We consider online $k$-means clustering where each new point is assigned to the nearest cluster center, after which the algorithm may update its centers. The loss incurred is the sum of squared distances from new points to their assigned cluster centers. The goal over a data stream $X$ is to achieve loss that is a constant factor of $L(X, OPT_k)$, the best possible loss using $k$ fixed points in hindsight.
We propose a data parameter, $Λ(X)$, such that for any algorithm maintaining $O(k\text{poly}(\log n))$ centers at time $n$, there exists a data stream $X$ for which a loss of $Ω(Λ(X))$ is inevitable.
We then give a randomized algorithm that achieves clustering loss $O(Λ(X) + L(X, OPT_k))$. Our algorithm uses $O(k\text{poly}(\log n))$ memory and maintains $O(k\text{poly}(\log n))$ cluster centers. Our algorithm also enjoys a running time of $O(k\text{poly}(\log n))$ and is the first algorithm to achieve polynomial space and time complexity in this setting. It also is the first to have provable guarantees without making any assumptions on the input data.
This paper shows that one can be competitive with the k-means objective while operating online. In this model, the algorithm receives vectors v_1,...,v_n one by one in an arbitrary order. For each vector the algorithm outputs a cluster identifier before receiving the next one. Our online algorithm generates ~O(k) clusters whose k-means cost is ~O(W*). Here, W* is the optimal k-means cost using k clusters and ~O suppresses poly-logarithmic factors. We also show that, experimentally, it is not much worse than k-means++ while operating in a strictly more constrained computational model.
We study (Euclidean) $k$-median and $k$-means with constraints in the streaming model. There have been recent efforts to design unified algorithms to solve constrained $k$-means problems without using knowledge of the specific constraint at hand aside from mild assumptions like the polynomial computability of feasibility under the constraint (compute if a clustering satisfies the constraint) or the presence of an efficient assignment oracle (given a set of centers, produce an optimal assignment of points to the centers which satisfies the constraint). These algorithms have a running time expon…
Number of connected devices is steadily increasing and these devices continuously generate data streams. Real-time processing of data streams is arousing interest despite many challenges. Clustering is one of the most suitable methods for real-time data stream processing, because it can be applied with less prior information about the data and it does not need labeled instances. However, data stream clustering differs from traditional clustering in many aspects and it has several challenging issues. Here, we provide information regarding the concepts and common characteristics of data streams,…
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…
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…
North Carolina A&T State University（北卡罗来纳农业技术州立大学）；Raytheon Technologies Research Center（雷神技术研究中心）
The non-stationary nature of data streams strongly challenges traditional machine learning techniques. Although some solutions have been proposed to extend traditional machine learning techniques for handling data streams, these approaches either require an initial label set or rely on specialized design parameters. The overlap among classes and the labeling of data streams constitute other major challenges for classifying data streams. In this paper, we proposed a clustering-based data stream classification framework to handle non-stationary data streams without utilizing an initial label set…
Singapore University of Technology and Design（新加坡科技设计大学）
We study dynamic clustering problems from the perspective of online learning. We consider an online learning problem, called \textit{Dynamic $k$-Clustering}, in which $k$ centers are maintained in a metric space over time (centers may change positions) such as a dynamically changing set of $r$ clients is served in the best possible way. The connection cost at round $t$ is given by the \textit{$p$-norm} of the vector consisting of the distance of each client to its closest center at round $t$, for some $p\geq 1$ or $p = \infty$. We present a \textit{$Θ\left( \min(k,r) \right)$-regret} polynomia…
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 …
We consider a new setting of online clustering of contextual cascading bandits, an online learning problem where the underlying cluster structure over users is unknown and needs to be learned from a random prefix feedback. More precisely, a learning agent recommends an ordered list of items to a user, who checks the list and stops at the first satisfactory item, if any. We propose an algorithm of CLUB-cascade for this setting and prove a $T$-step regret bound of order $\tilde{O}(\sqrt{T})$. Previous work corresponds to the degenerate case of only one cluster, and our general regret bound in th…
Southwest University（西南大学）；University of Chinese Academy of Sciences（中国科学院大学）
