The last decades have seen a surge of interests in distributed computing thanks to advances in clustered computing and big data technology. Existing distributed algorithms typically assume {\it all the data are already in one place}, and divide the data and conquer on multiple machines. However, it is increasingly often that the data are located at a number of distributed sites, and one wishes to compute over all the data with low communication overhead. For spectral clustering, we propose a novel framework that enables its computation over such distributed data, with "minimal" communications while a major speedup in computation. The loss in accuracy is negligible compared to the non-distributed setting. Our approach allows local parallel computing at where the data are located, thus turns the distributed nature of the data into a blessing; the speedup is most substantial when the data are evenly distributed across sites. Experiments on synthetic and large UC Irvine datasets show almost no loss in accuracy with our approach while about 2x speedup under various settings with two distributed sites. As the transmitted data need not be in their original form, our framework readily addresses the privacy concern for data sharing in distributed computing.
This paper provides new algorithms for distributed clustering for two popular center-based objectives, k-median and k-means. These algorithms have provable guarantees and improve communication complexity over existing approaches. Following a classic approach in clustering by \cite{har2004coresets}, we reduce the problem of finding a clustering with low cost to the problem of finding a coreset of small size. We provide a distributed method for constructing a global coreset which improves over the previous methods by reducing the communication complexity, and which works over general communicati…
Distributed Clustering based on Distributional Kernel
National Key Laboratory for Novel Software Technology, Nanjing University（南京大学计算机软件新技术国家重点实验室）；School of Artificial Intelligence, Nanjing University（南京大学人工智能学院）；School of Information Technology, Deakin University（迪肯大学信息技术学院）
In this paper we target the class of modal clustering methods where clusters are defined in terms of the local modes of the probability density function which generates the data. The most well-known modal clustering method is the k-means clustering. Mean Shift clustering is a generalization of the k-means clustering which computes arbitrarily shaped clusters as defined as the basins of attraction to the local modes created by the density gradient ascent paths. Despite its potential, the Mean Shift approach is a computationally expensive method for unsupervised learning. Thus, we introduce two …
Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）；University of Colorado Boulder（科罗拉多大学博尔德分校）
The unsupervised learning of community structure, in particular the partitioning vertices into clusters or communities, is a canonical and well-studied problem in exploratory graph analysis. However, like most graph analyses the introduction of immense scale presents challenges to traditional methods. Spectral clustering in distributed memory, for example, requires hundreds of expensive bulk-synchronous communication rounds to compute an embedding of vertices to a few eigenvectors of a graph associated matrix. Furthermore, the whole computation may need to be repeated if the underlying graph c…
Distributed Gradient Clustering: Convergence and the Effect of Initialization
Carnegie Mellon University（卡内基梅隆大学）；Indian Institute of Technology Kharagpur（印度理工学院克勒格布尔分校）；Faculty of Technical Sciences, University of Novi Sad（诺维萨德大学技术科学学院）；Faculty of Sciences, University of Novi Sad（诺维萨德大学理学院）
College of Information and Computer Sciences, University of Massachusetts, Amherst（马萨诸塞大学阿默斯特分校信息与计算机科学学院）；Google Research New York（谷歌纽约研究院）
In this paper, we present distributed generalized clustering algorithms that can handle large scale data across multiple machines in spite of straggling or unreliable machines. We propose a novel data assignment scheme that enables us to obtain global information about the entire data even when some machines fail to respond with the results of the assigned local computations. The assignment scheme leads to distributed algorithms with good approximation guarantees for a variety of clustering and dimensionality reduction problems.
