슬라이딩 윈도우상의 빠른 점진적 밀도 기반 클러스터링

학위논문(박사) -- 서울대학교대학원 : 공과대학 컴퓨터공학부, 2022. 8. 문봉기.Given the prevalence of mobile and IoT devices, continuous clustering against streaming data has become an essential tool of increasing importance for data analytics. Among many clustering approaches, density-based clustering has garnered much attention due to its unique advantage that it can detect clusters of an arbitrary shape when noise exists. However, when the clusters need to be updated continuously along with an evolving input dataset, a relatively high computational cost is required. Particularly, deleting data points from the clusters causes severe performance degradation. In this dissertation, the performance limits of the incremental density-based clustering over sliding windows are addressed. Ultimately, two algorithms, DISC and DenForest, are proposed. The first algorithm DISC is an incremental density-based clustering algorithm that efficiently produces the same clustering results as DBSCAN over sliding windows. It focuses on redundancy issues that occur when updating clusters. When multiple data points are inserted or deleted individually, surrounding data points are explored and retrieved redundantly. DISC addresses these issues and improves the performance by updating multiple points in a batch. It also presents several optimization techniques. The second algorithm DenForest is an incremental density-based clustering algorithm that primarily focuses on the deletion process. Unlike previous methods that manage clusters as a graph, DenForest manages clusters as a group of spanning trees, which contributes to very efficient deletion performance. Moreover, it provides a batch-optimized technique to improve the insertion performance. To prove the effectiveness of the two algorithms, extensive evaluations were conducted, and it is demonstrated that DISC and DenForest outperform the state-of-the-art density-based clustering algorithms significantly.모바일 및 IoT 장치가 널리 보급됨에 따라 스트리밍 데이터상에서 지속적으로 클러스터링 작업을 수행하는 것은 데이터 분석에서 점점 더 중요해지는 필수 도구가 되었습니다. 많은 클러스터링 방법 중에서 밀도 기반 클러스터링은 노이즈가 존재할 때 임의의 모양의 클러스터를 감지할 수 있다는 고유한 장점을 가지고 있으며 이에 따라 많은 관심을 받았습니다. 그러나 밀도 기반 클러스터링은 변화하는 입력 데이터 셋에 따라 지속적으로 클러스터를 업데이트해야 하는 경우 비교적 높은 계산 비용이 필요합니다. 특히, 클러스터에서의 데이터 점들의 삭제는 심각한 성능 저하를 초래합니다. 본 박사 학위 논문에서는 슬라이딩 윈도우상의 밀도 기반 클러스터링의 성능 한계를 다루며 궁극적으로 두 가지 알고리즘을 제안합니다. 첫 번째 알고리즘인 DISC는 슬라이딩 윈도우상에서 DBSCAN과 동일한 클러스터링 결과를 찾는 점진적 밀도 기반 클러스터링 알고리즘입니다. 해당 알고리즘은 클러스터 업데이트 시에 발생하는 중복 문제들에 초점을 둡니다. 밀도 기반 클러스터링에서는 여러 데이터 점들을 개별적으로 삽입 혹은 삭제할 때 주변 점들을 불필요하게 중복적으로 탐색하고 회수합니다. DISC 는 배치 업데이트로 이 문제를 해결하여 성능을 향상시키며 여러 최적화 방법들을 제안합니다. 두 번째 알고리즘인 DenForest 는 삭제 과정에 초점을 둔 점진적 밀도 기반 클러스터링 알고리즘입니다. 클러스터를 그래프로 관리하는 이전 방법들과 달리 DenForest 는 클러스터를 신장 트리의 그룹으로 관리함으로써 효율적인 삭제 성능에 기여합니다. 나아가 배치 최적화 기법을 통해 삽입 성능 향상에도 기여합니다. 