Online streaming feature selection (OSFS), which conducts feature selection in an online manner, plays an important role in dealing with high-dimensional data. In many real applications such as intelligent healthcare platform, streaming feature always has some missing data, which raises a crucial challenge in conducting OSFS, i.e., how to establish the uncertain relationship between sparse streaming features and labels. Unfortunately, existing OSFS algorithms never consider such uncertain relationship. To fill this gap, we in this paper propose an online sparse streaming feature selection with…
University at Buffalo, State University of New York (SUNY)（纽约州立大学布法罗分校）
Most current clustering based anomaly detection methods use scoring schema and thresholds to classify anomalies. These methods are often tailored to target specific data sets with "known" number of clusters. The paper provides a streaming clustering and anomaly detection algorithm that does not require strict arbitrary thresholds on the anomaly scores or knowledge of the number of clusters while performing probabilistic anomaly detection and clustering simultaneously. This ensures that the cluster formation is not impacted by the presence of anomalous data, thereby leading to more reliable def…
College of Mathematics and Informatics, South China Agricultural University（华南农业大学数学与信息学院）；Key Laboratory of Smart Agricultural Technology in Tropical South China, Ministry of Agriculture and Rural Affairs（农业农村部华南热带智慧农业技术重点实验室）；School of Computer Science and Engineering, Sun Yat-sen University（中山大学计算机学院）
Contrastive deep clustering has recently gained significant attention with its ability of joint contrastive learning and clustering via deep neural networks. Despite the rapid progress, previous works mostly require both positive and negative sample pairs for contrastive clustering, which rely on a relative large batch-size. Moreover, they typically adopt a two-stream architecture with two augmented views, which overlook the possibility and potential benefits of multi-stream architectures (especially with heterogeneous or hybrid networks). In light of this, this paper presents a new end-to-end…
Practical tools for clustering streaming data must be fast enough to handle the arrival rate of the observations. Typically, they also must adapt on the fly to possible lack of stationarity; i.e., the data statistics may be time-dependent due to various forms of drifts, changes in the number of clusters, etc. The Dirichlet Process Mixture Model (DPMM), whose Bayesian nonparametric nature allows it to adapt its complexity to the data, seems a natural choice for the streaming-data case. In its classical formulation, however, the DPMM cannot capture common types of drifts in the data statistics. …
Offline k-means clustering was studied extensively, and algorithms with a constant approximation are available. However, online clustering is still uncharted. New factors come into play: the ordering of the dataset and whether the number of points, n, is known in advance or not. Their exact effects are unknown. In this paper we focus on the online setting where the decisions are irreversible: after a point arrives, the algorithm needs to decide whether to take the point as a center or not, and this decision is final. How many centers are needed and sufficient to achieve constant approximation …
University of South Australia（南澳大学）；University of Massachusetts Boston（马萨诸塞大学波士顿分校）；University of Vermont（佛蒙特大学）
As an emerging research direction, online streaming feature selection deals with sequentially added dimensions in a feature space while the number of data instances is fixed. Online streaming feature selection provides a new, complementary algorithmic methodology to enrich online feature selection, especially targets to high dimensionality in big data analytics. This paper introduces the first comprehensive open-source library for use in MATLAB that implements the state-of-the-art algorithms of online streaming feature selection. The library is designed to facilitate the development of new alg…
The staggering amount of streaming time series coming from the real world calls for more efficient and effective online modeling solution. For time series modeling, most existing works make some unrealistic assumptions such as the input data is of fixed length or well aligned, which requires extra effort on segmentation or normalization of the raw streaming data. Although some literature claim their approaches to be invariant to data length and misalignment, they are too time-consuming to model a streaming time series in an online manner. We propose a novel and more practical online modeling a…
The Chinese University of Hong Kong（香港中文大学）；Microsoft（微软）；University of Cambridge（剑桥大学）
We generalize the setting of online clustering of bandits by allowing non-uniform distribution over user frequencies. A more efficient algorithm is proposed with simple set structures to represent clusters. We prove a regret bound for the new algorithm which is free of the minimal frequency over users. The experiments on both synthetic and real datasets consistently show the advantage of the new algorithm over existing methods.
