are used, and exponential and hinge loss penalties are adopted for the two measures respectively. It is well known that the so-called "multiplicative update rules" result in a much faster convergence than gradient descend for matrix factorisation. However, applying such update rules to RPR-NMF and also proving its convergence is not straightforward. Thus, we use reasonable approximations to relax the complexity brought by the penalties, which are practically verified. Experiments on both synthetic datasets and real datasets demonstrate that our algorithms have advantages on gaining close approximation, satisfying a high proportion of expected constraints, and achieving superior performance compared with other algorithms.Comment: 13 pages, 10 figure

Distributionally Robust Optimization

This chapter presents a class of distributionally robust optimization problems in which a decision-maker has to choose an action in an uncertain environment. The decision-maker has a continuous action space and aims to learn her optimal strategy. The true distribution of the uncertainty is unknown to the decision-maker. This chapter provides alternative ways to select a distribution based on empirical observations of the decision-maker. This leads to a distributionally robust optimization problem. Simple algorithms, whose dynamics are inspired from the gradient flows, are proposed to find local optima. The method is extended to a class of optimization problems with orthogonal constraints and coupled constraints over the simplex set and polytopes. The designed dynamics do not use the projection operator and are able to satisfy both upper- and lower-bound constraints. The convergence rate of the algorithm to generalized evolutionarily stable strategy is derived using a mean regret estimate. Illustrative examples are provided

Recent strategies for constructing efficient interfacial solar evaporation systems

Interfacial solar evaporation (ISE) is a promising technology to relieve worldwide freshwater shortages owing to its high energy conversion efficiency and environmentally sustainable potential. So far, many innovative materials and evaporators have been proposed and applied in ISE to enable highly controllable and efficient solar-to-thermal energy conversion. With rational design, solar evaporators can achieve excellent energy management for lowering energy loss, harvesting extra energy, and efficiently utilizing energy in the system to improve freshwater production. Beyond that, a strategy of reducing water vaporization enthalpy by introducing molecular engineering for water-state regulation has also been demonstrated as an effective approach to boost ISE. Based on these, this article discusses the energy nexus in two-dimensional (2D) and three-dimensional (3D) evaporators separately and reviews the strategies for design and fabrication of highly efficient ISE systems. The summarized work offers significant perspectives for guiding the future design of ISE systems with efficient energy management, which pave pathways for practical applications