Multiplayer games have a long history in being used as key testbeds for evaluation and training in artificial intelligence (AI), aptly referred to as the "Drosophila of AI". Traditionally, researchers have focused on using games to build strong AI agents that, e.g., achieve human-level performance. This progress, however, also requires a classification of how 'interesting' a game is for an artificial agent, which requires characterization of games and their topological landscape. Tackling this latter question not only facilitates an understanding of the characteristics of learnt AI agents in games, but can also help determine what game an AI should address next as part of its training. Here, we show how network measures applied to so-called response graphs of large-scale games enable the creation of a useful landscape of games, quantifying the relationships between games of widely varying sizes, characteristics, and complexities. We illustrate our findings in various domains, ranging from well-studied canonical games to significantly more complex empirical games capturing the performance of trained AI agents pitted against one another. Our results culminate in a demonstration of how one can leverage this information to automatically generate new and interesting games, including mixtures of empirical games synthesized from real world games.

Data deduplication is the task of detecting records in a database that correspond to the same real-world entity. Our goal is to develop a procedure that samples uniformly from the set of entities present in the database in the presence of duplicates. We accomplish this by a two-stage process. In the first step, we estimate the frequencies of all the entities in the database. In the second step, we use rejection sampling to obtain a (approximately) uniform sample from the set of entities. However, efficiently estimating the frequency of all the entities is a non-trivial task and not attainable in the general case. Hence, we consider various natural properties of the data under which such frequency estimation (and consequently uniform sampling) is possible. Under each of those assumptions, we provide sampling algorithms and give proofs of the complexity (both statistical and computational) of our approach. We complement our study by conducting extensive experiments on both real and synthetic datasets.

Graph learning has emerged as a promising technique for multi-view clustering with its ability to learn a unified and robust graph from multiple views. However, existing graph learning methods mostly focus on the multi-view consistency issue, yet often neglect the inconsistency across multiple views, which makes them vulnerable to possibly low-quality or noisy datasets. To overcome this limitation, we propose a new multi-view graph learning framework, which for the first time simultaneously and explicitly models multi-view consistency and multi-view inconsistency in a unified objective function, through which the consistent and inconsistent parts of each single-view graph as well as the unified graph that fuses the consistent parts can be iteratively learned. Though optimizing the objective function is NP-hard, we design a highly efficient optimization algorithm which is able to obtain an approximate solution with linear time complexity in the number of edges in the unified graph. Furthermore, our multi-view graph learning approach can be applied to both similarity graphs and dissimilarity graphs, which lead to two graph fusion-based variants in our framework. Experiments on twelve multi-view datasets have demonstrated the robustness and efficiency of the proposed approach.

Multi-view clustering methods have been a focus in recent years because of their superiority in clustering performance. However, typical traditional multi-view clustering algorithms still have shortcomings in some aspects, such as removal of redundant information, utilization of various views and fusion of multi-view features. In view of these problems, this paper proposes a new multi-view clustering method, low-rank subspace multi-view clustering based on adaptive graph regularization. We construct two new data matrix decomposition models into a unified optimization model. In this framework, we address the significance of the common knowledge shared by the cross view and the unique knowledge of each view by presenting new low-rank and sparse constraints on the sparse subspace matrix. To ensure that we achieve effective sparse representation and clustering performance on the original data matrix, adaptive graph regularization and unsupervised clustering constraints are also incorporated in the proposed model to preserve the internal structural features of the data. Finally, the proposed method is compared with several state-of-the-art algorithms. Experimental results for five widely used multi-view benchmarks show that our proposed algorithm surpasses other state-of-the-art methods by a clear margin.

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Variational autoencoders (VAEs) have been shown to be able to generate game levels but require manual exploration of the learned latent space to generate outputs with desired attributes. While conditional VAEs address this by allowing generation to be conditioned on labels, such labels have to be provided during training and thus require prior knowledge which may not always be available. In this paper, we apply Gaussian Mixture VAEs (GMVAEs), a variant of the VAE which imposes a mixture of Gaussians (GM) on the latent space, unlike regular VAEs which impose a unimodal Gaussian. This allows GMVAEs to cluster levels in an unsupervised manner using the components of the GM and then generate new levels using the learned components. We demonstrate our approach with levels from Super Mario Bros., Kid Icarus and Mega Man. Our results show that the learned components discover and cluster level structures and patterns and can be used to generate levels with desired characteristics.