Many modern clustering methods scale well to a large number of data items, N, but not to a large number of clusters, K. This paper introduces PERCH, a new non-greedy algorithm for online hierarchical clustering that scales to both massive N and K--a problem setting we term extreme clustering. Our algorithm efficiently routes new data points to the leaves of an incrementally-built tree. Motivated by the desire for both accuracy and speed, our approach performs tree rotations for the sake of enhancing subtree purity and encouraging balancedness. We prove that, under a natural separability assump…
Google Inc.（谷歌公司）；Carnegie Mellon University（卡内基梅隆大学）
We present a novel algorithm, called Links, designed to perform online clustering on unit vectors in a high-dimensional Euclidean space. The algorithm is appropriate when it is necessary to cluster data efficiently as it streams in, and is to be contrasted with traditional batch clustering algorithms that have access to all data at once. For example, Links has been successfully applied to embedding vectors generated from face images or voice recordings for the purpose of recognizing people, thereby providing real-time identification during video or audio capture.
Learning from data streams is among the most vital fields of contemporary data mining. The online analysis of information coming from those potentially unbounded data sources allows for designing reactive up-to-date models capable of adjusting themselves to continuous flows of data. While a plethora of shallow methods have been proposed for simpler low-dimensional streaming problems, almost none of them addressed the issue of learning from complex contextual data, such as images or texts. The former is represented mainly by adaptive decision trees that have been proven to be very efficient in …
With the dawn of the Big Data era, data sets are growing rapidly. Data is streaming from everywhere - from cameras, mobile phones, cars, and other electronic devices. Clustering streaming data is a very challenging problem. Unlike the traditional clustering algorithms where the dataset can be stored and scanned multiple times, clustering streaming data has to satisfy constraints such as limit memory size, real-time response, unknown data statistics and an unknown number of clusters. In this paper, we present a novel online clustering algorithm which can be used to cluster streaming data withou…
Michigan State University（密歇根州立大学）；Singapore Management University（新加坡管理大学）；Institute for Infocomm Research, A*STAR（新加坡科技研究局资讯通信研究院）
The amount of data in our society has been exploding in the era of big data today. In this paper, we address several open challenges of big data stream classification, including high volume, high velocity, high dimensionality, high sparsity, and high class-imbalance. Many existing studies in data mining literature solve data stream classification tasks in a batch learning setting, which suffers from poor efficiency and scalability when dealing with big data. To overcome the limitations, this paper investigates an online learning framework for big data stream classification tasks. Unlike some e…
Traditional feature selections need to know the feature space before learning, and online streaming feature selection (OSFS) is proposed to process streaming features on the fly. Existing methods divide features into relevance or irrelevance without missing data, and deleting irrelevant features may lead to in-formation loss. Motivated by this, we focus on completing the streaming feature matrix and division of feature correlation and propose online sparse streaming feature selection based on adapted classification (OS2FS-AC). This study uses Latent Factor Analysis (LFA) to pre-estimate missed…
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…
Learning Self-Growth Maps for Fast and Accurate Imbalanced Streaming Data Clustering
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, Hong Kong Baptist University（香港 Baptist 大学计算机科学系）
Poznan University of Technology（波兹南理工大学）；Institute of Computing Science（计算科学研究所）
This work is aimed at the experimental studying the influence of local data characteristics and drifts on the difficulties of learning various online classifiers from multi-class imbalanced data streams. Firstly we present a categorization of these data factors and drifts in the context of imbalanced streams, then we introduce the generators of synthetic streams that model these factors and drifts. The results of many experiments with synthetically generated data streams have shown a much greater role of the overlapping between many minority classes (the type of borderline examples) than for s…
