Descent methods for Nonnegative Matrix Factorization

In this paper, we present several descent methods that can be applied to nonnegative matrix factorization and we analyze a recently developped fast block coordinate method called Rank-one Residue Iteration (RRI). We also give a comparison of these different methods and show that the new block coordinate method has better properties in terms of approximation error and complexity. By interpreting this method as a rank-one approximation of the residue matrix, we prove that it \emph{converges} and also extend it to the nonnegative tensor factorization and introduce some variants of the method by imposing some additional controllable constraints such as: sparsity, discreteness and smoothness.Comment: 47 pages. New convergence proof using damped version of RRI. To appear in Numerical Linear Algebra in Signals, Systems and Control. Accepted. Illustrating Matlab code is included in the source bundl

Nature, Self, and Being in the World: Revealing a Flourishing Ethics in Landscape Architecture through Poignant Landscape Experiences

Poignant landscapes are gateways to our existential belongingness because they allow us to be moved by the world. Landscape architects have the potential to shape the worlds landscapes, as settings for poignant life experiences, and yet, an issue lies in the praxis of the profession. Contemporary landscape architecture and environmental ethics, as part of contemporary society, are enmeshed in binary narratives. Because interpretations of landscapes are inseparable from notions of nature, which hermeneutically carry existential stories of human-world relationships, when an enigmatic natural world was abandoned for the objectivity of biology and space, the worldview of landscapes also split into binary narratives of human versus nature, sacred versus profane, and poetic versus practical. Moreover, with the expansion of secularism and nondualist cosmologies such as Daoism and Indigenous teachings into the Western world, polarised moral judgements, which are loosely based on past Christian narratives, become paradoxical and unsupportive towards resolving contemporary social and ecological disputes. Therefore, this project argues for an approach to ethics based on the idea of flourishing, which sees morality as relational and that ethical individuals make autonomous choices to flourish within a world of social and ecological systems. To return to the roots of being, this research asks landscape architects what a flourishing life and a flourishing environment really means to them. Poignant experiences with landscapes are used to provoke memory and awareness of being in the world and the sense of connectivity with other existences in the human, ecological, or spiritual worlds. Through the analysis of professional codes and mandates, a survey of landscape architects, and interviews with flourishing landscape architects, the research explores how the landscape architect, as a professional identity and as an archetype in the collective consciousness, is interpreted, performed, and communicated in landscape architecture. A hermeneutic approach was used to unravel concepts of nature, landscape, experience, poignancy, and ethical choice-making. The analysis reveals that a reflexive process that is simultaneously personal and collective can increase experiential awareness, expand horizons for meanings, and create opportunities for shifting paradigms essential to achieving a sense of human belongingness in the world

Generalized diffusion theory of hydrodynamical particle migration in suspensions. Part 1: The case of equal densities

The general continuum theory has been developed for two-phase flows of fluid with deformable particles, where the micro-deformation of particles and the relative motion between phases have been taken into account [1-3]. This paper is concerned with using the simplest model from developed general theory for modeling of particle migration in suspensions- one of the most important and complicated aspects of particle-liquid two-phase flows, that has been observed and studied by many authors. For this purpose it is considered the motion of Newtonian fluid-rotating rigid spherical particles two-phase continuum with specialized nonlinear constitutive equations, when the particle and fluid have equal densities. The obtained equation system has been used for studying quantitatively particle migration problem in the circular Couette flow