Spectral clustering has been one of the widely used methods for community detection in networks. However, large-scale networks bring computational challenge to it. In this paper, we study spectral clustering using randomized sketching algorithms from a statistical perspective, where we typically assume the network data are generated from a stochastic block model. To do this, we first use the recent developed sketching algorithms to derive two randomized spectral clustering algorithms, namely, the random projection-based and the random sampling-based spectral clustering. Then we study the theoretical bounds of the resulting algorithms in terms of the approximation error for the population adjacency matrix, the misclustering error, and the estimation error for the link probability matrix. It turns out that, under mild conditions, the randomized spectral clustering algorithms perform similarly to the original one. We also conduct numerical experiments to support the theoretical findings.

This paper proposes a novel deep subspace clustering approach which uses convolutional autoencoders to transform input images into new representations lying on a union of linear subspaces. The first contribution of our work is to insert multiple fully-connected linear layers between the encoder layers and their corresponding decoder layers to promote learning more favorable representations for subspace clustering. These connection layers facilitate the feature learning procedure by combining low-level and high-level information for generating multiple sets of self-expressive and informative representations at different levels of the encoder. Moreover, we introduce a novel loss minimization problem which leverages an initial clustering of the samples to effectively fuse the multi-level representations and recover the underlying subspaces more accurately. The loss function is then minimized through an iterative scheme which alternatively updates the network parameters and produces new clusterings of the samples. Experiments on four real-world datasets demonstrate that our approach exhibits superior performance compared to the state-of-the-art methods on most of the subspace clustering problems.

We present a method for learning options from segmented demonstration trajectories. The trajectories are first segmented into skills using nonparametric Bayesian clustering and a reward function for each segment is then learned using inverse reinforcement learning. From this, a set of inferred trajectories for the demonstration are generated. Option initiation sets and termination conditions are learned from these trajectories using the one-class support vector machine clustering algorithm. We demonstrate our method in the four rooms domain, where an agent is able to autonomously discover usable options from human demonstration. Our results show that these inferred options can then be used to improve learning and planning.

A Classification-Based Approach to Semi-Supervised Clustering with Pairwise Constraints Marek Smieja a,, Łukasz Struski a, Mário A. T. Figueiredo b a Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland b Instituto de T elecomunicações, Instituto Superior Técnico, Universidade de Lisboa, Lisbon, PortugalAbstract In this paper, we introduce a neural network framework for semi-supervised clustering (SSC) with pairwise (must-link or cannot-link) constraints. In contrast to existing approaches, we decompose SSC into two simpler classification tasks/stages: the first stage uses a pair of Siamese neural networks to label the unlabeled pairs of points as must-link or cannot-link; the second stage uses the fully pairwise-labeled dataset produced by the first stage in a supervised neural-network-based clustering method. The proposed approach, S 3 C 2 (Semi-Supervised Siamese C lassifiers for C lustering), is motivated by the observation that binary classification (such as assigning pairwise relations) is usually easier than multi-class clustering with partial supervision. On the other hand, being classification-based, our method solves only well-defined classification problems, rather than less well specified clustering tasks. Extensive experiments on various datasets demonstrate the high performance of the proposed method. Keywords: semi-supervised clustering, deep learning, neural networks, pairwise constraints 1. Introduction Clustering is an important unsupervised learning tool often used to analyze the structure of complex high-dimensional data. Semi-supervised clustering (SSC) methods tackle this issue by leveraging partial prior information about class labels, with the goal of obtaining partitions that are better aligned with true classes [1, 2, 3, 4, 5, 6]. One typical way of injecting class label information into clustering is in the form of pairwise constraints (typically, must-link and cannot-link constraints), or pairwise preferences (e.g., should-link and shouldn't-link), which indicate whether a given pair of points is believed to belong to the same or different classes. Most SSC approaches rely on adapting existing unsupervised clustering methods to handle partial (namely, pairwise) information [7, 8, 4, 5, 6, 9]. This requires transferring class-label knowledge into a clustering algorithm, which is often unnatural and puts a higher weight on clustering structure than on class labels.

This paper provides a systematic and comprehensive survey that reviews the latest research efforts focused on machine learning (ML) based performance improvement of wireless networks, while considering all layers of the protocol stack (PHY, MAC and network). First, the related work and paper contributions are discussed, followed by providing the necessary background on data-driven approaches and machine learning for non-machine learning experts to understand all discussed techniques. Then, a comprehensive review is presented on works employing ML-based approaches to optimize the wireless communication parameters settings to achieve improved network quality-of-service (QoS) and quality-of-experience (QoE). We first categorize these works into: radio analysis, MAC analysis and network prediction approaches, followed by subcategories within each. Finally, open challenges and broader perspectives are discussed.

