Simultaneous clustering and optimization (SCO) has recently drawn much attention due to its wide range of practical applications. Many methods have been previously proposed to solve this problem and obtain the optimal model. However, when a dataset evolves over time, those existing methods have to update the model frequently to guarantee accuracy; such updating is computationally infeasible. In this paper, we propose a new formulation of SCO to handle evolving datasets. Specifically, we propose a new variant of the alternating direction method of multipliers (ADMM) to solve this problem efficiently. The guarantee of model accuracy is analyzed theoretically for two specific tasks: ridge regression and convex clustering. Extensive empirical studies confirm the effectiveness of our method.
The problem of organizing data that evolves over time into clusters is encountered in a number of practical settings. We introduce evolutionary subspace clustering, a method whose objective is to cluster a collection of evolving data points that lie on a union of low-dimensional evolving subspaces. To learn the parsimonious representation of the data points at each time step, we propose a non-convex optimization framework that exploits the self-expressiveness property of the evolving data while taking into account representation from the preceding time step. To find an approximate solution to …
Clustering is a difficult and widely-studied data mining task, with many varieties of clustering algorithms proposed in the literature. Nearly all algorithms use a similarity measure such as a distance metric (e.g. Euclidean distance) to decide which instances to assign to the same cluster. These similarity measures are generally pre-defined and cannot be easily tailored to the properties of a particular dataset, which leads to limitations in the quality and the interpretability of the clusters produced. In this paper, we propose a new approach to automatically evolving similarity functions fo…
The task of clustering unlabeled time series and sequences entails a particular set of challenges, namely to adequately model temporal relations and variable sequence lengths. If these challenges are not properly handled, the resulting clusters might be of suboptimal quality. As a key solution, we present a joint clustering and feature learning framework for time series based on deep learning. For a given set of time series, we train a recurrent network to represent, or embed, each time series in a vector space such that a divergence-based clustering loss function can discover the underlying c…
The University of Sydney（悉尼大学）；Beijing University of Technology（北京工业大学）
Massive volumes of high-dimensional data that evolves over time is continuously collected by contemporary information processing systems, which brings up the problem of organizing this data into clusters, i.e. achieve the purpose of dimensional deduction, and meanwhile learning its temporal evolution patterns. In this paper, a framework for evolutionary subspace clustering, referred to as LSTM-ESCM, is introduced, which aims at clustering a set of evolving high-dimensional data points that lie in a union of low-dimensional evolving subspaces. In order to obtain the parsimonious data representa…
National University of Defense Technology（国防科技大学）；XIDIAN University（西安电子科技大学）；Zhejiang Normal University（浙江师范大学）；Dongguan University of Technology（东莞理工学院）
Recently, network lasso has drawn many attentions due to its remarkable performance on simultaneous clustering and optimization. However, it usually suffers from the imperfect data (noise, missing values etc), and yields sub-optimal solutions. The reason is that it finds the similar instances according to their features directly, which is usually impacted by the imperfect data, and thus returns sub-optimal results. In this paper, we propose triangle lasso to avoid its disadvantage. Triangle lasso finds the similar instances according to their neighbours. If two instances have many common neigh…
University College London（伦敦大学学院）；University of Manchester（曼彻斯特大学）；vTime（vTime公司）
Comprehensive benchmarking of clustering algorithms is rendered difficult by two key factors: (i)~the elusiveness of a unique mathematical definition of this unsupervised learning approach and (ii)~dependencies between the generating models or clustering criteria adopted by some clustering algorithms and indices for internal cluster validation. Consequently, there is no consensus regarding the best practice for rigorous benchmarking, and whether this is possible at all outside the context of a given application. Here, we argue that synthetic datasets must continue to play an important role in …
Nankai University（南开大学）；Cardiff University（卡迪夫大学）；Chinese Academy of Sciences（中国科学院）
In this paper we propose a unified framework to simultaneously discover the number of clusters and group the data points into them using subspace clustering. Real data distributed in a high-dimensional space can be disentangled into a union of low-dimensional subspaces, which can benefit various applications. To explore such intrinsic structure, state-of-the-art subspace clustering approaches often optimize a self-representation problem among all samples, to construct a pairwise affinity graph for spectral clustering. However, a graph with pairwise similarities lacks robustness for segmentatio…
MIT（麻省理工学院）；Duke University（杜克大学）；Ohio State University（俄亥俄州立大学）