Insight Centre for Data Analytics School of Computer Science University College Dublin（都柏林大学学院计算机科学学院数据洞察中心）；School of Computer Science University College Dublin（都柏林大学学院计算机科学学院）
In this paper, we present a new approach of distributed clustering for spatial datasets, based on an innovative and efficient aggregation technique. This distributed approach consists of two phases: 1) local clustering phase, where each node performs a clustering on its local data, 2) aggregation phase, where the local clusters are aggregated to produce global clusters. This approach is characterised by the fact that the local clusters are represented in a simple and efficient way. And The aggregation phase is designed in such a way that the final clusters are compact and accurate while the ov…
We consider $K$-means clustering in networked environments (e.g., internet of things (IoT) and sensor networks) where data is inherently distributed across nodes and processing power at each node may be limited. We consider a clustering algorithm referred to as networked $K$-means, or $NK$-means, which relies only on local neighborhood information exchange. Information exchange is limited to low-dimensional statistics and not raw data at the agents. The proposed approach develops a parametric family of multi-agent clustering objectives (parameterized by $ρ$) and associated distributed $NK$-mea…
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of algorithmic design methods for graph clustering. However, most of these methods are based on complicated spectral techniques or convex optimisation, and cannot be applied directly for clustering many networks that occur in practice, whose information is often collected on different sites. Designing a simple and distributed clustering algorithm is of great interest, …
The goal of unsupervised representation learning is to extract a new representation of data, such that solving many different tasks becomes easier. Existing methods typically focus on vectorized data and offer little support for relational data, which additionally describe relationships among instances. In this work we introduce an approach for relational unsupervised representation learning. Viewing a relational dataset as a hypergraph, new features are obtained by clustering vertices and hyperedges. To find a representation suited for many relational learning tasks, a wide range of similarit…
In this work, we study the $k$-median and $k$-means clustering problems when the data is distributed across many servers and can contain outliers. While there has been a lot of work on these problems for worst-case instances, we focus on gaining a finer understanding through the lens of beyond worst-case analysis. Our main motivation is the following: for many applications such as clustering proteins by function or clustering communities in a social network, there is some unknown target clustering, and the hope is that running a $k$-median or $k$-means algorithm will produce clusterings which …
Low-Rank Representation (LRR) highly suffers from discarding the locality information of data points in subspace clustering, as it may not incorporate the data structure nonlinearity and the non-uniform distribution of observations over the ambient space. Thus, the information of the observational density is lost by the state-of-art LRR models, as they take a constant number of adjacent neighbors into account. This, as a result, degrades the subspace clustering accuracy in such situations. To cope with deficiency, in this paper, we propose to consider a hypergraph model to facilitate having a …
Indiana University（印第安纳大学）；University of Bristol（布里斯托大学）；IBM Research Almaden（IBM阿尔马登研究院）
Clustering large datasets is a fundamental problem with a number of applications in machine learning. Data is often collected on different sites and clustering needs to be performed in a distributed manner with low communication. We would like the quality of the clustering in the distributed setting to match that in the centralized setting for which all the data resides on a single site. In this work, we study both graph and geometric clustering problems in two distributed models: (1) a point-to-point model, and (2) a model with a broadcast channel. We give protocols in both models which we sh…
In this paper, we consider the $k$-center/median/means clustering with outliers problems (or the $(k, z)$-center/median/means problems) in the distributed setting. Most previous distributed algorithms have their communication costs linearly depending on $z$, the number of outliers. Recently Guha et al. overcame this dependence issue by considering bi-criteria approximation algorithms that output solutions with $2z$ outliers. For the case where $z$ is large, the extra $z$ outliers discarded by the algorithms might be too large, considering that the data gathering process might be costly. In thi…
Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；University of Chinese Academy of Sciences（中国科学院大学）；Center for Excellence in Animal Evolution and Genetics, Chinese Academy of Sciences（中国科学院动物进化与遗传前沿交叉卓越创新中心）；Yunnan University（云南大学）
Matrix decomposition is one of the fundamental tools to discover knowledge from big data generated by modern applications. However, it is still inefficient or infeasible to process very big data using such a method in a single machine. Moreover, big data are often distributedly collected and stored on different machines. Thus, such data generally bear strong heterogeneous noise. It is essential and useful to develop distributed matrix decomposition for big data analytics. Such a method should scale up well, model the heterogeneous noise, and address the communication issue in a distributed sys…
