We introduce a principled method for the signed clustering problem, where the goal is to partition a graph whose edge weights take both positive and negative values, such that edges within the same cluster are mostly positive, while edges spanning across clusters are mostly negative. Our method relies on a graph-based diffuse interface model formulation utilizing the Ginzburg-Landau functional, based on an adaptation of the classic numerical Merriman-Bence-Osher (MBO) scheme for minimizing such graph-based functionals. The proposed objective function aims to minimize the total weight of inter-cluster positively-weighted edges, while maximizing the total weight of the inter-cluster negatively-weighted edges. Our method scales to large sparse networks, and can be easily adjusted to incorporate labelled data information, as is often the case in the context of semi-supervised learning. We tested our method on a number of both synthetic stochastic block models and real-world data sets (including financial correlation matrices), and obtained promising results that compare favourably against a number of state-of-the-art approaches from the recent literature.

Convex clustering is a promising new approach to the classical problem of clustering, combining strong performance in empirical studies with rigorous theoretical foundations. Despite these advantages, convex clustering has not been widely adopted, due to its computationally intensive nature and its lack of compelling visualizations. To address these impediments, we introduce Algorithmic Regularization, an innovative technique for obtaining high-quality estimates of regularization paths using an iterative one-step approximation scheme. We justify our approach with a novel theoretical result, guaranteeing global convergence of the approximate path to the exact solution under easily-checked non-data-dependent assumptions. The application of algorithmic regularization to convex clustering yields the Convex Clustering via Algorithmic Regularization Paths (CARP) algorithm for computing the clustering solution path. On example data sets from genomics and text analysis, CARP delivers over a 100-fold speed-up over existing methods, while attaining a finer approximation grid than standard methods. Furthermore, CARP enables improved visualization of clustering solutions: the fine solution grid returned by CARP can be used to construct a convex clustering-based dendrogram, as well as forming the basis of a dynamic path-wise visualization based on modern web technologies. Our methods are implemented in the open-source R package clustRviz, available at https://github.com/DataSlingers/clustRviz.

Abstract--Recently, a number of works have studied clustering strategies that combine classical clustering algorithms and deep learning methods. These approaches follow either a sequential way, where a deep representation is learned using a deep autoencoder before obtaining clusters with k-means, or a simultaneous way,where deep representation and clusters are learned jointly by optimizing a single objective function. Both strategies improve clustering performance, however the robustness of these approaches is impeded by several deep autoencoder setting issues, among which the weights initialization, the width and number of layers or the number of epochs. To alleviate the impact of such hyperparameters setting on the clustering performance, we propose a new model which combines the spectral clustering and deep autoencoder strengths in an ensemble learning framework. Extensive experiments on various benchmark datasets demonstrate thepotential and robustness of our approach compared to state-of-the art deep clustering methods. I. INTRODUCTION Learning from large amount of data is a very challenging task. Several dimensionality reduction and clustering techniques thatare well studied in the literature aim to learn a suitable and simplified data representation from original dataset; see for instance [1-3]. While many approaches have been proposed to address the dimensionality reduction and clustering tasks, deep learning-based methods recently demonstrate promisingresults.

For example, in unsupervised machine learning, to evaluate theperformance of a clustering method, researchers typically assess agreement between a reference standard partition that purports to represent the true cluster structure of the objects (golden standard), and a trial partition produced by the method that is being evaluated (Wallace 1983; Halkidi, Batiskis and Vazirgiannis 2002; Jain 2010). High agreement between the two partitions may indicate good recovery of the true cluster structure. Agreement between partitions can be assessed with so-called external validity indices (Albatineh, Niewiadomska-Bugaj and Mihalko 2006; Brun et al. 2007; Warrens 2008a,2008b; Pfitzner et al. 2009). External validity indices can be roughly categorized into three approaches, namely 1) counting object pairs, 2) information theory (Vinh, Epps and Bailey 2010; Lei et al. 2016), and 3) matching sets (Rezaei and Fränti 2016). Most external validity indices are of the pair-counting approach, which is based on counting pairs of objects placed in identical and different clusters.

Ankle sprains and instability are major public health concerns. Up to 70% of individuals do not fully recover from a single ankle sprain and eventually develop chronic ankle instability (CAI). The diagnosis of CAI has been mainly based on self-report rather than objective biomechanical measures. The goal of this study is to quantitatively recognize the motion pattern of a multi-joint coordination using biosensor data from bilateral hip, knee, and ankle joints, and further distinguish between CAI and healthy cohorts. We propose an analytic framework, where a nonlinear subspace clustering method is developed to learn the motion dynamic patterns from an inter-connected network of multiply joints. A support vector machine model is trained with a leave-one-subject-out cross validation to validate the learned measures compared to traditional statistical measures. The computational results showed >70% classification accuracy on average based on the dataset of 48 subjects (25 with CAI and 23 normal controls) examined in our designed experiment. It is found that CAI can be observed from other joints (e.g., hips) significantly, which reflects the fact that there are interactions in the multi-joint coordination system. The developed method presents a potential to support the decisions with motion patterns during diagnosis, treatment, rehabilitation of gait abnormality caused by physical injury (e.g., ankle sprains in this study) or even central nervous system disorders.