This paper presents a novel algorithm, based upon the dependent Dirichlet process mixture model (DDPMM), for clustering batch-sequential data containing an unknown number of evolving clusters. The algorithm is derived via a low-variance asymptotic analysis of the Gibbs sampling algorithm for the DDPMM, and provides a hard clustering with convergence guarantees similar to those of the k-means algorithm. Empirical results from a synthetic test with moving Gaussian clusters and a test with real ADS-B aircraft trajectory data demonstrate that the algorithm requires orders of magnitude less computa…
University of Minnesota（明尼苏达大学）；Iowa State University（爱荷华州立大学）
Most learning approaches treat dimensionality reduction (DR) and clustering separately (i.e., sequentially), but recent research has shown that optimizing the two tasks jointly can substantially improve the performance of both. The premise behind the latter genre is that the data samples are obtained via linear transformation of latent representations that are easy to cluster; but in practice, the transformation from the latent space to the data can be more complicated. In this work, we assume that this transformation is an unknown and possibly nonlinear function. To recover the `clustering-fr…
This paper introduces a novel technique to track structures in time evolving graphs. The method is based on a parameter free approach for three-dimensional co-clustering of the source vertices, the target vertices and the time. All these features are simultaneously segmented in order to build time segments and clusters of vertices whose edge distributions are similar and evolve in the same way over the time segments. The main novelty of this approach lies in that the time segments are directly inferred from the evolution of the edge distribution between the vertices, thus not requiring the use…
An Adaptive Resonance Theory-based Topological Clustering Algorithm with a Self-Adjusting Vigilance Parameter
Graduate School of Informatics, Department of Core Informatics, Osaka Metropolitan University（信息学研究生学校，核心信息学系，大阪 metropolitan 大学）；Faculty of Environmental, Life, Natural Science and Technology, Okayama University（环境、生命、自然科学和技术学院，广岛大学）；Guangdong Provincial Key Laboratory of Brain-inspired Intelligent Computation, Department of Computer Science and Engineering, Southern University of Science and Technology（脑启发智能计算广东省重点实验室，计算机科学与工程系，南方科技大学）
Arizona State University（亚利桑那州立大学）；Stony Brook University（石溪大学）
We propose a new clustering method based on optimal transportation. We solve optimal transportation with variational principles, and investigate the use of power diagrams as transportation plans for aggregating arbitrary domains into a fixed number of clusters. We iteratively drive centroids through target domains while maintaining the minimum clustering energy by adjusting the power diagrams. Thus, we simultaneously pursue clustering and the Wasserstein distances between the centroids and the target domains, resulting in a measure-preserving mapping. We demonstrate the use of our method in do…
In this thesis, we propose several modelling strategies to tackle evolving data in different contexts. In the framework of static clustering, we start by introducing a soft kernel spectral clustering (SKSC) algorithm, which can better deal with overlapping clusters with respect to kernel spectral clustering (KSC) and provides more interpretable outcomes. Afterwards, a whole strategy based upon KSC for community detection of static networks is proposed, where the extraction of a high quality training sub-graph, the choice of the kernel function, the model selection and the applicability to larg…
Memorial Sloan-Kettering Cancer Center（纪念斯隆-凯特琳癌症中心）；Humboldt University of Berlin（柏林洪堡大学）；University of Basel（巴塞尔大学）；University of Zurich（苏黎世大学）；ETH Zurich（苏黎世联邦理工学院）
We present a novel probabilistic clustering model for objects that are represented via pairwise distances and observed at different time points. The proposed method utilizes the information given by adjacent time points to find the underlying cluster structure and obtain a smooth cluster evolution. This approach allows the number of objects and clusters to differ at every time point, and no identification on the identities of the objects is needed. Further, the model does not require the number of clusters being specified in advance -- they are instead determined automatically using a Dirichle…
Federal University of Lavras (UFLA)（拉夫拉斯联邦大学（UFLA））
Time-varying classifiers, namely, evolving classifiers, play an important role in a scenario in which information is available as a never-ending online data stream. We present a new unsupervised learning method for numerical data called evolving Internal-eXternal Fuzzy clustering method (Fuzzy eIX). We develop the notion of double-boundary fuzzy granules and elaborate on its implications. Type 1 and type 2 fuzzy inference systems can be obtained from the projection of Fuzzy eIX granules. We perform the principle of the balanced information granularity within Fuzzy eIX classifiers to achieve a …
This paper introduces a model based upon games on an evolving network, and develops three clustering algorithms according to it. In the clustering algorithms, data points for clustering are regarded as players who can make decisions in games. On the network describing relationships among data points, an edge-removing-and-rewiring (ERR) function is employed to explore in a neighborhood of a data point, which removes edges connecting to neighbors with small payoffs, and creates new edges to neighbors with larger payoffs. As such, the connections among data points vary over time. During the evolu…
Clustering Time-Evolving Networks Using the Spatio-Temporal Graph Laplacian
