Spectral clustering has found extensive use in many areas. Most traditional spectral clustering algorithms work in three separate steps: similarity graph construction; continuous labels learning; discretizing the learned labels by k-means clustering. Such common practice has two potential flaws, which may lead to severe information loss and performance degradation. First, predefined similarity graph might not be optimal for subsequent clustering. It is well-accepted that similarity graph highly affects the clustering results. To this end, we propose to automatically learn similarity information from data and simultaneously consider the constraint that the similarity matrix has exact c connected components if there are c clusters. Second, the discrete solution may deviate from the spectral solution since k-means method is well-known as sensitive to the initialization of cluster centers. In this work, we transform the candidate solution into a new one that better approximates the discrete one. Finally, those three subtasks are integrated into a unified framework, with each subtask iteratively boosted by using the results of the others towards an overall optimal solution. It is known that the performance of a kernel method is largely determined by the choice of kernels. To tackle this practical problem of how to select the most suitable kernel for a particular data set, we further extend our model to incorporate multiple kernel learning ability. Extensive experiments demonstrate the superiority of our proposed method as compared to existing clustering approaches.

Mixed data with both categorical and continuous features are ubiquitous in real-world applications. Learning a good representation of mixed data is critical yet challenging for further learning tasks. Existing methods for representing mixed data often overlook the heterogeneous coupling relationships between categorical and continuous features as well as the discrimination between objects. To address these issues, we propose an auto-instructive representation learning scheme to enable margin-enhanced distance metric learning for a discrimination-enhanced representation. Accordingly, we design a metric-based auto-instructor (MAI) model which consists of two collaborative instructors. Each instructor captures the feature-level couplings in mixed data with fully connected networks, and guides the infinite-margin metric learning for the peer instructor with a contrastive order. By feeding the learned representation into both partition-based and density-based clustering methods, our experiments on eight UCI datasets show highly significant learning performance improvement and much more distinguishable visualization outcomes over the baseline methods.

Semi-supervised or constrained community detection incorporates side information to findcommunities of interest in complex networks. The supervision is often represented as constraints such as known labels and pairwise constraints. Existing constrained community detection approaches often fail to fully benefit from the available side information. This results in poor performance for scenarios such as: when the constraints are required to be fully satisfied, when there is a high confidence about the correctness of the supervision information, and in situations where the side information is expensive or hard to achieve and is only available in a limited amount. In this paper, we propose a new constrained community detection algorithm based on Lagrangian multipliers to incorporate and fully satisfy the instance level supervisio nconstraints. Our proposed algorithm can more fully utilise available side information and find better quality solutions. Our experiments on real and synthetic data sets show our proposed LagCCD algorithm outperforms existing algorithms in terms of solution quality, ability to satisfy the constraints and noise resistance.

Clustering of data points is a fundamental tool in data analysis. We consider points X in a relaxed metric space, where the triangle inequality holds within a constant factor. A clustering of X is a partition of X defined by a set of points Q (centroids), according to the closest centroid. The cost of clustering X by Q is V ( Q )= ∑ x ∈ X d xQ . This formulation generalizes classic k- means clustering, which uses squared distances. Two basic tasks, parametrized by k ≥ 1, are cost estimation, which returns (approximate) V ( Q ) for queries Q such that | Q | =  k and clustering, which returns an (approximate) minimizer of V ( Q ) of size | Q |=  k . When the data set X is very large, we seek efficient constructions of small samples that can act as surrogates for performing these tasks. Existing constructions that provide quality guarantees, however, are either worst-case, and unable to benefit from structure of real data sets, or make explicit strong assumptions on the structure. We show here how to avoid both these pitfalls using adaptive designs. The core of our design are the novel one2all probabilities, computed for a set M of centroids and α ≥ 1:  The clustering cost of  each Q with cost V ( Q ) ≥ V(M)/α can be estimated well from a sample of size O (α | M | ε -2 ). For cost estimation, we apply one2all with a bicriteria approximate M , while adaptively balancing | M | and α to optimize sample size per quality. For clustering, we present a wrapper that adaptively applies a base clustering algorithm to a sample S, using the smallest sample that provides the desired statistical guarantees on quality. We demonstrate experimentally the huge gains of using our adaptive instead of worst-case methods.

Parameter tying is a regularization method in which parameters (weights) of a machine learning model are partitioned into groups by leveraging prior knowledge and all parameters in each group are constrained to take the same value. In this paper, we consider the problem of parameter learning in Markov networks and propose a novel approach called automatic parameter tying (APT) that uses automatic instead of a priori and soft instead of hard parameter tying as a regularization method to alleviate overfitting. The key idea behind APT is to set up the learning problem as the task of finding parameters and groupings of parameters such that the likelihood plus a regularization term is maximized. The regularization term penalizes models where parameter values deviate from their group mean parameter value. We propose and use a block coordinate ascent algorithm to solve the optimization task. We analyze the sample complexity of our new learning algorithm and show that it yields optimal parameters with high probability when the groups are well separated. Experimentally, we show that our method improves upon L 2 regularization and suggest several pragmatic techniques for good practical performance.