In this work, we consider to improve the model estimation efficiency by aggregating the neighbors' information as well as identify the subgroup membership for each node in the network. A tree-based $l_1$ penalty is proposed to save the computation and communication cost. We design a decentralized generalized alternating direction method of multiplier algorithm for solving the objective function in parallel. The theoretical properties are derived to guarantee both the model consistency and the algorithm convergence. Thorough numerical experiments are also conducted to back up our theory, which …
A Unified Framework for Center-based Clustering of Distributed Data
Carnegie Mellon University（卡内基梅隆大学）；Faculty of Technical Sciences, University of Novi Sad（诺维萨德大学技术科学学院）；Faculty of Sciences, University of Novi Sad（诺维萨德大学理学院）
University of Oxford（牛津大学）；Technion（以色列理工学院）；MTA-SZTE Research Group on Artificial Intelligence（匈牙利科学院-塞格德大学人工智能研究组）；University of Insubria（因苏布里亚大学）
We provide two distributed confidence ball algorithms for solving linear bandit problems in peer to peer networks with limited communication capabilities. For the first, we assume that all the peers are solving the same linear bandit problem, and prove that our algorithm achieves the optimal asymptotic regret rate of any centralised algorithm that can instantly communicate information between the peers. For the second, we assume that there are clusters of peers solving the same bandit problem within each cluster, and we prove that our algorithm discovers these clusters, while achieving the opt…
Academy of Arts and Design, Tsinghua University（清华大学美术学院）；Massachusetts Institute of Technology（麻省理工学院）
Electronic medical records (EMRs) supports the development of machine learning algorithms for predicting disease incidence, patient response to treatment, and other healthcare events. But insofar most algorithms have been centralized, taking little account of the decentralized, non-identically independently distributed (non-IID), and privacy-sensitive characteristics of EMRs that can complicate data collection, sharing and learning. To address this challenge, we introduced a community-based federated machine learning (CBFL) algorithm and evaluated it on non-IID ICU EMRs. Our algorithm clustere…
Inria（法国国家信息与自动化研究所）；CEA（法国原子能和替代能源委员会）；University Paris-Saclay（巴黎萨克雷大学）；Institut de Mathématiques de Toulouse（图卢兹数学研究所）；Université de Toulouse（图卢兹大学）；CNRS（法国国家科学研究中心）
In this work, we revisit fast dimension reduction approaches, as with random projections and random sampling. Our goal is to summarize the data to decrease computational costs and memory footprint of subsequent analysis. Such dimension reduction can be very efficient when the signals of interest have a strong structure, such as with images. We focus on this setting and investigate feature clustering schemes for data reductions that capture this structure. An impediment to fast dimension reduction is that good clustering comes with large algorithmic costs. We address it by contributing a linear…
Kernel-based clustering algorithm can identify and capture the non-linear structure in datasets, and thereby it can achieve better performance than linear clustering. However, computing and storing the entire kernel matrix occupy so large memory that it is difficult for kernel-based clustering to deal with large-scale datasets. In this paper, we employ incomplete Cholesky factorization to accelerate kernel clustering and save memory space. The key idea of the proposed kernel $k$-means clustering using incomplete Cholesky factorization is that we approximate the entire kernel matrix by the prod…
South China Agricultural University（华南农业大学）；Sun Yat-sen University（中山大学）
Despite significant progress, there remain three limitations to the previous multi-view clustering algorithms. First, they often suffer from high computational complexity, restricting their feasibility for large-scale datasets. Second, they typically fuse multi-view information via one-stage fusion, neglecting the possibilities in multi-stage fusions. Third, dataset-specific hyperparameter-tuning is frequently required, further undermining their practicability. In light of this, we propose a fast multi-view clustering via ensembles (FastMICE) approach. Particularly, the concept of random view …
Near-Optimal Resilient Aggregation Rules for Distributed Learning Using 1-Center and 1-Mean Clustering with Outliers
College of Computer Science, Sichuan University（四川大学计算机学院）；School of Statistics and Data Science, Nankai University（南开大学统计与数据科学学院）；School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology（瑞典皇家理工学院电气工程与计算机科学学院）；School of Robotics, Hunan University（湖南大学机器人学院）
University of Maryland（马里兰大学）；Imperial College London（伦敦帝国学院）
Distributed implementations are crucial in speeding up large scale machine learning applications. Distributed gradient descent (GD) is widely employed to parallelize the learning task by distributing the dataset across multiple workers. A significant performance bottleneck for the per-iteration completion time in distributed synchronous GD is $straggling$ workers. Coded distributed computation techniques have been introduced recently to mitigate stragglers and to speed up GD iterations by assigning redundant computations to workers. In this paper, we consider gradient coding (GC), and propose …