두 알고리즘의 효율성을 입증하기 위해 광범위한 평가를 수행하였으며 DISC 및 DenForest 는 최신의 밀도 기반 클러스터링 알고리즘들보다 뛰어난 성능을 보여주었습니다.1 Introduction 1 1.1 Overview of Dissertation 3 2 Related Works 7 2.1 Clustering 7 2.2 Density-Based Clustering for Static Datasets 8 2.2.1 Extension of DBSCAN 8 2.2.2 Approximation of Density-Based Clustering 9 2.2.3 Parallelization of Density-Based Clustering 10 2.3 Incremental Density-Based Clustering 10 2.3.1 Approximated Density-Based Clustering for Dynamic Datasets 11 2.4 Density-Based Clustering for Data Streams 11 2.4.1 Micro-clusters 12 2.4.2 Density-Based Clustering in Damped Window Model 12 2.4.3 Density-Based Clustering in Sliding Window Model 13 2.5 Non-Density-Based Clustering 14 2.5.1 Partitional Clustering and Hierarchical Clustering 14 2.5.2 Distribution-Based Clustering 15 2.5.3 High-Dimensional Data Clustering 15 2.5.4 Spectral Clustering 16 3 Background 17 3.1 DBSCAN 17 3.1.1 Reformulation of Density-Based Clustering 19 3.2 Incremental DBSCAN 20 3.3 Sliding Windows 22 3.3.1 Density-Based Clustering over Sliding Windows 23 3.3.2 Slow Deletion Problem 24 4 Avoiding Redundant Searches in Updating Clusters 26 4.1 The DISC Algorithm 27 4.1.1 Overview of DISC 27 4.1.2 COLLECT 29 4.1.3 CLUSTER 30 4.1.3.1 Splitting a Cluster 32 4.1.3.2 Merging Clusters 37 4.1.4 Horizontal Manner vs. Vertical Manner 38 4.2 Checking Reachability 39 4.2.1 Multi-Starter BFS 40 4.2.2 Epoch-Based Probing of R-tree Index 41 4.3 Updating Labels 43 5 Avoiding Graph Traversals in Updating Clusters 45 5.1 The DenForest Algorithm 46 5.1.1 Overview of DenForest 47 5.1.1.1 Supported Types of the Sliding Window Model 48 5.1.2 Nostalgic Core and Density-based Clusters 49 5.1.2.1 Cluster Membership of Border 51 5.1.3 DenTree 51 5.2 Operations of DenForest 54 5.2.1 Insertion 54 5.2.1.1 MST based on Link-Cut Tree 57 5.2.1.2 Time Complexity of Insert Operation 58 5.2.2 Deletion 59 5.2.2.1 Time Complexity of Delete Operation 61 5.2.3 Insertion/Deletion Examples 64 5.2.4 Cluster Membership 65 5.2.5 Batch-Optimized Update 65 5.3 Clustering Quality of DenForest 68 5.3.1 Clustering Quality for Static Data 68 5.3.2 Discussion 70 5.3.3 Replaceability 70 5.3.3.1 Nostalgic Cores and Density 71 5.3.3.2 Nostalgic Cores and Quality 72 5.3.4 1D Example 74 6 Evaluation 76 6.1 Real-World Datasets 76 6.2 Competing Methods 77 6.2.1 Exact Methods 77 6.2.2 Non-Exact Methods 77 6.3 Experimental Settings 78 6.4 Evaluation of DISC 78 6.4.1 Parameters 79 6.4.2 Baseline Evaluation 79 6.4.3 Drilled-Down Evaluation 82 6.4.3.1 Effects of Threshold Values 82 6.4.3.2 Insertions vs. Deletions 83 6.4.3.3 Range Searches 84 6.4.3.4 MS-BFS and Epoch-Based Probing 85 6.4.4 Comparison with Summarization/Approximation-Based Methods 86 6.5 Evaluation of DenForest 90 6.5.1 Parameters 90 6.5.2 Baseline Evaluation 91 6.5.3 Drilled-Down Evaluation 94 6.5.3.1 Varying Size of Window/Stride 94 6.5.3.2 Effect of Density and Distance Thresholds 95 6.5.3.3 Memory Usage 98 6.5.3.4 Clustering Quality over Sliding Windows 98 6.5.3.5 Clustering Quality under Various Density and Distance Thresholds 101 6.5.3.6 Relaxed Parameter Settings 102 6.5.4 Comparison with Summarization-Based Methods 102 7 Future Work: Extension to Varying/Relative Densities 105 8 Conclusion 107 Abstract (In Korean) 120박