We study the problem of robust attributed graph clustering. In real data, the clustering structure is often obfuscated due to anomalies or corruptions. While robust methods have been recently introduced that handle anomalies as part of the clustering process, they all fail to account for one core aspect: Since attributed graphs consist of two views (network structure and attributes) anomalies might materialize only partially, i.e. instances might be corrupted in one view but perfectly fit in the other. In this case, we can still derive meaningful cluster assignments. Existing works only consider complete anomalies. In this paper, we present a novel probabilistic generative model (PAICAN) that explicitly models partial anomalies by generalizing ideas of Degree Corrected Stochastic Block Models and Bernoulli Mixture Models. We provide a highly scalable variational inference approach with runtime complexity linear in the number of edges. The robustness of our model w.r.t. anomalies is demonstrated by our experimental study, outperforming state-of-the-art competitors.

In the past decade, various sparse learning based unsupervised feature selection methods have been developed. However, most existing studies adopt a two-step strategy, i.e., selecting the top-m features according to a calculated descending order and then performing K-means clustering, resulting in a group of sub-optimal features. To address this problem, we propose a Dependence Guided Unsupervised Feature Selection (DGUFS) method to select features and partition data in a joint manner. Our proposed method enhances the inter-dependence among original data, cluster labels, and selected features. In particular, a projection-free feature selection model is proposed based on l20-norm equality constraints. We utilize the learned cluster labels to fill in the information gap between original data and selected features. Two dependence guided terms are consequently proposed for our model. More specifically, one term increases the dependence of desired cluster labels on original data, while the other term maximizes the dependence of selected features on cluster labels to guide the process of feature selection. Last but not least, an iterative algorithm based on Alternating Direction Method of Multipliers (ADMM) is designed to solve the constrained minimization problem efficiently. Extensive experiments on different datasets consistently demonstrate that our proposed method significantly outperforms state-of-the-art baselines.

We consider the following general graph clustering problem: given a complete undirected graph G=(V,E,c) with an edge weight function c:E->Q, we are asked to find a partition C of V that maximizes the sum of edge weights within the clusters in C. Owing to its high generality, this problem has a wide variety of real-world applications, including correlation clustering, group technology, and community detection. In this study, we investigate the design of mathematical programming formulations and constraint satisfaction formulations for the problem. First, we present a novel integer linear programming (ILP) formulation that has far fewer constraints than the standard ILP formulation by Groetschel and Wakabayashi (1989). Second, we propose an ILP-based exact algorithm that solves an ILP problem obtained by modifying our above ILP formulation and then performs simple post-processing to produce an optimal solution to the original problem. Third, we present maximum satisfiability (MaxSAT) counterparts of both our ILP formulation and ILP-based exact algorithm. Computational experiments using well-known real-world datasets demonstrate that our ILP-based approaches and their MaxSAT counterparts are highly effective in terms of both memory efficiency and computation time.

In the past decade, various multi-view outlier detection methods have been designed to detect horizontal outliers that exhibit inconsistent across-view characteristics. The existing works assume that all objects are present in all views. However, in real-world applications, it is often the incomplete case that every view may suffer from some missing samples, resulting in partial objects difficult to detect outliers from. To address this problem, we propose a novel Collective Learning (CL) based framework to detect outliers from partial multi-view data in a self-guided way. More specifically, by well exploiting the inter-dependence among different views, we develop an algorithm to reconstruct missing samples based on learning. Furthermore, we propose similarity-based outlier detection to break through the dilemma that the number of clusters is unknown priori. Then, the calculated outlier scores act as the confidence levels in CL and in turn guide the reconstruction of missing data. Learning-based missing sample recovery and similarity-based outlier detection are iteratively performed in a self-guided manner. Experimental results on benchmark datasets show that our proposed approach consistently and significantly outperforms state-of-the-art baselines.

In this paper, we propose a novel unsupervised clustering approach exploiting the hidden information that is indirectly introduced through a pseudo classification objective. Specifically, we randomly assign a pseudo parent-class label to each observation which is then modified by applying the domain specific transformation associated with the assigned label. Generated pseudo observation-label pairs are subsequently used to train a neural network with Auto-clustering Output Layer (ACOL) that introduces multiple softmax nodes for each pseudo parent-class. Due to the unsupervised objective based on Graph-based Activity Regularization (GAR) terms, softmax duplicates of each parent-class are specialized as the hidden information captured through the help of domain specific transformations is propagated during training. Ultimately we obtain a k-means friendly latent representation. Furthermore, we demonstrate how the chosen transformation type impacts performance and helps propagate the latent information that is useful in revealing unknown clusters. Our results show state-of-the-art performance for unsupervised clustering tasks on MNIST, SVHN and USPS datasets, with the highest accuracies reported to date in the literature.