We propose an algorithm for clustering high dimensional data. If $P$ features for $N$ objects are represented in an $N\times P$ matrix ${\bf X}$, where $N\ll P$, the method is based on exploiting the cluster-dependent structure of the $N\times N$ matrix ${\bf XX}^T$. Computational burden thus depends primarily on $N$, the number of objects to be clustered, rather than $P$, the number of features that are measured. This makes the method particularly useful in high dimensional settings, where it is substantially faster than a number of other popular clustering algorithms. Aside from an upper bou…
In this paper, we introduce an algorithm for performing spectral clustering efficiently. Spectral clustering is a powerful clustering algorithm that suffers from high computational complexity, due to eigen decomposition. In this work, we first build the adjacency matrix of the corresponding graph of the dataset. To build this matrix, we only consider a limited number of points, called landmarks, and compute the similarity of all data points with the landmarks. Then, we present a definition of the Laplacian matrix of the graph that enable us to perform eigen decomposition efficiently, using a d…
Department of Computer Science, KU Leuven（比利时鲁汶大学计算机科学系）
Constraint-based clustering algorithms exploit background knowledge to construct clusterings that are aligned with the interests of a particular user. This background knowledge is often obtained by allowing the clustering system to pose pairwise queries to the user: should these two elements be in the same cluster or not? Active clustering methods aim to minimize the number of queries needed to obtain a good clustering by querying the most informative pairs first. Ideally, a user should be able to answer a couple of these queries, inspect the resulting clustering, and repeat these two steps un…
Nowadays processing of Big Security Data, such as log messages, is commonly used for intrusion detection purposed. Its heterogeneous nature, as well as combination of numerical and categorical attributes does not allow to apply the existing data mining methods directly on the data without feature preprocessing. Therefore, a rather computationally expensive conversion of categorical attributes into vector space should be utilised for analysis of such data. However, a well-known k-modes algorithm allows to cluster the categorical data directly and avoid conversion into the vector space. The exis…
Coordinated Sciences Laboratory（协同科学实验室）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Federated learning systems that jointly preserve Byzantine robustness and privacy have remained an open problem. Robust aggregation, the standard defense for Byzantine attacks, generally requires server access to individual updates or nonlinear computation -- thus is incompatible with privacy-preserving methods such as secure aggregation via multiparty computation. To this end, we propose SHARE (Secure Hierarchical Robust Aggregation), a distributed learning framework designed to cryptographically preserve client update privacy and robustness to Byzantine adversaries simultaneously. The key id…
Clustering is inherently ill-posed: there often exist multiple valid clusterings of a single dataset, and without any additional information a clustering system has no way of knowing which clustering it should produce. This motivates the use of constraints in clustering, as they allow users to communicate their interests to the clustering system. Active constraint-based clustering algorithms select the most useful constraints to query, aiming to produce a good clustering using as few constraints as possible. We propose COBRA, an active method that first over-clusters the data by running K-mean…
Aalto University（阿尔托大学）；Universitat Politècnica de Catalunya（加泰罗尼亚理工大学）
Kernel functions are a powerful tool to enhance the $k$-means clustering algorithm via the kernel trick. It is known that the parameters of the chosen kernel function can have a dramatic impact on the result. In supervised settings, these can be tuned via cross-validation, but for clustering this is not straightforward and heuristics are usually employed. In this paper we study the impact of kernel parameters on kernel $k$-means. In particular, we derive a lower bound, tight up to constant factors, below which the parameter of the RBF kernel will render kernel $k$-means meaningless. We argue t…
Clustering in graphs has been a well-known research problem, particularly because most Internet and social network data is in the form of graphs. Organizations widely use spectral clustering algorithms to find clustering in graph datasets. However, applying spectral clustering to a large dataset is challenging due to computational overhead. While the distributed spectral clustering algorithm exists, they face the problem of data privacy and increased communication costs between the clients. Thus, in this paper, we propose a spectral clustering algorithm using federated learning (FL) to overcom…
We describe a new optimization scheme for finding high-quality correlation clusterings in planar graphs that uses weighted perfect matching as a subroutine. Our method provides lower-bounds on the energy of the optimal correlation clustering that are typically fast to compute and tight in practice. We demonstrate our algorithm on the problem of image segmentation where this approach outperforms existing global optimization techniques in minimizing the objective and is competitive with the state of the art in producing high-quality segmentations.