On the tradeoff between stability and fit

In computing, as in many aspects of life, changes incur cost. Many optimization problems are formulated as a one-time instance starting from scratch. However, a common case that arises is when we already have a set of prior assignments and must decide how to respond to a new set of constraints, given that each change from the current assignment comes at a price. That is, we would like to maximize the fitness or efficiency of our system, but we need to balance it with the changeout cost from the previous state. We provide a precise formulation for this tradeoff and analyze the resulting stable extensions of some fundamental problems in measurement and analytics. Our main technical contribution is a stable extension of Probability Proportional to Size (PPS) weighted random sampling, with applications to monitoring and anomaly detection problems. We also provide a general framework that applies to top-k, minimum spanning tree, and assignment. In both cases, we are able to provide exact solutions and discuss efficient incremental algorithms that can find new solutions as the input changes

Models and Algorithms for Persistent Queries over Streaming Graphs

It is natural to model and represent interaction data as graphs in a broad range of domains such as online social networks, protein interaction data, and e-commerce applications. A number of emerging applications require continuous processing and querying of interaction data that evolves at a high rate, in near real-time, which can be modelled as a streaming graph. Persistent queries, where queries are registered into the system and new results are generated incrementally as the graph edges arrive, facilitate online analysis and real-time monitoring over streaming data. Processing persistent queries over streaming graphs combines two seemingly different but challenging problems: graph querying and streaming processing. Existing systems fail to support these workloads due to (i) the complexity of graph queries that feature recursive path navigations, subgraph patterns, and path manipulation, and (ii) the unboundedness and growth rate of streaming graphs that make it infeasible to employ batch algorithms. Consequently, a growing number of applications rely on specialized solutions tailored to specific application needs. This thesis introduces foundational techniques for efficient processing of persistent queries over streaming graphs to support this emerging class of applications in a principled manner. The main contribution of this thesis is the design and development of a general-purpose streaming graph query processing framework. The novel challenges of persistent queries over streaming graphs dictate rethinking the components of the well-established query processor architecture, and this thesis introduces the models and algorithms to address these challenges uniformly. The central notion of Streaming Graph Query precisely characterizes the semantics of persistent queries over streaming graphs, making it possible to reason about the expressiveness and the complexity of queries targeted by the aforementioned applications. Streaming Graph Algebra, defined as a closure of a set of operators over streaming graphs, provides the primitive building blocks for evaluating and optimizing streaming graph queries. Efficient, incremental algorithms as the physical implementations of streaming graph algebra operators are provided, enabling streaming graph queries to be evaluated in a data-driven fashion. It is shown that the proposed algebra constitutes the foundational tool for the cost-based optimization of streaming graph queries by providing an algebraic basis for query evaluation. Overall, this thesis provides principled solutions to fundamental challenges for efficient querying of streaming graphs and describes the design and implementation of a general-purpose streaming graph query processing framework

Scalable Statistical Modeling and Query Processing over Large Scale Uncertain Databases

The past decade has witnessed a large number of novel applications that generate imprecise, uncertain and incomplete data. Examples include monitoring infrastructures such as RFIDs, sensor networks and web-based applications such as information extraction, data integration, social networking and so on. In my dissertation, I addressed several challenges in managing such data and developed algorithms for efficiently executing queries over large volumes of such data. Specifically, I focused on the following challenges. First, for meaningful analysis of such data, we need the ability to remove noise and infer useful information from uncertain data. To address this challenge, I first developed a declarative system for applying dynamic probabilistic models to databases and data streams. The output of such probabilistic modeling is probabilistic data, i.e., data annotated with probabilities of correctness/existence. Often, the data also exhibits strong correlations. Although there is prior work in managing and querying such probabilistic data using probabilistic databases, those approaches largely assume independence and cannot handle probabilistic data with rich correlation structures. Hence, I built a probabilistic database system that can manage large-scale correlations and developed algorithms for efficient query evaluation. Our system allows users to provide uncertain data as input and to specify arbitrary correlations among the entries in the database. In the back end, we represent correlations as a forest of junction trees, an alternative representation for probabilistic graphical models (PGM). We execute queries over the probabilistic database by transforming them into message passing algorithms (inference) over the junction tree. However, traditional algorithms over junction trees typically require accessing the entire tree, even for small queries. Hence, I developed an index data structure over the junction tree called INDSEP that allows us to circumvent this process and thereby scalably evaluate inference queries, aggregation queries and SQL queries over the probabilistic database. Finally, query evaluation in probabilistic databases typically returns output tuples along with their probability values. However, the existing query evaluation model provides very little intuition to the users: for instance, a user might want to know Why is this tuple in my result? or Why does this output tuple have such high probability? or Which are the most influential input tuples for my query ?'' Hence, I designed a query evaluation model, and a suite of algorithms, that provide users with explanations for query results, and enable users to perform sensitivity analysis to better understand the query results

