Knowledge graphs (KGs) store rich facts about the real world. In this paper, we study KG alignment, which aims to find alignment between not only entities but also relations and classes in different KGs. Alignment at the entity level can cross-fertilize alignment at the schema level. We propose a new KG alignment approach, called DAAKG, based on deep learning and active learning. With deep learning, it learns the embeddings of entities, relations and classes, and jointly aligns them in a semi-supervised manner. With active learning, it estimates how likely an entity, relation or class pair can be inferred, and selects the best batch for human labeling. We design two approximation algorithms for efficient solution to batch selection. Our experiments on benchmark datasets show the superior accuracy and generalization of DAAKG and validate the effectiveness of all its modules.

Two-dimensional (2D) materials have wide applications in superconductors, quantum, and topological materials. However, their rational design is not well established, and currently less than 6,000 experimentally synthesized 2D materials have been reported. Recently, deep learning, data-mining, and density functional theory (DFT)-based high-throughput calculations are widely performed to discover potential new materials for diverse applications. Here we propose a generative material design pipeline, namely material transformer generator(MTG), for large-scale discovery of hypothetical 2D materials. We train two 2D materials composition generators using self-learning neural language models based on Transformers with and without transfer learning. The models are then used to generate a large number of candidate 2D compositions, which are fed to known 2D materials templates for crystal structure prediction. Next, we performed DFT computations to study their thermodynamic stability based on energy-above-hull and formation energy. We report four new DFT-verified stable 2D materials with zero e-above-hull energies, including NiCl$_4$, IrSBr, CuBr$_3$, and CoBrCl. Our work thus demonstrates the potential of our MTG generative materials design pipeline in the discovery of novel 2D materials and other functional materials.

Clustering is a central approach for unsupervised learning. After clustering is applied, the most fundamental analysis is to quantitatively compare clusterings. Such comparisons are crucial for the evaluation of clustering methods as well as other tasks such as consensus clustering. It is often argued that, in order to establish a baseline, clustering similarity should be assessed in the context of a random ensemble of clusterings. The prevailing assumption for the random clustering ensemble is the permutation model in which the number and sizes of clusters are fixed. However, this assumption does not necessarily hold in practice; for example, multiple runs of K-means clustering returns clusterings with a fixed number of clusters, while the cluster size distribution varies greatly. Here, we derive corrected variants of two clustering similarity measures (the Rand index and Mutual Information) in the context of two random clustering ensembles in which the number and sizes of clusters vary. In addition, we study the impact of one-sided comparisons in the scenario with a reference clustering. The consequences of different random models are illustrated using synthetic examples, handwriting recognition, and gene expression data. We demonstrate that the choice of random model can have a drastic impact on the ranking of similar clustering pairs, and the evaluation of a clustering method with respect to a random baseline; thus, the choice of random clustering model should be carefully justified.

Clustering is one of the most universal approaches for understanding complex data. A pivotal aspect of clustering analysis is quantitatively comparing clusterings; clustering comparison is the basis for tasks such as clustering evaluation, consensus clustering, and tracking the temporal evolution of clusters. For example, the extrinsic evaluation of clustering methods requires comparing the uncovered clusterings to planted clusterings or known metadata. Yet, as we demonstrate, existing clustering comparison measures have critical biases which un- dermine their usefulness, and no measure accommodates both overlapping and hierarchical clusterings. Here we unify the comparison of disjoint, overlapping, and hierarchically struc- tured clusterings by proposing a new element-centric framework: elements are compared based on the relationships induced by the cluster structure, as opposed to the traditional cluster-centric philosophy. We demonstrate that, in contrast to standard clustering simi- larity measures, our framework does not suffer from critical biases and naturally provides unique insights into how the clusterings differ. We illustrate the strengths of our framework by revealing new insights into the organization of clusters in two applications: the improved classification of schizophrenia based on the overlapping and hierarchical community struc- ture of fMRI brain networks, and the disentanglement of various social homophily factors in Facebook social networks. The universality of clustering suggests far-reaching impact of our framework throughout all areas of science.

Fast and frugal heuristics are well studied models of bounded rationality. Psychological research has proposed the take-the-best heuristic as a successful strategy in decision making with limited resources. Take-thebest searches for a sufficiently good ordering of cues (features) in a task where objects are to be compared lexicographically. We investigate the complexity of the problem of approximating optimal cue permutations for lexicographic strategies. We show that no efficient algorithm can approximate the optimum to within any constant factor, if P NP. We further consider a greedy approach for building lexicographic strategies and derive tight bounds for the performance ratio of a new and simple algorithm. This algorithm is proven to perform better than take-the-best.

Fast and frugal heuristics are well studied models of bounded rationality. Psychological research has proposed the take-the-best heuristic as a successful strategy in decision making with limited resources. Take-thebest searches for a sufficiently good ordering of cues (features) in a task where objects are to be compared lexicographically. We investigate the complexity of the problem of approximating optimal cue permutations for lexicographic strategies. We show that no efficient algorithm can approximate the optimum to within any constant factor, if P NP. We further consider a greedy approach for building lexicographic strategies and derive tight bounds for the performance ratio of a new and simple algorithm. This algorithm is proven to perform better than take-the-best.

Fast and frugal heuristics are well studied models of bounded rationality. Psychologicalresearch has proposed the take-the-best heuristic as a successful strategy in decision making with limited resources. Take-thebest searchesfor a sufficiently good ordering of cues (features) in a task where objects are to be compared lexicographically. We investigate the complexity of the problem of approximating optimal cue permutations for lexicographic strategies. We show that no efficient algorithm can approximate theoptimum to within any constant factor, if P NP. We further consider a greedy approach for building lexicographic strategies and derive tight bounds for the performance ratio of a new and simple algorithm. This algorithm is proven to perform better than take-the-best.