Maxwell Institute for Mathematical Sciences（麦克斯韦数学研究所）；University of Edinburgh（爱丁堡大学）；Heriot–Watt University（赫瑞瓦特大学）；Zuse Institute Berlin（柏林祖斯研究所）；School of Mathematical & Computer Sciences（数学与计算机科学学院）
Evolving Restricted Boltzmann Machine-Kohonen Network for Online Clustering
Institute for Infocomm Research, Agency for Science, Technology and Research (A*STAR)（新加坡科研局信息通信研究所）；Birla Institute of Technology and Science, Pilani（贝拉理工科学大学皮拉尼分校）；University of Iceland（冰岛大学）；School of Computer Science and Engineering, Nanyang Technological University（南洋理工大学计算机科学与工程学院）；A*STAR Centre for Frontier AI Research（新加坡科研局前沿人工智能研究中心）
Fraunhofer-Chalmers Research Centre for Industrial Mathematics（弗劳恩霍夫-查尔姆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）
Contraction Clustering (RASTER) is a single-pass algorithm for density-based clustering of 2D data. It can process arbitrary amounts of data in linear time and in constant memory, quickly identifying approximate clusters. It also exhibits good scalability in the presence of multiple CPU cores. RASTER exhibits very competitive performance compared to standard clustering algorithms, but at the cost of decreased precision. Yet, RASTER is limited to batch processing and unable to identify clusters that only exist temporarily. In contrast, S-RASTER is an adaptation of RASTER to the stream processin…
Sequence clustering in a streaming environment is challenging because it is computationally expensive, and the sequences may evolve over time. K-medoids or Partitioning Around Medoids (PAM) is commonly used to cluster sequences since it supports alignment-based distances, and the k-centers being actual data items helps with cluster interpretability. However, offline k-medoids has no support for concept drift, while also being prohibitively expensive for clustering data streams. We therefore propose SECLEDS, a streaming variant of the k-medoids algorithm with constant memory footprint. SECLEDS …
Naval Surface Warfare Center Dahlgren Division（美国海军水面战中心达尔格伦分部）；Johns Hopkins University（约翰霍普金斯大学）
Our problem of interest is to cluster vertices of a graph by identifying underlying community structure. Among various vertex clustering approaches, spectral clustering is one of the most popular methods because it is easy to implement while often outperforming more traditional clustering algorithms. However, there are two inherent model selection problems in spectral clustering, namely estimating both the embedding dimension and number of clusters. This paper attempts to address the issue by establishing a novel model selection framework specifically for vertex clustering on graphs under a st…
In this paper, we study different discrete data clustering methods, which use the Model-Based Clustering (MBC) framework with the Multinomial distribution. Our study comprises several relevant issues, such as initialization, model estimation and model selection. Additionally, we propose a novel MBC method by efficiently combining the partitional and hierarchical clustering techniques. We conduct experiments on both synthetic and real data and evaluate the methods using accuracy, stability and computation time. Our study identifies appropriate strategies to be used for discrete data analysis wi…
University of Florida Informatics Institute（佛罗里达大学信息学研究所）；Rice University（莱斯大学）
Clustering is a ubiquitous problem in data science and signal processing. In many applications where we observe noisy signals, it is common practice to first denoise the data, perhaps using wavelet denoising, and then to apply a clustering algorithm. In this paper, we develop a sparse convex wavelet clustering approach that simultaneously denoises and discovers groups. Our approach utilizes convex fusion penalties to achieve agglomeration and group-sparse penalties to denoise through sparsity in the wavelet domain. In contrast to common practice which denoises then clusters, our method is a un…
Booth School of Business（布斯商学院）；The University of Chicago（芝加哥大学）；IBM Research（IBM研究院）；Michigan State University（密歇根州立大学）
We consider multi-response and multitask regression models, where the parameter matrix to be estimated is expected to have an unknown grouping structure. The groupings can be along tasks, or features, or both, the last one indicating a bi-cluster or "checkerboard" structure. Discovering this grouping structure along with parameter inference makes sense in several applications, such as multi-response Genome-Wide Association Studies. This additional structure can not only can be leveraged for more accurate parameter estimation, but it also provides valuable information on the underlying data mec…
EmbedTrack -- Simultaneous Cell Segmentation and Tracking Through Learning Offsets and Clustering Bandwidths
Institute for Automation and Applied Informatics, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院自动化与应用信息研究所）；Institute of Biological and Chemical Systems - Biological Information Processing, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院生物与化学系统研究所——生物信息处理分部）
Aix Marseille Université（艾克斯-马赛大学）；Université de Toulon（土伦大学）
This paper introduces a novel mixture model-based approach for simultaneous clustering and optimal segmentation of functional data which are curves presenting regime changes. The proposed model consists in a finite mixture of piecewise polynomial regression models. Each piecewise polynomial regression model is associated with a cluster, and within each cluster, each piecewise polynomial component is associated with a regime (i.e., a segment). We derive two approaches for learning the model parameters. The former is an estimation approach and consists in maximizing the observed-data likelihood …