Data Stream Clustering: A Review

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, such as concept drift, data structures for data streams, time window models and outlier detection. We comprehensively review recent data stream clustering algorithms and analyze them in terms of the base clustering technique, computational complexity and clustering accuracy. A comparison of these algorithms is given along with still open problems. We indicate popular data stream repositories and datasets, stream processing tools and platforms. Open problems about data stream clustering are also discussed.Comment: Has been accepted for publication in Artificial Intelligence Revie

Provably-Efficient and Internally-Deterministic Parallel Union-Find

Determining the degree of inherent parallelism in classical sequential algorithms and leveraging it for fast parallel execution is a key topic in parallel computing, and detailed analyses are known for a wide range of classical algorithms. In this paper, we perform the first such analysis for the fundamental Union-Find problem, in which we are given a graph as a sequence of edges, and must maintain its connectivity structure under edge additions. We prove that classic sequential algorithms for this problem are well-parallelizable under reasonable assumptions, addressing a conjecture by [Blelloch, 2017]. More precisely, we show via a new potential argument that, under uniform random edge ordering, parallel union-find operations are unlikely to interfere: $T$ concurrent threads processing the graph in parallel will encounter memory contention $O(T^2 \cdot \log |V| \cdot \log |E|)$ times in expectation, where $|E|$ and $|V|$ are the number of edges and nodes in the graph, respectively. We leverage this result to design a new parallel Union-Find algorithm that is both internally deterministic, i.e., its results are guaranteed to match those of a sequential execution, but also work-efficient and scalable, as long as the number of threads $T$ is $O(|E|^{\frac{1}{3} - \varepsilon})$, for an arbitrarily small constant $\varepsilon > 0$, which holds for most large real-world graphs. We present lower bounds which show that our analysis is close to optimal, and experimental results suggesting that the performance cost of internal determinism is limited

Pattern mining under different conditions

New requirements and demands on pattern mining arise in modern applications, which cannot be fulfilled using conventional methods. For example, in scientific research, scientists are more interested in unknown knowledge, which usually hides in significant but not frequent patterns. However, existing itemset mining algorithms are designed for very frequent patterns. Furthermore, scientists need to repeat an experiment many times to ensure reproducibility. A series of datasets are generated at once, waiting for clustering, which can contain an unknown number of clusters with various densities and shapes. Using existing clustering algorithms is time-consuming because parameter tuning is necessary for each dataset. Many scientific datasets are extremely noisy. They contain considerably more noises than in-cluster data points. Most existing clustering algorithms can only handle noises up to a moderate level. Temporal pattern mining is also important in scientific research. Existing temporal pattern mining algorithms only consider pointbased events. However, most activities in the real-world are interval-based with a starting and an ending timestamp. This thesis developed novel pattern mining algorithms for various data mining tasks under different conditions. The first part of this thesis investigates the problem of mining less frequent itemsets in transactional datasets. In contrast to existing frequent itemset mining algorithms, this part focus on itemsets that occurred not that frequent. Algorithms NIIMiner, RaCloMiner, and LSCMiner are proposed to identify such kind of itemsets efficiently. NIIMiner utilizes the negative itemset tree to extract all patterns that occurred less than a given support threshold in a top-down depth-first manner. RaCloMiner combines existing bottom-up frequent itemset mining algorithms with a top-down itemset mining algorithm to achieve a better performance in mining less frequent patterns. LSCMiner investigates the problem of mining less frequent closed patterns. The second part of this thesis studied the problem of interval-based temporal pattern mining in the stream environment. Interval-based temporal patterns are sequential patterns in which each event is aligned with a starting and ending temporal information. The ability to handle interval-based events and stream data is lacking in existing approaches. A novel intervalbased temporal pattern mining algorithm for stream data is described in this part. The last part of this thesis studies new problems in clustering on numeric datasets. The first problem tackled in this part is shape alternation adaptivity in clustering. In applications such as scientific data analysis, scientists need to deal with a series of datasets generated from one experiment. Cluster sizes and shapes are different in those datasets. A kNN density-based clustering algorithm, kadaClus, is proposed to provide the shape alternation adaptability so that users do not need to tune parameters for each dataset. The second problem studied in this part is clustering in an extremely noisy dataset. Many real-world datasets contain considerably more noises than in-cluster data points. A novel clustering algorithm, kenClus, is proposed to identify clusters in arbitrary shapes from extremely noisy datasets. Both clustering algorithms are kNN-based, which only require one parameter k. In each part, the efficiency and effectiveness of the presented techniques are thoroughly analyzed. Intensive experiments on synthetic and real-world datasets are conducted to show the benefits of the proposed algorithms over conventional approaches