This paper presents an adaptive resonance theory predictive mapping (ARTMAP) model which uses incremental cluster validity indices (iCVIs) to perform unsupervised learning, namely iCVI-ARTMAP. Incorporating iCVIs to the decision-making and many-to-one mapping capabilities of ARTMAP can improve the choices of clusters to which samples are incrementally assigned. These improvements are accomplished by intelligently performing the operations of swapping sample assignments between clusters, splitting and merging clusters, and caching the values of variables when iCVI values need to be recomputed. Using recursive formulations enables iCVI-ARTMAP to considerably reduce the computational burden associated with cluster validity index (CVI)-based offline clustering. Depending on the iCVI and the data set, it can achieve running times up to two orders of magnitude shorter than when using batch CVI computations. In this work, the incremental versions of Calinski-Harabasz, WB-index, Xie-Beni, Davies-Bouldin, Pakhira-Bandyopadhyay-Maulik, and negentropy increment were integrated into fuzzy ARTMAP. Experimental results show that, with proper choice of iCVI, iCVI-ARTMAP outperformed fuzzy adaptive resonance theory (ART), dual vigilance fuzzy ART, kmeans, spectral clustering, Gaussian mixture models and hierarchical agglomerative clustering algorithms in most of the synthetic benchmark data sets. It also performed competitively on real world image benchmark data sets when clustering on projections and on latent spaces generated by a deep clustering model. Naturally, the performance of iCVI-ARTMAP is subject to the selected iCVI and its suitability to the data at hand; fortunately, it is a general model wherein other iCVIs can be easily embedded.

Clustering analysis has been widely used in trust evaluation on various complex networks such as wireless sensors networks and online social networks. Spectral clustering is one of the most commonly used algorithms for graph-structured data (networks). However, the conventional spectral clustering is inherently difficult to work with large-scale networks due to the fact that it needs computationally expensive matrix manipulations. To deal with large networks, in this paper, we propose an efficient graph clustering algorithm, KCoreMotif, specifically for large networks by exploiting k-core decomposition and motifs. The essential idea behind the proposed clustering algorithm is to perform the efficient motif-based spectral clustering algorithm on k-core subgraphs, rather than on the entire graph. More specifically, (1) we first conduct the k-core decomposition of the large input network; (2) we then perform the motif-based spectral clustering for the top k-core subgraphs; (3) we group the remaining vertices in the rest (k-1)-core subgraphs into previously found clusters; and finally obtain the desired clusters of the large input network. To evaluate the performance of the proposed graph clustering algorithm KCoreMotif, we use both the conventional and the motif-based spectral clustering algorithms as the baselines and compare our algorithm with them for 18 groups of real-world datasets. Comparative results demonstrate that the proposed graph clustering algorithm is accurate yet efficient for large networks, which also means that it can be further used to evaluate the intra-cluster and inter-cluster trusts on large networks.

Datasets in high-dimension do not typically form clusters in their original space; the issue is worse when the number of points in the dataset is small. We propose a low-computation method to find statistically significant clustering structures in a small dataset. The method proceeds by projecting the data on a random line and seeking binary clusterings in the resulting one-dimensional data. Non-linear separations are obtained by extending the feature space using monomials of higher degrees in the original features. The statistical validity of the clustering structures obtained is tested in the projected one-dimensional space, thus bypassing the challenge of statistical validation in high-dimension. Projecting on a random line is an extreme dimension reduction technique that has previously been used successfully as part of a hierarchical clustering method for high-dimensional data. Our experiments show that with this simplified framework, statistically significant clustering structures can be found with as few as 100-200 points, depending on the dataset. The different structures uncovered are found to persist as more points are added to the dataset.

Topological learning is a wide research area aiming at uncovering the mutual spatial relationships between the elements of a set. Some of the most common and oldest approaches involve the use of unsupervised competitive neural networks. However, these methods are not based on gradient optimization which has been proven to provide striking results in feature extraction also in unsupervised learning. Unfortunately, by focusing mostly on algorithmic efficiency and accuracy, deep clustering techniques are composed of overly complex feature extractors, while using trivial algorithms in their top layer. The aim of this work is to present a novel comprehensive theory aspiring at bridging competitive learning with gradient-based learning, thus allowing the use of extremely powerful deep neural networks for feature extraction and projection combined with the remarkable flexibility and expressiveness of competitive learning. In this paper we fully demonstrate the theoretical equivalence of two novel gradient-based competitive layers. Preliminary experiments show how the dual approach, trained on the transpose of the input matrix i.e. $X^T$, lead to faster convergence rate and higher training accuracy both in low and high-dimensional scenarios.