TECNALIA（特克纳利亚研究院）；University of the Basque Country（巴斯克地区大学）；University of Granada（格拉纳达大学）
In recent years, Multifactorial Optimization (MFO) has gained a notable momentum in the research community. MFO is known for its inherent capability to efficiently address multiple optimization tasks at the same time, while transferring information among such tasks to improve their convergence speed. On the other hand, the quantum leap made by Deep Q Learning (DQL) in the Machine Learning field has allowed facing Reinforcement Learning (RL) problems of unprecedented complexity. Unfortunately, complex DQL models usually find it difficult to converge to optimal policies due to the lack of explor…
The clustering of data into physically meaningful subsets often requires assumptions regarding the number, size, or shape of the subgroups. Here, we present a new method, simultaneous coherent structure coloring (sCSC), which accomplishes the task of unsupervised clustering without a priori guidance regarding the underlying structure of the data. sCSC performs a sequence of binary splittings on the dataset such that the most dissimilar data points are required to be in separate clusters. To achieve this, we obtain a set of orthogonal coordinates along which dissimilarity in the dataset is maxi…
ETH Zurich（苏黎世联邦理工学院）；Google Brain（谷歌大脑）；Google Research（谷歌研究院）
Scaling clustering algorithms to massive data sets is a challenging task. Recently, several successful approaches based on data summarization methods, such as coresets and sketches, were proposed. While these techniques provide provably good and small summaries, they are inherently problem dependent - the practitioner has to commit to a fixed clustering objective before even exploring the data. However, can one construct small data summaries for a wide range of clustering problems simultaneously? In this work, we affirmatively answer this question by proposing an efficient algorithm that const…
University of Edinburgh（爱丁堡大学）；University of Surrey（萨里大学）；Samsung AI Centre（三星人工智能中心）
We address the problem of simultaneously learning a k-means clustering and deep feature representation from unlabelled data, which is of interest due to the potential of deep k-means to outperform traditional two-step feature extraction and shallow-clustering strategies. We achieve this by developing a gradient-estimator for the non-differentiable k-means objective via the Gumbel-Softmax reparameterisation trick. In contrast to previous attempts at deep clustering, our concrete k-means model can be optimised with respect to the canonical k-means objective and is easily trained end-to-end witho…
Islamic Azad University, Karaj Branch（伊斯兰阿扎德大学卡拉伊分校）；University Putra Malaysia (UPM)（马来西亚博特拉大学）
Very large databases are required to store massive amounts of data that are continuously inserted and queried. Analyzing huge data sets and extracting valuable pattern in many applications are interesting for researchers. We can identify two main groups of techniques for huge data bases mining. One group refers to streaming data and applies mining techniques whereas second group attempts to solve this problem directly with efficient algorithms. Recently many researchers have focused on data stream as an efficient strategy against huge data base mining instead of mining on entire data base. The…
University Sorbonne Paris Nord（索邦巴黎北大学）；Higher School of Computer Science (ESI-SBA)（高等计算机科学学院（ESI-SBA））
The analysis of data streams has received considerable attention over the past few decades due to sensors, social media, etc. It aims to recognize patterns in an unordered, infinite, and evolving stream of observations. Clustering this type of data requires some restrictions in time and memory. This paper introduces a new data stream clustering method (IMOC-Stream). This method, unlike the other clustering algorithms, uses two different objective functions to capture different aspects of the data. The goal of IMOC-Stream is to: 1) reduce computation time by using idle times to apply genetic op…
MPI for Biological Cybernetics（马克斯·普朗克生物控制论研究所）；Univ. of Minnesota（明尼苏达大学）
In the past few years powerful generalizations to the Euclidean k-means problem have been made, such as Bregman clustering [7], co-clustering (i.e., simultaneous clustering of rows and columns of an input matrix) [9,18], and tensor clustering [8,34]. Like k-means, these more general problems also suffer from the NP-hardness of the associated optimization. Researchers have developed approximation algorithms of varying degrees of sophistication for k-means, k-medians, and more recently also for Bregman clustering [2]. However, there seem to be no approximation algorithms for Bregman co- and tens…
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；University of Chinese Academy of Sciences（中国科学院大学）；CAS Center for Excellence in Brain Science and Intelligence Technology（中国科学院脑科学与智能技术卓越创新中心）
Monaural speech dereverberation is a very challenging task because no spatial cues can be used. When the additive noises exist, this task becomes more challenging. In this paper, we propose a joint training method for simultaneous speech denoising and dereverberation using deep embedding features, which is based on the deep clustering (DC). DC is a state-of-the-art method for speech separation that includes embedding learning and K-means clustering. As for our proposed method, it contains two stages: denoising and dereverberation. At the denoising stage, the DC network is leveraged to extract …
