Node embedding learns a low-dimensional representation for each node in the graph. Recent progress on node embedding shows that proximity matrix factorization methods gain superb performance and scale to large graphs with millions of nodes. Existing
approaches first define a proximity matrix and then learn the embeddings that fit the proximity by matrix factorization. Most existing matrix factorization methods adopt the same proximity for different tasks, while it is observed that different tasks and datasets may require different proximity, limiting their representation power. Motivated by this, we propose {em Lemane}, a framework with trainable proximity measures, which can be learned to best suit the datasets and tasks at hand automatically. Our method is end-to-end, which incorporates differentiable SVD in the pipeline so that the parameters can be trained via backpropagation. However, this learning process is still expensive on large graphs. To improve the scalability, we train proximity measures only on carefully subsampled graphs, and then apply standard proximity matrix factorization on the original graph using the learned proximity. Note that, computing the learned proximities for each pair is still expensive for large graphs, and existing techniques for computing proximities are not applicable to the learned proximities. Thus, we present generalized push techniques to make our solution scalable to large graphs with millions of nodes. Extensive experiments show that our proposed solution outperforms existing solutions on both link prediction and node classification tasks on almost all datasets.
In the past three decades, a large number of metaheuristics have been proposed and shown high performance in solving complex optimization problems. While most variation operators in existing metaheuristics are empirically designed, this paper aims to
design new operators automatically, which are expected to be search space independent and thus exhibit robust performance on different problems. For this purpose, this work first investigates the influence of translation invariance, scale invariance, and rotation invariance on the search behavior and performance of some representative operators. Then, we deduce the generic form of translation, scale, and rotation invariant operators. Afterwards, a principled approach is proposed for the automated design of operators, which searches for high-performance operators based on the deduced generic form. The experimental results demonstrate that the operators generated by the proposed approach outperform state-of-the-art ones on a variety of problems with complex landscapes and up to 1000 decision variables.
Over the last three decades, a large number of evolutionary algorithms have been developed for solving multiobjective optimization problems. However, there lacks an up-to-date and comprehensive software platform for researchers to properly benchmark
existing algorithms and for practitioners to apply selected algorithms to solve their real-world problems. The demand of such a common tool becomes even more urgent, when the source code of many proposed algorithms has not been made publicly available. To address these issues, we have developed a MATLAB platform for evolutionary multi-objective optimization in this paper, called PlatEMO, which includes more than 50 multi-objective evolutionary algorithms and more than 100 multi-objective test problems, along with several widely used performance indicators. With a user-friendly graphical user interface, PlatEMO enables users to easily compare several evolutionary algorithms at one time and collect statistical results in Excel or LaTeX files. More importantly, PlatEMO is completely open source, such that users are able to develop new algorithms on the basis of it. This paper introduces the main features of PlatEMO and illustrates how to use it for performing comparative experiments, embedding new algorithms, creating new test problems, and developing performance indicators. Source code of PlatEMO is now available at: http://bimk.ahu.edu.cn/index.php?s=/Index/Software/index.html.