Dimensionality reduction is considered as an important step for ensuring competitive performance in unsupervised learning such as anomaly detection. Non-negative matrix factorization (NMF) is a popular and widely used method to accomplish this goal. But NMF, together with its recent, enhanced version, like graph regularized NMF or symmetric NMF, do not have the provision to include the neighborhood structure information and, as a result, may fail to provide satisfactory performance in presence of nonlinear manifold structure. To address that shortcoming, we propose to consider and incorporate the neighborhood structural similarity information within the NMF framework by modeling the data through a minimum spanning tree. What motivates our choice is the understanding that in the presence of complicated data structure, a minimum spanning tree can approximate the intrinsic distance between two data points better than a simple Euclidean distance does, and consequently, it constitutes a more reasonable basis for differentiating anomalies from the normal class data. We label the resulting method as the neighborhood structure assisted NMF. By comparing the formulation and properties of the neighborhood structure assisted NMF with other versions of NMF including graph regularized NMF and symmetric NMF, it is apparent that the inclusion of the neighborhood structure information using minimum spanning tree makes a key difference. We further devise both offline and online algorithmic versions of the proposed method. Empirical comparisons using twenty benchmark datasets as well as an industrial dataset extracted from a hydropower plant demonstrate the superiority of the neighborhood structure assisted NMF and support our claim of merit.

They offer a completely different challenge to a supervised learning problem -- there's much more room for experimenting with the data that I have. It's no wonder that the majority of developments and breakthroughs in the machine learning space are happening in the unsupervised learning domain. And one of the most popular techniques in unsupervised learning is clustering. It's a concept we typically learn early on in our machine learning journey and it's simple enough to grasp. I'm sure you've come across or even worked on projects like customer segmentation, market basket analysis, etc.

Mutual independence is a key concept in statistics that characterizes the structural relationships between variables. Existing methods to investigate mutual independence rely on the definition of two competing models, one being nested into the other and used to generate a null distribution for a statistic of interest, usually under the asymptotic assumption of large sample size. As such, these methods have a very restricted scope of application. In the present manuscript, we propose to change the investigation of mutual independence from a hypothesis-driven task that can only be applied in very specific cases to a blind and automated search within patterns of mutual independence. To this end, we treat the issue as one of model comparison that we solve in a Bayesian framework. We show the relationship between such an approach and existing methods in the case of multivariate normal distributions as well as cross-classified multinomial distributions. We propose a general Markov chain Monte Carlo (MCMC) algorithm to numerically approximate the posterior distribution on the space of all patterns of mutual independence. The relevance of the method is demonstrated on synthetic data as well as two real datasets, showing the unique insight provided by this approach.

Most of the current complex networks that are of interest to practitioners possess a certain community structure that plays an important role in understanding the properties of these networks. Moreover, many machine learning algorithms and tools that are developed for complex networks try to take advantage of the existence of communities to improve their performance or speed. As a result, there are many competing algorithms for detecting communities in large networks. Unfortunately, these algorithms are often quite sensitive and so they cannot be fine-tuned for a given, but a constantly changing, real-world network at hand. It is therefore important to test these algorithms for various scenarios that can only be done using synthetic graphs that have built-in community structure, power-law degree distribution, and other typical properties observed in complex networks. The standard and extensively used method for generating artificial networks is the LFR graph generator. Unfortunately, this model has some scalability limitations and it is challenging to analyze it theoretically. Finally, the mixing parameter $\mu$, the main parameter of the model guiding the strength of the communities, has a non-obvious interpretation and so can lead to unnaturally-defined networks. In this paper, we provide an alternative random graph model with community structure and power-law distribution for both degrees and community sizes, the Artificial Benchmark for Community Detection (ABCD). We show that the new model solves the three issues identified above and more. The conclusion is that these models produce comparable graphs but ABCD is fast, simple, and can be easily tuned to allow the user to make a smooth transition between the two extremes: pure (independent) communities and random graph with no community structure.

In this research, an extensive literature review was performed on the recent developments of the ambulance routing problem (ARP) and ambulance location problem (ALP). Both are respective modifications of the vehicle routing problem (VRP) and maximum covering problem (MCP), with modifications to objective functions and constraints. Although alike, a key distinction is emergency service systems (EMS) are considered critical and the optimization of these has become all the more important as a result. Similar to their parent problems, these are NP-hard and must resort to approximations if the space size is too large. Much of the current work has simply been on modifying existing systems through simulation to achieve a more acceptable result. There has been attempts towards using meta-heuristics, though practical experimentation is lacking when compared to VRP or MCP. The contributions of this work are a comprehensive survey of current methodologies, summarized models, and suggested future improvements.