We introduce a novel algorithm to perform graph clustering in the edge streaming setting. In this model, the graph is presented as a sequence of edges that can be processed strictly once. Our streaming algorithm has an extremely low memory footprint as it stores only three integers per node and does not keep any edge in memory. We provide a theoretical justification of the design of the algorithm based on the modularity function, which is a usual metric to evaluate the quality of a graph partition. We perform experiments on massive real-life graphs ranging from one million to more than one bil…
Online Sparse Feature Selection in Data Streams via Differential Evolution
Chongqing University of Posts and Telecommunications（重庆邮电大学）；Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences（中国科学院重庆绿色智能技术研究院）
Hierarchical clustering is a widely used approach for clustering datasets at multiple levels of granularity. Despite its popularity, existing algorithms such as hierarchical agglomerative clustering (HAC) are limited to the offline setting, and thus require the entire dataset to be available. This prohibits their use on large datasets commonly encountered in modern learning applications. In this paper, we consider hierarchical clustering in the online setting, where points arrive one at a time. We propose two algorithms that seek to optimize the Moseley and Wang (MW) revenue function, a varian…
Consider a heterogeneous data stream being generated by the nodes of a graph. The data stream is in essence composed by multiple streams, possibly of different nature that depends on each node. At a given moment $τ$, a change-point occurs for a subset of nodes $C$, signifying the change in the probability distribution of their associated streams. In this paper we propose an online non-parametric method to infer $τ$ based on the direct estimation of the likelihood-ratio between the post-change and the pre-change distribution associated with the data stream of each node. We propose a kernel-base…
A deep clustering network is desired for data streams because of its aptitude in extracting natural features thus bypassing the laborious feature engineering step. While automatic construction of the deep networks in streaming environments remains an open issue, it is also hindered by the expensive labeling cost of data streams rendering the increasing demand for unsupervised approaches. This paper presents an unsupervised approach of deep clustering network construction on the fly via simultaneous deep learning and clustering termed Autonomous Deep Clustering Network (ADCN). It combines the f…
McGill University（麦吉尔大学）；New York University（纽约大学）；University of Michigan（密歇根大学）；Amazon（亚马逊）；Alibaba Group（阿里巴巴集团）
We consider a context-based dynamic pricing problem of online products, which have low sales. Sales data from Alibaba, a major global online retailer, illustrate the prevalence of low-sale products. For these products, existing single-product dynamic pricing algorithms do not work well due to insufficient data samples. To address this challenge, we propose pricing policies that concurrently perform clustering over product demand and set individual pricing decisions on the fly. By clustering data and identifying products that have similar demand patterns, we utilize sales data from products wit…
StreamSplat: Towards Online Dynamic 3D Reconstruction from Uncalibrated Video Streams
University of British Columbia（不列颠哥伦比亚大学）；Vector Institute for AI（人工智能向量研究所）；Canada CIFAR AI Chair（加拿大CIFAR人工智能主席）；Nanyang Technological University（南洋理工大学）
Act Now: A Novel Online Forecasting Framework for Large-Scale Streaming Data
School of Information Science and Engineering, Shandong University（山东大学信息科学与工程学院）；School of Control Science and Engineering, Shandong University（山东大学控制科学与工程学院）；Ocean College, Jiangsu University of Science and Technology（江苏科技大学海洋学院）；School of Qilu Transportation, Shandong University（山东大学齐鲁交通学院）；Shandong Key Laboratory of Intelligent Communication and Sensing-Computing Integration（山东省智能通信与感知计算集成重点实验室）
Old Dominion University（奥多明尼昂大学）；University of Pennsylvania（宾夕法尼亚大学）
This paper investigates a new online learning problem with doubly-streaming data, where the data streams are described by feature spaces that constantly evolve, with new features emerging and old features fading away. The challenges of this problem are two folds: 1) Data samples ceaselessly flowing in may carry shifted patterns over time, requiring learners to update hence adapt on-the-fly. 2) Newly emerging features are described by very few samples, resulting in weak learners that tend to make error predictions. A plausible idea to overcome the challenges is to establish relationship between…
L3S Research Center（L3S研究中心）；Leibniz University of Hannover（汉诺威莱布尼茨大学）；Carnegie Mellon University（卡内基梅隆大学）