Federated Learning (FL) under distributed concept drift is a largely unexplored area. Although concept drift is itself a well-studied phenomenon, it poses particular challenges for FL, because drifts arise staggered in time and space (across clients). To the best of our knowledge, this work is the first to explicitly study data heterogeneity in both dimensions. We first demonstrate that prior solutions to drift adaptation that use a single global model are ill-suited to staggered drifts, necessitating multiple-model solutions. We identify the problem of drift adaptation as a time-varying clust…
The most widely used internal measure for clustering evaluation is the silhouette coefficient, whose naive computation requires a quadratic number of distance calculations, which is clearly unfeasible for massive datasets. Surprisingly, there are no known general methods to efficiently approximate the silhouette coefficient of a clustering with rigorously provable high accuracy. In this paper, we present the first scalable algorithm to compute such a rigorous approximation for the evaluation of clusterings based on any metric distances. Our algorithm hinges on a Probability Proportional to Siz…
This paper presents a Fast Synchronization Clustering algorithm (FSynC), which is an improved version of SynC algorithm. In order to decrease the time complexity of the original SynC algorithm, we combine grid cell partitioning method and Red-Black tree to construct the near neighbor point set of every point. By simulated experiments of some artificial data sets and several real data sets, we observe that FSynC algorithm can often get less time than SynC algorithm for many kinds of data sets. At last, it gives some research expectations to popularize this algorithm.
Missouri University of Science and Technology（密苏里科技大学）
This paper presents a novel adaptive resonance theory (ART)-based modular architecture for unsupervised learning, namely the distributed dual vigilance fuzzy ART (DDVFA). DDVFA consists of a global ART system whose nodes are local fuzzy ART modules. It is equipped with the distinctive features of distributed higher-order activation and match functions, using dual vigilance parameters responsible for cluster similarity and data quantization. Together, these allow DDVFA to perform unsupervised modularization, create multi-prototype clustering representations, retrieve arbitrarily-shaped clusters…
Rice University（莱斯大学）；Baylor College of Medicine（贝勒医学院）
Consensus clustering has been widely used in bioinformatics and other applications to improve the accuracy, stability and reliability of clustering results. This approach ensembles cluster co-occurrences from multiple clustering runs on subsampled observations. For application to large-scale bioinformatics data, such as to discover cell types from single-cell sequencing data, for example, consensus clustering has two significant drawbacks: (i) computational inefficiency due to repeatedly applying clustering algorithms, and (ii) lack of interpretability into the important features for different…
Rice University（莱斯大学）；University of Texas at Austin（德克萨斯大学奥斯汀分校）；Department of Electrical and Computer Engineering, Rice University（莱斯大学电气与计算机工程系）；Department of Mathematics, University of Texas at Austin（德克萨斯大学奥斯汀分校数学系）
Across many areas, from neural tracking to database entity resolution, manual assessment of clusters by human experts presents a bottleneck in rapid development of scalable and specialized clustering methods. To solve this problem we develop C-FAR, a novel method for Fast, Automated and Reproducible assessment of multiple hierarchical clustering algorithms simultaneously. Our algorithm takes any number of hierarchical clustering trees as input, then strategically queries pairs for human feedback, and outputs an optimal clustering among those nominated by these trees. While it is applicable to …
We present a new fast online clustering algorithm that reliably recovers arbitrary-shaped data clusters in high throughout data streams. Unlike the existing state-of-the-art online clustering methods based on k-means or k-medoid, it does not make any restrictive generative assumptions. In addition, in contrast to existing nonparametric clustering techniques such as DBScan or DenStream, it gives provable theoretical guarantees. To achieve fast clustering, we propose to represent each cluster by a skeleton set which is updated continuously as new data is seen. A skeleton set consists of weighted…
