Currently, the problem of uncovering complex network structure and dynamics from time series is prominent in many fields. Despite the recent progress in this area, reconstructing large-scale networks from limited data remains a tough problem. Existing works treat connections of nodes as continuous values, leaving a challenge of setting a proper cut-off value to distinguish whether the connections exist or not. Besides, their performances on large-scale networks are far from satisfactory. Considering the reconstruction error and sparsity as two objectives, this article proposes a subspace learning-based evolutionary multiobjective network reconstruction algorithm, called SLEMO-NR, to solve the aforementioned problems. In the evolutionary process, we assume that binary-coded individuals obey the Bernoulli distribution and can use the probability and natural parameter as alternative representations. Moreover, our approach utilizes the logistic principal component analysis (LPCA) to learn a subspace containing the features of the network structure. The offspring solutions are generated in the learned subspace and then can be mapped back to the original space via LPCA. Benefitting from the alternative representations, a preference-based local search operator (PLSO) is proposed to concentrate on finding solutions approximate to the true sparsity. The experimental results on synthetic networks and six real-world networks demonstrate that, due to the well-learned network structure subspace and the preference-based strategy, our approach is effective in reconstructing large-scale networks compared to six existing methods.

中文翻译：

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通过逻辑主成分分析解决大规模网络重建问题的多目标进化方法


目前，从时间序列中揭示复杂网络结构和动态的问题在许多领域都很突出。尽管该领域最近取得了进展，但从有限的数据重建大规模网络仍然是一个难题。现有的工作将节点的连接视为连续值，因此设置适当的截止值来区分连接是否存在是一个挑战。此外，它们在大规模网络上的表现也远不能令人满意。本文考虑重构误差和稀疏性两个目标，提出一种基于子空间学习的进化多目标网络重构算法SLEMO-NR来解决上述问题。在进化过程中，我们假设二进制编码的个体服从伯努利分布，并且可以使用概率和自然参数作为替代表示。此外，我们的方法利用逻辑主成分分析（LPCA）来学习包含网络结构特征的子空间。后代解在学习的子空间中生成，然后可以通过 LPCA 映射回原始空间。受益于替代表示，提出了一种基于偏好的局部搜索算子（PLSO），专注于寻找接近真实稀疏性的解决方案。合成网络和六个现实世界网络的实验结果表明，由于充分学习的网络结构子空间和基于偏好的策略，与六种现有方法相比，我们的方法在重建大规模网络方面是有效的。