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.

In this paper, we introduce the group concept into multi-agent reinforcement learning. In this method, agents are divided into several groups and each group completes a specific subtask so that agents can cooperate to complete the main task. Existing methods use the communication vector to exchange information between agents. This may encounter communication redundancy. To solve this problem, we propose a MARL method based on graph clustering. It allows agents to adaptively learn group features and replaces the communication operation. In our method, agent features are divide into two types, including in-group features and individual features. They represent the generality and differences between agents, respectively. Based on the graph attention network(GAT), we introduce the graph clustering method as a punishment to optimize agent group feature. Then these features are used to generate individual Q value. To overcome the consistent problem brought by GAT, we introduce the split loss to distinguish agent features. Our method is easy to convert into the CTDE framework via using Kullback-Leibler divergence method. Empirical results are evaluated on a challenging set of StarCraft II micromanagement tasks. The result shows that our method outperforms existing multi-agent reinforcement learning methods and the performance increases with the number of agents increasing.

We propose a data-driven method to extract dissimilarity between materials, with respect to a given target physical property. The technique is based on an ensemble method with Kernel ridge regression as the predicting model; multiple random subset sampling of the materials is done to generate prediction models and the corresponding contributions of the reference training materials in detail. The distribution of the predicted values for each material can be approximated by a Gaussian mixture model. The reference training materials contributed to the prediction model that accurately predicts the physical property value of a specific material, are considered to be similar to that material, or vice versa. Evaluations using synthesized data demonstrate that the proposed method can effectively measure the dissimilarity between data instances. An application of the analysis method on the data of Curie temperature (TC) of binary 3d transition metal 4f rare earth binary alloys also reveals meaningful results on the relations between the materials. The proposed method can be considered as a potential tool for obtaining a deeper understanding of the structure of data, with respect to a target property, in particular.

Even with the rise in popularity of over-parameterized models, simple dimensionality reduction and clustering methods, such as PCA and k-means, are still routinely used in an amazing variety of settings. A primary reason is the combination of simplicity, interpretability and computational efficiency. The focus of this article is on improving upon PCA and k-means, by allowing non-linear relations in the data and more flexible cluster shapes, without sacrificing the key advantages. The key contribution is a new framework for Principal Elliptical Analysis (PEA), defining a simple and computationally efficient alternative to PCA that fits the best elliptical approximation through the data. We provide theoretical guarantees on the proposed PEA algorithm using Vapnik-Chervonenkis (VC) theory to show strong consistency and uniform concentration bounds.