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

Studying Community Dynamics with an Incremental Graph Mining Algorithm

The widespread usage of the Web and later of the Web 2.0 for social interactions has stimulated scholars of different disciplines in studying electronic communities. Traditionally, communities are observed as a static phenomenon. However, they are evolving constellations, which emerge, lose members and obtain new ones and potentially, grow, coerce, split or decline. Such dynamic phenomena require the study of social networks across the time axis. We propose the graph mining algorithm DENGRAPH for the discovery and monitoring of evolving communities. Data mining methods are successfully used for community discovery but are mostly limited to the static perspective. Taking a dynamic perspective implies the study of a stream of interactions among community members. Accordingly, our DENGRAPH is an incremental graph mining algorithm, which detects and adapts communities over time. We report on our first results in applying DENGRAPH on the social network of mail interactions of ENRON

Coping With New Challengens for Density-Based Clustering

Knowledge Discovery in Databases (KDD) is the non-trivial process of identifying valid, novel, potentially useful, and ultimately understandable patterns in data. The core step of the KDD process is the application of a Data Mining algorithm in order to produce a particular enumeration of patterns and relationships in large databases. Clustering is one of the major data mining tasks and aims at grouping the data objects into meaningful classes (clusters) such that the similarity of objects within clusters is maximized, and the similarity of objects from different clusters is minimized. Beside many others, the density-based clustering notion underlying the algorithm DBSCAN and its hierarchical extension OPTICS has been proposed recently, being one of the most successful approaches to clustering. In this thesis, our aim is to advance the state-of-the-art clustering, especially density-based clustering by identifying novel challenges for density-based clustering and proposing innovative and solid solutions for these challenges. We describe the development of the industrial prototype BOSS (Browsing OPTICS plots for Similarity Search) which is a first step towards developing a comprehensive, scalable and distributed computing solution designed to make the efficiency and analytical capabilities of OPTICS available to a broader audience. For the development of BOSS, several key enhancements of OPTICS are required which are addressed in this thesis. We develop incremental algorithms of OPTICS to efficiently reconstruct the hierarchical clustering structure in frequently updated databases, in particular, when a set of objects is inserted in or deleted from the database. We empirically show that these incremental algorithms yield significant speed-up factors over the original OPTICS algorithm. Furthermore, we propose a novel algorithm for automatic extraction of clusters from hierarchical clustering representations that outperforms comparative methods, and introduce two novel approaches for selecting meaningful representatives, using the density-based concepts of OPTICS and producing better results than the related medoid approach. Another major challenge for density-based clustering is to cope with high dimensional data. Many today's real-world data sets contain a large number of measurements (or features) for a single data object. Usually, global feature reduction techniques cannot be applied to these data sets. Thus, the task of feature selection must be combined with and incooperated into the clustering process. In this thesis, we present original extensions and enhancements of the density-based clustering notion to cope with high dimensional data. In particular, we propose an algorithm called SUBCLU (density based SUBspace CLUstering) that extends DBSCAN to the problem of subspace clustering. SUBCLU efficiently computes all clusters that would have been found if DBSCAN is applied to all possible subspaces of the feature space. An experimental evaluation on real-world data sets illustrates that SUBCLU is more effective than existing subspace clustering algorithms because it is able to find clusters of arbitrary size and shape, and produces determine results. A semi-hierarchical extension of SUBCLU called RIS (Ranking Interesting Subspaces) is proposed that does not compute the subspace clusters directly, but generates a list of subspaces ranked by their clustering characteristics. A hierarchical clustering algorithm can be applied to these interesting subspaces in order to compute a hierarchical (subspace) clustering. A comparative evaluation of RIS and SUBCLU shows that RIS in combination with OPTICS can achieve an information gain over SUBCLU. In addition, we propose the algorithm 4C (Computing Correlation Connected Clusters) that extends the concepts of DBSCAN to compute density-based correlation clusters. 4C benefits from an innovative, well-defined and effective clustering model, outperforming related approaches in terms of clustering quality on real-world data sets.Knowledge Discovery in Databases (KDD) ist der Prozess der (semi-)automatischen Extraktion von Wissen aus Datenbanken, das gültig, bisher unbekannt und potentiell nützlich für eine gegebene Anwendung ist. Der zentrale Schritt des KDD-Prozesses ist das Data Mining. Eine der wichtigsten Aufgaben des Data Mining ist Clustering. Dabei sollen die Objekte einer Datenbank in Gruppen (Cluster) partitioniert werden, so dass Objekte eines Clusters möglichst ähnlich und Objekte verschiedener Cluster möglichst unähnlich zu einander sind. Das dichtebasierte Clustermodell und die darauf aufbauenden Algorithmen DBSCAN und OPTICS sind unter einer Vielzahl anderer Clustering-Ansätze eine der erfolgreichsten Methoden zum Clustering. Im Rahmen dieser Dissertation wollen wir den aktuellen Stand der Technik im Bereich Clustering und speziell im Bereich dichtebasiertes Clustering voranbringen. Dazu erarbeiten wir neue Herausforderungen für das dichtebasierte Clustermodell und schlagen dazu innovative Lösungen vor. Zunächst steht die Entwicklung des industriellen Prototyps BOSS (Browsing OPTICS plots for Similarity Search) im Mittelpunkt dieser Arbeit. BOSS ist ein erster Beitrag zu einer umfassenden, skalierbaren und verteilten Softwarelösung, die eine Nutzung der Effizienzvorteile und die analytischen Möglichkeiten des dichtebasierten, hierarchischen Clustering-Algorithmus OPTICS für ein breites Publikum ermöglichen. Zur Entwicklung von BOSS werden drei entscheidende Erweiterungen von OPTICS benötigt: Wir entwickeln eine inkrementelle Version von OPTICS um nach einem Update der Datenbank (Einfügen/Löschen einer Menge von Objekten) die hierarchische Clustering Struktur effizient zu reorganisieren. Anhand von Experimenten mit synthetischen und realen Daten zeigen wir, dass die vorgeschlagenen, inkrementellen Algorithmen deutliche Beschleunigungsfaktoren gegenüber dem originalen OPTICS-Algorithmus erzielen. Desweiteren schlagen wir einen neuen Algorithmus zur automatischen Clusterextraktion aus hierarchischen Repräsentationen und zwei innovative Methoden zur automatischen Auswahl geeigneter Clusterrepräsentaten vor. Unsere neuen Techniken erzielen bei Tests auf mehreren realen Datenbanken im Vergleich zu den konkurrierenden Verfahren bessere Ergebnisse. Eine weitere Herausforderung für Clustering-Verfahren stellen hochdimensionale Featureräume dar. Reale Datensätze beinhalten dank moderner Verfahren zur Datenerhebung häufig sehr viele Merkmale. Teile dieser Merkmale unterliegen oft Rauschen oder Abhängigkeiten und können meist nicht im Vorfeld ausgesiebt werden, da diese Effekte jeweils in Teilen der Datenbank unterschiedlich ausgeprägt sind. Daher muss die Wahl der Features mit dem Data-Mining-Verfahren verknüpft werden. Im Rahmen dieser Arbeit stellen wir innovative Erweiterungen des dichtebasierten Clustermodells für hochdimensionale Daten vor. Wir entwickeln SUBCLU (dichtebasiertes SUBspace CLUstering), ein auf DBSCAN basierender Subspace Clustering Algorithmus. SUBCLU erzeugt effizient alle Cluster, die gefunden werden, wenn man DBSCAN auf alle möglichen Teilräume des Datensatzes anwendet. Experimente auf realen Daten zeigen, dass SUBCLU effektiver als vergleichbare Algorithmen ist. RIS (Ranking Interesting Subspaces), eine semi-hierarchische Erweiterung von SUBCLU, wird vorgeschlagen, das nicht mehr direkt die Teilraumcluster berechnet, sondern eine Liste von Teilräumen geordnet anhand ihrer Clustering-Qualität erzeugt. Dadurch können hierarchische Partitionierungen auf ausgewählten Teilräumen erzeugt werden. Experimente belegen, dass RIS in Kombination mit OPTICS ein Informationsgewinn gegenüber SUBCLU erreicht. Außerdem stellen wir den neuartigen Korrelationscluster Algorithmus 4C (Computing Correlation Connected Clusters) vor. 4C basiert auf einem innovativen und wohldefinierten Clustermodell und erzielt in unseren Experimenten mit realen Daten bessere Ergebnisse als vergleichbare Clustering-Ansätze

