Geographic variation of the Perny's Long-nosed squirrels (Dremomys pernyi) (Milne-Edwards, 1867) (Rodentia : Sciuridae) from southwestern China based on cranial morphometric variables

A sample of 114 specimens of Dremomys pernyi was investigated, 73 of which had intact skulls and were subjected to multivariate, coefficient of difference (C. D.), and cluster analyses. Results indicate that 4 subspecies (groups) of Dremomys pernyi inhabi

Geographic variation of the Anderson's Niviventer (Niviventer andersoni) (Thomas, 1911) (Rodentia: Muridae) of two new subspecies in China verified with cranial morphometric variables and pelage characteristics

A total of 66 specimens of Niviventer andersoni with intact skulls was investigated on pelage characteristics and cranial morphometric variables. The data were subjected to principal component analyses as well as to discriminant analyses, and measurement

Geographic and economic setting of Lake Victoria

Lake Victoria, besides being the second largest in the world after Lake Superior, is the largest tropical lake. Its waters are shared by Kenya (6% of the surface area), Uganda (43%), and Tanzania (51%). Before dramatic structural and functional changes manifested in the lake's ecosystem especially in the 1980s, fish life flourished in the lake's entire water column at all times of the year. Currently, the situation is much more different from what it was in the past. The exponential increase in the introduced Nile perch (Lates niloticus) and Nile tilapia (Oreochromis niloticus) stocks, siltation, wetland degradation and eutrophication have characterised the lake ecosystem. The two exotic species and the small native cyprinid (Rastrineobola argentea) form the basis of the commercial fishery that was once dominated by two native tilapiines (Oreochromis esculentus and Oreochromis variabilis) and five other large-bodied endemic fishes. Severe deoxygenation observed at shallow depths (Ochumba 1990; Hecky et al., 1994) indicates that a large volume of the lake is unable to sustain fish life. The Lake Victoria catchment is one of the most densely populated areas in East Africa, encompassing a population of about 30 million people. Widespread poverty resulting from high inflation rates, lack of opportunities and general unemployment have characterised the lakeside communities over much of the last two decades. The biophysical environment in which Lake Victoria exists makes the lake particularly susceptible to changes that occur as a result of human modification to the watershed or the lake itself, thus rendering benefits from the lake unsustainable.

Structure Discovery in Nonparametric Regression through Compositional Kernel Search

Despite its importance, choosing the structural form of the kernel in nonparametric regression remains a black art. We define a space of kernel structures which are built compositionally by adding and multiplying a small number of base kernels. We present a method for searching over this space of structures which mirrors the scientific discovery process. The learned structures can often decompose functions into interpretable components and enable long-range extrapolation on time-series datasets. Our structure search method outperforms many widely used kernels and kernel combination methods on a variety of prediction tasks.

Convex relaxation of mixture regression with efficient algorithms

We develop a convex relaxation of maximum a posteriori estimation of a mixture of regression models. Although our relaxation involves a semidefinite matrix variable, we reformulate the problem to eliminate the need for general semidefinite programming. In particular, we provide two reformulations that admit fast algorithms. The first is a max-min spectral reformulation exploiting quasi-Newton descent. The second is a min-min reformulation consisting of fast alternating steps of closed-form updates. We evaluate the methods against Expectation-Maximization in a real problem of motion segmentation from video data.

Linear regression under fixed-rank constraints: A Riemannian approach

In this paper, we tackle the problem of learning a linear regression model whose parameter is a fixed-rank matrix. We study the Riemannian manifold geometry of the set of fixed-rank matrices and develop efficient line-search algorithms. The proposed algorithms have many applications, scale to high-dimensional problems, enjoy local convergence properties and confer a geometric basis to recent contributions on learning fixed-rank matrices. Numerical experiments on benchmarks suggest that the proposed algorithms compete with the state-of-the-art, and that manifold optimization offers a versatile framework for the design of rank-constrained machine learning algorithms. Copyright 2011 by the author(s)/owner(s).

Regression on fixed-rank positive semidefinite matrices: A Riemannian approach

The paper addresses the problem of learning a regression model parameterized by a fixed-rank positive semidefinite matrix. The focus is on the nonlinear nature of the search space and on scalability to high-dimensional problems. The mathematical developments rely on the theory of gradient descent algorithms adapted to the Riemannian geometry that underlies the set of fixedrank positive semidefinite matrices. In contrast with previous contributions in the literature, no restrictions are imposed on the range space of the learned matrix. The resulting algorithms maintain a linear complexity in the problem size and enjoy important invariance properties. We apply the proposed algorithms to the problem of learning a distance function parameterized by a positive semidefinite matrix. Good performance is observed on classical benchmarks. © 2011 Gilles Meyer, Silvere Bonnabel and Rodolphe Sepulchre.