Constructing a Non-Negative Low Rank and Sparse Graph with Data-Adaptive Features

This paper aims at constructing a good graph for discovering intrinsic data structures in a semi-supervised learning setting. Firstly, we propose to build a non-negative low-rank and sparse (referred to as NNLRS) graph for the given data representation. Specifically, the weights of edges in the graph are obtained by seeking a nonnegative low-rank and sparse matrix that represents each data sample as a linear combination of others. The so-obtained NNLRS-graph can capture both the global mixture of subspaces structure (by the low rankness) and the locally linear structure (by the sparseness) of the data, hence is both generative and discriminative. Secondly, as good features are extremely important for constructing a good graph, we propose to learn the data embedding matrix and construct the graph jointly within one framework, which is termed as NNLRS with embedded features (referred to as NNLRS-EF). Extensive experiments on three publicly available datasets demonstrate that the proposed method outperforms the state-of-the-art graph construction method by a large margin for both semi-supervised classification and discriminative analysis, which verifies the effectiveness of our proposed method

Social Equity Matters in Payments for Ecosystem Services

Although conservation efforts have sometimes succeeded in meeting environmental goals at the expense of equity considerations, the changing context of conservation and a growing body of evidence increasingly suggest that equity considerations should be integrated into conservation planning and implementation. However, this approach is often perceived to be at odds with the prevailing focus on economic efficiency that characterizes many payment for ecosystem services (PES) schemes. Drawing from examples across the literature, we show how the equity impacts of PES can create positive and negative feedbacks that influence ecological outcomes. We caution against equity-blind PES, which overlooks these relationships as a result of a primary and narrow focus on economic efficiency. We call for further analysis and better engagement between the social and ecological science communities to understand the relationships and trade-offs among efficiency, equity, and ecological outcomes