Distributed controllers are oftentimes used in large-scale SDN deployments where they run a myriad of network applications simultaneously. Such applications could have different consistency and availability preferences. These controllers need to communicate via east/west interfaces in order to synchronize their state information. The consistency and the availability of the distributed state information are governed by an underlying consistency model. Earlier, we suggested the use of adaptively-consistent controllers that can autonomously tune their consistency parameters in order to meet the p…
Imperial College London（帝国理工学院）；University of Maryland, College Park（马里兰大学帕克分校）
Gradient descent (GD) methods are commonly employed in machine learning problems to optimize the parameters of the model in an iterative fashion. For problems with massive datasets, computations are distributed to many parallel computing servers (i.e., workers) to speed up GD iterations. While distributed computing can increase the computation speed significantly, the per-iteration completion time is limited by the slowest straggling workers. Coded distributed computing can mitigate straggling workers by introducing redundant computations; however, existing coded computing schemes are mainly d…
One-Shot Federated Clustering of Non-Independent Completely Distributed Data
School of Computer Science and Technology, Guangdong University of Technology（广东工业大学计算机科学与技术学院）；Department of Computer Science, Beijing Normal-Hong Kong Baptist University（北京师范大学-香港 Baptist大学计算机科学系）；Department of Computer Science, Harbin Institute of Technology（哈尔滨工业大学计算机科学系）
Correlation clustering is a widely studied framework for clustering based on pairwise similarity and dissimilarity scores, but its best approximation algorithms rely on impractical linear programming relaxations. We present faster approximation algorithms that avoid these relaxations, for two well-studied special cases: cluster editing and cluster deletion. We accomplish this by drawing new connections to edge labeling problems related to the principle of strong triadic closure. This leads to faster and more practical linear programming algorithms, as well as extremely scalable combinatorial t…
Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；School of Mathematical Sciences, University of Chinese Academy of Sciences（中国科学院大学数学科学学院）；LSEC（科学与工程计算国家重点实验室）
Density-based clustering algorithms are widely used for discovering clusters in pattern recognition and machine learning since they can deal with non-hyperspherical clusters and are robustness to handle outliers. However, the runtime of density-based algorithms are heavily dominated by finding fixed-radius near neighbors and calculating the density, which is time-consuming. Meanwhile, the traditional acceleration methods using indexing technique such as KD tree is not effective in processing high-dimensional data. In this paper, we propose a fast region query algorithm named fast principal com…
Contraction Clustering (RASTER): A Very Fast Big Data Algorithm for Sequential and Parallel Density-Based Clustering in Linear Time, Constant Memory, and a Single Pass
Fraunhofer-Chalmers Research Centre for Industrial Mathematics（弗劳恩霍夫-查尔默斯工业数学研究中心）；Fraunhofer Center for Machine Learning（弗劳恩霍夫机器学习中心）
University of Maryland（马里兰大学）；Imperial College London（帝国理工学院）
In distributed synchronous gradient descent (GD) the main performance bottleneck for the per-iteration completion time is the slowest \textit{straggling} workers. To speed up GD iterations in the presence of stragglers, coded distributed computation techniques are implemented by assigning redundant computations to workers. In this paper, we propose a novel gradient coding (GC) scheme that utilizes dynamic clustering, denoted by GC-DC, to speed up the gradient calculation. Under time-correlated straggling behavior, GC-DC aims at regulating the number of straggling workers in each cluster based …