High accuracy context recovery using clustering mechanisms

This paper examines the recovery of user context in indoor environmnents with existing wireless infrastructures to enable assistive systems. We present a novel approach to the extraction of user context, casting the problem of context recovery as an unsupervised, clustering problem. A well known density-based clustering technique, DBSCAN, is adapted to recover user context that includes user motion state, and significant places the user visits from WiFi observations consisting of access point id and signal strength. Furthermore, user rhythms or sequences of places the user visits periodically are derived from the above low level contexts by employing state-of-the-art probabilistic clustering technique, the Latent Dirichiet Allocation (LDA), to enable a variety of application services. Experimental results with real data are presented to validate the proposed unsupervised learning approach and demonstrate its applicability.<br /

Representative Points and Cluster Attributes Based Incremental Sequence Clustering Algorithm

In order to improve the execution time and clustering quality of sequence clustering algorithm in large-scale dynamic dataset, a novel algorithm RPCAISC (Representative Points and Cluster Attributes Based Incremental Sequence Clustering) was presented. In this paper, density factor is defined. The primary representative point that has a density factor less than the prescribed threshold will be deleted directly. New representative points can be reselected from non-representative points. Moreover, the representative points of each cluster are modeled using the K-nearest neighbor method. The definition of the relevant degree (RD) between clusters was also proposed. The RD is computed by comprehensively considering the correlations of objects within a cluster and between different clusters. Then, whether the two clusters need to merge is determined. Additionally, the cluster attributes of the initial clustering are retained with this process. By calculating the matching degree between the incremental sequence and the existing cluster attributes, dynamic sequence clustering can be achieved. The theoretic experimental results and analysis prove that RPCAISC has better correct rate of clustering results and execution efficiency