Data-driven learning algorithms are employed in many online applications, in which data become available over time, like network monitoring, stock price prediction, job applications, etc. The underlying data distribution might evolve over time calling for model adaptation as new instances arrive and old instances become obsolete. In such dynamic environments, the so-called data streams, fairness-aware learning cannot be considered as a one-off requirement, but rather it should comprise a continual requirement over the stream. Recent fairness-aware stream classifiers ignore the problem of class…
Vicomtech Foundation（Vicomtech基金会）；University of the Basque Country（巴斯克大学）
In this work, we address the problem of large-scale online face clustering: given a continuous stream of unknown faces, create a database grouping the incoming faces by their identity. The database must be updated every time a new face arrives. In addition, the solution must be efficient, accurate and scalable. For this purpose, we present an online gaussian mixture-based clustering method (OGMC). The key idea of this method is the proposal that an identity can be represented by more than just one distribution or cluster. Using feature vectors (f-vectors) extracted from the incoming faces, OGM…
School of Computing and Information Systems, University of Melbourne（墨尔本大学计算与信息系统学院）
Cluster analysis is used to explore structure in unlabeled data sets in a wide range of applications. An important part of cluster analysis is validating the quality of computationally obtained clusters. A large number of different internal indices have been developed for validation in the offline setting. However, this concept has not been extended to the online setting. A key challenge is to find an efficient incremental formulation of an index that can capture both cohesion and separation of the clusters over potentially infinite data streams. In this paper, we develop two online versions (…
This paper focuses on multi-enrollment speaker recognition which naturally occurs in the task of online speaker clustering, and studies the properties of different scoring back-ends in this scenario. First, we show that popular cosine scoring suffers from poor score calibration with a varying number of enrollment utterances. Second, we propose a simple replacement for cosine scoring based on an extremely constrained version of probabilistic linear discriminant analysis (PLDA). The proposed model improves over the cosine scoring for multi-enrollment recognition while keeping the same performanc…
Ulsan National Institute of Science and Technology (UNIST)（蔚山国家科学技术研究所）
While several techniques for detecting trace-level anomalies in event logs in offline settings have appeared recently in the literature, such techniques are currently lacking for online settings. Event log anomaly detection in online settings can be crucial for discovering anomalies in process execution as soon as they occur and, consequently, allowing to promptly take early corrective actions. This paper describes a novel approach to event log anomaly detection on event streams that uses statistical leverage. Leverage has been used extensively in statistics to develop measures to identify out…
The Chinese University of Hong Kong（香港中文大学）；Nanyang Technological University（南洋理工大学）；A*STAR（新加坡科技研究局）
Joint clustering and feature learning methods have shown remarkable performance in unsupervised representation learning. However, the training schedule alternating between feature clustering and network parameters update leads to unstable learning of visual representations. To overcome this challenge, we propose Online Deep Clustering (ODC) that performs clustering and network update simultaneously rather than alternatingly. Our key insight is that the cluster centroids should evolve steadily in keeping the classifier stably updated. Specifically, we design and maintain two dynamic memory modu…
This work tackles the problem of unsupervised modeling and extraction of the main contrastive sentential reasons conveyed by divergent viewpoints on polarized issues. It proposes a pipeline approach centered around the detection and clustering of phrases, assimilated to argument facets using a novel Phrase Author Interaction Topic-Viewpoint model. The evaluation is based on the informativeness, the relevance and the clustering accuracy of extracted reasons. The pipeline approach shows a significant improvement over state-of-the-art methods in contrastive summarization on online debate datasets…
We develop a data driven approach to perform clustering and end-to-end feature learning simultaneously for streaming data that can adaptively detect novel clusters in emerging data. Our approach, Adaptive Nonparametric Variational Autoencoder (AdapVAE), learns the cluster membership through a Bayesian Nonparametric (BNP) modeling framework with Deep Neural Networks (DNNs) for feature learning. We develop a joint online variational inference algorithm to learn feature representations and clustering assignments simultaneously via iteratively optimizing the Evidence Lower Bound (ELBO). We resolve…
