How Do Landscape Heterogeneity, Community Structure, and Topographical Factors Contribute to the Plant Diversity of Urban Remnant Vegetation at Different Scales?

In highly fragmented urban areas, plant diversity of remnant vegetation may depend not only on community structure and topographical factors, but also on landscape heterogeneity. Different buffer radius settings can affect the relative importance of these factors to plant diversity. The aim of this study was to examine the relative importance of landscape heterogeneity, community structure, and topographical factors on plant diversity under different buffer radii in biodiversity hotspots. We established 48 plots of remnant vegetation in Guangzhou city, one of the biodiversity hotspots. A buffer radius of 500 m, 1000 m, and 2000 m was established around the center of each sample plot, and 17 landscape heterogeneity indices in each buffer were calculated by FRAGSTATS 4.2 software. Combined with the community structure and topographical factors, the impact factors of plant diversity under different buffer radii were analyzed by multiple regression analysis. We found the following: (1) The combined explanatory power of the three factors accounted for 43% of the species diversity indices and 62% of the richness index at its peak. The three impact factors rarely act independently and usually create comprehensive cumulative effects. (2) Scale does matter in urban landscape studies. At a 500 m buffer radius, community structure combined with road disturbance indices was strongly related to diversity indices in herb and shrub layers. The stand age was negatively correlated with the tree-layer richness index. As the scale increased, the diversity indices and richness index in the three layers decreased or increased under the influence of comprehensive factors. (3) The richness index in the herb layer was more responsive to impact factors than other biodiversity indices. Except for the herb layer, the interpretation of landscape heterogeneity for each plant diversity index was more stable than that for the other two factors. Road disturbance indices, combined with the other six landscape pattern metrics, can well indicate species diversity and richness. We suggest that the vegetation area of remnant patches within a radius of 500-2000 m should be appropriately increased to protect plant diversity, and the negative effects of road disturbance should also be considered.

Low-rank structure learning via nonconvex heuristic recovery.

In this paper, we propose a nonconvex framework to learn the essential low-rank structure from corrupted data. Different from traditional approaches, which directly utilizes convex norms to measure the sparseness, our method introduces more reasonable nonconvex measurements to enhance the sparsity in both the intrinsic low-rank structure and the sparse corruptions. We will, respectively, introduce how to combine the widely used ℓp norm (0 < p < 1) and log-sum term into the framework of low-rank structure learning. Although the proposed optimization is no longer convex, it still can be effectively solved by a majorization-minimization (MM)-type algorithm, with which the nonconvex objective function is iteratively replaced by its convex surrogate and the nonconvex problem finally falls into the general framework of reweighed approaches. We prove that the MM-type algorithm can converge to a stationary point after successive iterations. The proposed model is applied to solve two typical problems: robust principal component analysis and low-rank representation. Experimental results on low-rank structure learning demonstrate that our nonconvex heuristic methods, especially the log-sum heuristic recovery algorithm, generally perform much better than the convex-norm-based method (0 < p < 1) for both data with higher rank and with denser corruptions.

Graph Laplace for occluded face completion and recognition.

This paper proposes a spectral-graph-based algorithm for face image repairing, which can improve the recognition performance on occluded faces. The face completion algorithm proposed in this paper includes three main procedures: 1) sparse representation for partially occluded face classification; 2) image-based data mining; and 3) graph Laplace (GL) for face image completion. The novel part of the proposed framework is GL, as named from graphical models and the Laplace equation, and can achieve a high-quality repairing of damaged or occluded faces. The relationship between the GL and the traditional Poisson equation is proven. We apply our face repairing algorithm to produce completed faces, and use face recognition to evaluate the performance of the algorithm. Experimental results verify the effectiveness of the GL method for occluded face completion.

Cutting plane method for continuously constrained kernel-based regression.

Incorporating constraints into the kernel-based regression is an effective means to improve regression performance. Nevertheless, in many applications, the constraints are continuous with respect to some parameters so that computational difficulties arise. Discretizing the constraints is a reasonable solution for these difficulties. However, in the context of kernel-based regression, most of existing works utilize the prior discretization strategy; this strategy suffers from a few inherent deficiencies: it cannot ensure that the regression result totally fulfills the original constraints and can hardly tackle high-dimensional problems. This paper proposes a cutting plane method (CPM) for constrained kernel-based regression problems and a relaxed CPM (R-CPM) for high-dimensional problems. The CPM discretizes the continuous constraints iteratively and ensures that the regression result strictly fulfills the original constraints. For high-dimensional problems, the R-CPM accepts a slight and controlled violation to attain a dimensional-independent computational complexity. The validity of the proposed methods is verified by numerical experiments.