Sparse Coding on Symmetric Positive Definite Manifolds using Bregman Divergences

This paper introduces sparse coding and dictionary learning for Symmetric Positive Definite (SPD) matrices, which are often used in machine learning, computer vision and related areas. Unlike traditional sparse coding schemes that work in vector spaces, in this paper we discuss how SPD matrices can be described by sparse combination of dictionary atoms, where the atoms are also SPD matrices. We propose to seek sparse coding by embedding the space of SPD matrices into Hilbert spaces through two types of Bregman matrix divergences. This not only leads to an efficient way of performing sparse coding, but also an online and iterative scheme for dictionary learning. We apply the proposed methods to several computer vision tasks where images are represented by region covariance matrices. Our proposed algorithms outperform state-of-the-art methods on a wide range of classification tasks, including face recognition, action recognition, material classification and texture categorization

Halo Substructure and the Nature of Dark Matter

The ΛCDM paradigm has been very successful at predicting the properties of the large scale (> 10Mpc) Universe, but has recently struggled to explain phenomena observed on small scales, such as the central densities, abundances, and orbital configurations of satellite galaxies. This emergence of tension between observations and theory has co- incided with CERN measurements that disfavour the simplest supersymmetric models, which provide some of the most popular cold dark matter candidate particles. One pos- sible solution to some of these problems is that the dark matter may instead be made up of sterile neutrinos: these particles would have masses of 1-10keV and behave as ’warm’ dark matter (WDM), with consequences for the formation of galaxies. In this thesis we use high resolution simulations of Milky Way-analogue dark matter haloes to examine the role of filaments on satellite orbits and WDM on satellite abundance and structure. We find in the former case that dark matter filaments can funnel subhaloes into cor- related orbits and so ease the tension with observations. We also find that WDM is a possible solution to the problem of satellite galaxy densities, since structure formation is delayed in WDM and thus the centres of haloes form when the density of the Universe is lower. In order to generate the required number of satellite galaxies, we find that the WDM thermal-equivalent particle mass > 1.6keV. In addition to the work on satellite galaxies, we use a series of gas-hydrodynamic simulations of our Milky Way-analogue halo to examine the process of reionisation in WDM. We find that the suppression of small scale structure in the 1.4keV WDM model prevents the simulated L∗ galaxy, along with its satellites, from reionising its own local volume quickly enough to satisfy the reionisation redshift constraint set by the recent Planck satellite results, in contrast to CDM

Extrinsic Methods for Coding and Dictionary Learning on Grassmann Manifolds

Sparsity-based representations have recently led to notable results in various visual recognition tasks. In a separate line of research, Riemannian manifolds have been shown useful for dealing with features and models that do not lie in Euclidean spaces. With the aim of building a bridge between the two realms, we address the problem of sparse coding and dictionary learning over the space of linear subspaces, which form Riemannian structures known as Grassmann manifolds. To this end, we propose to embed Grassmann manifolds into the space of symmetric matrices by an isometric mapping. This in turn enables us to extend two sparse coding schemes to Grassmann manifolds. Furthermore, we propose closed-form solutions for learning a Grassmann dictionary, atom by atom. Lastly, to handle non-linearity in data, we extend the proposed Grassmann sparse coding and dictionary learning algorithms through embedding into Hilbert spaces. Experiments on several classification tasks (gender recognition, gesture classification, scene analysis, face recognition, action recognition and dynamic texture classification) show that the proposed approaches achieve considerable improvements in discrimination accuracy, in comparison to state-of-the-art methods such as kernelized Affine Hull Method and graph-embedding Grassmann discriminant analysis.Comment: Appearing in International Journal of Computer Visio

My Forget-me-not: Song

https://digitalcommons.library.umaine.edu/mmb-vp/5516/thumbnail.jp

Incorporating Environmental Impacts in the Measurement of Agricultural Productivity Growth

Agricultural production is known to have environmental impacts, both adverse and beneficial, and it is desirable to incorporate at least some of these impacts in an environmentally sensitive productivity index. In this paper, we construct indicators of water contamination from the use of agricultural chemicals. These environmental indicators are merged with data on marketed outputs and purchased inputs to form a state-by-year panel of relative levels of outputs and inputs, including environmental impacts. We do not have prices for these undesirable by products, since they are not marketed. Consequently, we calculate a series of Malmquist productivity indexes, which do not require price information. Our benchmark scenario is a conventional Malmquist productivity index based on marketed outputs and purchased inputs only. Our comparison scenarios consist of environmentally sensitive Malmquist productivity indexes that include indicators of risk to human health and to aquatic life from chronic exposure to pesticides. In addition, we derive a set of virtual prices of the undesirable by-products that can be used to calculate an environmentally sensitive Fisher index of productivity change.environmental impacts, productivity growth, Environmental Economics and Policy,

MODELING EXTENSIVE LIVESTOCK PRODUCTION SYSTEMS: AN APPLICATION TO SHEEP PRODUCTION IN KAZAKHSTAN

A stochastic dynamic programming model for extensive livestock systems is developed. The model optimizes sales/retention decisions when future forage production, which affects animal performance and hence profitability, is uncertain. The model is applied to sheep production in Kazakhstan to evaluate policy alternatives.Livestock Production/Industries,