A Survey on Behavioral Pattern Mining from Sensor Data in Internet of Things

The deployment of large-scale wireless sensor networks (WSNs) for the Internet of Things (IoT) applications is increasing day-by-day, especially with the emergence of smart city services. The sensor data streams generated from these applications are largely dynamic, heterogeneous, and often geographically distributed over large areas. For high-value use in business, industry and services, these data streams must be mined to extract insightful knowledge, such as about monitoring (e.g., discovering certain behaviors over a deployed area) or network diagnostics (e.g., predicting faulty sensor nodes). However, due to the inherent constraints of sensor networks and application requirements, traditional data mining techniques cannot be directly used to mine IoT data streams efficiently and accurately in real-time. In the last decade, a number of works have been reported in the literature proposing behavioral pattern mining algorithms for sensor networks. This paper presents the technical challenges that need to be considered for mining sensor data. It then provides a thorough review of the mining techniques proposed in the recent literature to mine behavioral patterns from sensor data in IoT, and their characteristics and differences are highlighted and compared. We also propose a behavioral pattern mining framework for IoT and discuss possible future research directions in this area. © 2013 IEEE

Learning in Dynamic Data-Streams with a Scarcity of Labels

Analysing data in real-time is a natural and necessary progression from traditional data mining. However, real-time analysis presents additional challenges to batch-analysis; along with strict time and memory constraints, change is a major consideration. In a dynamic stream there is an assumption that the underlying process generating the stream is non-stationary and that concepts within the stream will drift and change over time. Adopting a false assumption that a stream is stationary will result in non-adaptive models degrading and eventually becoming obsolete. The challenge of recognising and reacting to change in a stream is compounded by the scarcity of labels problem. This refers to the very realistic situation in which the true class label of an incoming point is not immediately available (or will never be available) or in situations where manually labelling incoming points is prohibitively expensive. The goal of this thesis is to evaluate unsupervised learning as the basis for online classification in dynamic data-streams with a scarcity of labels. To realise this goal, a novel stream clustering algorithm based on the collective behaviour of ants (Ant Colony Stream Clustering (ACSC)) is proposed. This algorithm is shown to be faster and more accurate than comparative, peer stream-clustering algorithms while requiring fewer sensitive parameters. The principles of ACSC are extended in a second stream-clustering algorithm named Multi-Density Stream Clustering (MDSC). This algorithm has adaptive parameters and crucially, can track clusters and monitor their dynamic behaviour over time. A novel technique called a Dynamic Feature Mask (DFM) is proposed to ``sit on top’’ of these stream-clustering algorithms and can be used to observe and track change at the feature level in a data stream. This Feature Mask acts as an unsupervised feature selection method allowing high-dimensional streams to be clustered. Finally, data-stream clustering is evaluated as an approach to one-class classification and a novel framework (named COCEL: Clustering and One class Classification Ensemble Learning) for classification in dynamic streams with a scarcity of labels is described. The proposed framework can identify and react to change in a stream and hugely reduces the number of required labels (typically less than 0.05% of the entire stream)