Abstract--In power systems, an asset class is a group of power equipment that has the same function and shares similar electrical or mechanical characteristics. Predicting failures for different asset classes is critical for electric utilities towards developing cost-effective asset management strategies. Previously, physical age based Weibull distribution has been widely used to failure prediction. However, this mathematical model cannot incorporate asset condition data such as inspection or testing results. As a result, the prediction cannot be very specific and accurate for individual assets. To solve this important problem, this paper proposes a novel and comprehensive data-driven approach based on asset condition data: K-means clustering as an unsupervised learning method is used to analyze the inner structure of historical asset condition data and produce the asset conditional ages; logistic regression as a supervised learning method takes in both asset physical ages and conditional ages to classify and predict asset statuses. Furthermore, an index called average aging rate is defined to quantify, track and estimate the relationship between asset physical age and conditional age. This approach was applied to an urban distribution system in West Canada to predict medium-voltage cable failures. Case studies and comparison with standard Weibull distribution are provided. The proposed approach demonstrates superior performance and practicality for predicting asset class failures in power systems. I. INTRODUCTION oday, more and more electric utilities are mandated by regulators to develop cost-effective long-term asset management strategies to reduce overall cost while maintaining system reliability [1-2]. Sophisticated and optimal asset management strategies can only be established based on the accurate prediction of asset failures in the future.

Variational Autoencoder (VAE), a simple and effective deep generative model, has led to a number of impressive empirical successes and spawned many advanced variants and theoretical investigations. However, recent studies demonstrate that, when equipped with expressive generative distributions (aka. decoders), VAE suffers from learning uninformative latent representations with the observation called KL Varnishing, in which case VAE collapses into an unconditional generative model. In this work, we introduce mutual posterior-divergence regularization, a novel regularization that is able to control the geometry of the latent space to accomplish meaningful representation learning, while achieving comparable or superior capability of density estimation. Experiments on three image benchmark datasets demonstrate that, when equipped with powerful decoders, our model performs well both on density estimation and representation learning.

A recommender system is an information filtering technology which can be used to predict preference ratings of items (products, services, movies, etc) and/or to output a ranking of items that are likely to be of interest to the user. Context-aware recommender systems (CARS) learn and predict the tastes and preferences of users by incorporating available contextual information in the recommendation process. One of the major challenges in context-aware recommender systems research is the lack of automatic methods to obtain contextual information for these systems. Considering this scenario, in this paper, we propose to use contextual information from topic hierarchies of the items (web pages) to improve the performance of context-aware recommender systems. The topic hierarchies are constructed by an extension of the LUPI-based Incremental Hierarchical Clustering method that considers three types of information: traditional bag-of-words (technical information), and the combination of named entities (privileged information I) with domain terms (privileged information II). We evaluated the contextual information in four context-aware recommender systems. Different weights were assigned to each type of information. The empirical results demonstrated that topic hierarchies with the combination of the two kinds of privileged information can provide better recommendations.

In this paper, we propose a method for clustering image-caption pairs by simultaneously learning image representations and text representations that are constrained to exhibit similar distributions. These image-caption pairs arise frequently in high-value applications where structured training data is expensive to produce but free-text descriptions are common. MultiDEC initializes parameters with stacked autoencoders, then iteratively minimizes the Kullback-Leibler divergence between the distribution of the images (and text) to that of a combined joint target distribution. We regularize by penalizing non-uniform distributions across clusters. The representations that minimize this objective produce clusters that outperform both single-view and multi-view techniques on large benchmark image-caption datasets.

Graph embedding aims to transfer a graph into vectors to facilitate subsequent graph analytics tasks like link prediction and graph clustering. Most approaches on graph embedding focus on preserving the graph structure or minimizing the reconstruction errors for graph data. They have mostly overlooked the embedding distribution of the latent codes, which unfortunately may lead to inferior representation in many cases. In this paper, we present a novel adversarially regularized framework for graph embedding. By employing the graph convolutional network as an encoder, our framework embeds the topological information and node content into a vector representation, from which a graph decoder is further built to reconstruct the input graph. The adversarial training principle is applied to enforce our latent codes to match a prior Gaussian or Uniform distribution. Based on this framework, we derive two variants of adversarial models, the adversarially regularized graph autoencoder (ARGA) and its variational version, adversarially regularized variational graph autoencoder (ARVGA), to learn the graph embedding effectively. We also exploit other potential variations of ARGA and ARVGA to get a deeper understanding on our designs. Experimental results compared among twelve algorithms for link prediction and twenty algorithms for graph clustering validate our solutions.