Diamond-based models for scientific visualization

Hierarchical spatial decompositions are a basic modeling tool in a variety of application domains including scientific visualization, finite element analysis and shape modeling and analysis. A popular class of such approaches is based on the regular simplex bisection operator, which bisects simplices (e.g. line segments, triangles, tetrahedra) along the midpoint of a predetermined edge. Regular simplex bisection produces adaptive simplicial meshes of high geometric quality, while simplifying the extraction of crack-free, or conforming, approximations to the original dataset. Efficient multiresolution representations for such models have been achieved in 2D and 3D by clustering sets of simplices sharing the same bisection edge into structures called diamonds. In this thesis, we introduce several diamond-based approaches for scientific visualization. We first formalize the notion of diamonds in arbitrary dimensions in terms of two related simplicial decompositions of hypercubes. This enables us to enumerate the vertices, simplices, parents and children of a diamond. In particular, we identify the number of simplices involved in conforming updates to be factorial in the dimension and group these into a linear number of subclusters of simplices that are generated simultaneously. The latter form the basis for a compact pointerless representation for conforming meshes generated by regular simplex bisection and for efficiently navigating the topological connectivity of these meshes. Secondly, we introduce the supercube as a high-level primitive on such nested meshes based on the atomic units within the underlying triangulation grid. We propose the use of supercubes to associate information with coherent subsets of the full hierarchy and demonstrate the effectiveness of such a representation for modeling multiresolution terrain and volumetric datasets. Next, we introduce Isodiamond Hierarchies, a general framework for spatial access structures on a hierarchy of diamonds that exploits the implicit hierarchical and geometric relationships of the diamond model. We use an isodiamond hierarchy to encode irregular updates to a multiresolution isosurface or interval volume in terms of regular updates to diamonds. Finally, we consider nested hypercubic meshes, such as quadtrees, octrees and their higher dimensional analogues, through the lens of diamond hierarchies. This allows us to determine the relationships involved in generating balanced hypercubic meshes and to propose a compact pointerless representation of such meshes. We also provide a local diamond-based triangulation algorithm to generate high-quality conforming simplicial meshes

Efficient computation of partition of unity interpolants through a block-based searching technique

In this paper we propose a new efficient interpolation tool, extremely suitable for large scattered data sets. The partition of unity method is used and performed by blending Radial Basis Functions (RBFs) as local approximants and using locally supported weight functions. In particular we present a new space-partitioning data structure based on a partition of the underlying generic domain in blocks. This approach allows us to examine only a reduced number of blocks in the search process of the nearest neighbour points, leading to an optimized searching routine. Complexity analysis and numerical experiments in two- and three-dimensional interpolation support our findings. Some applications to geometric modelling are also considered. Moreover, the associated software package written in \textsc{Matlab} is here discussed and made available to the scientific community

대용량 데이터 탐색을 위한 점진적 시각화 시스템 설계

학위논문(박사)--서울대학교 대학원 :공과대학 컴퓨터공학부,2020. 2. 서진욱.Understanding data through interactive visualization, also known as visual analytics, is a common and necessary practice in modern data science. However, as data sizes have increased at unprecedented rates, the computation latency of visualization systems becomes a significant hurdle to visual analytics. The goal of this dissertation is to design a series of systems for progressive visual analytics (PVA)—a visual analytics paradigm that can provide intermediate results during computation and allow visual exploration of these results—to address the scalability hurdle. To support the interactive exploration of data with billions of records, we first introduce SwiftTuna, an interactive visualization system with scalable visualization and computation components. Our performance benchmark demonstrates that it can handle data with four billion records, giving responsive feedback every few seconds without precomputation. Second, we present PANENE, a progressive algorithm for the Approximate k-Nearest Neighbor (AKNN) problem. PANENE brings useful machine learning methods into visual analytics, which has been challenging due to their long initial latency resulting from AKNN computation. In particular, we accelerate t-Distributed Stochastic Neighbor Embedding (t-SNE), a popular non-linear dimensionality reduction technique, which enables the responsive visualization of data with a few hundred columns. Each of these two contributions aims to address the scalability issues stemming from a large number of rows or columns in data, respectively. Third, from the users' perspective, we focus on improving the trustworthiness of intermediate knowledge gained from uncertain results in PVA. We propose a novel PVA concept, Progressive Visual Analytics with Safeguards, and introduce PVA-Guards, safeguards people can leave on uncertain intermediate knowledge that needs to be verified. We also present a proof-of-concept system, ProReveal, designed and developed to integrate seven safeguards into progressive data exploration. Our user study demonstrates that people not only successfully created PVA-Guards on ProReveal but also voluntarily used PVA-Guards to manage the uncertainty of their knowledge. Finally, summarizing the three studies, we discuss design challenges for progressive systems as well as future research agendas for PVA.현대 데이터 사이언스에서 인터랙티브한 시각화를 통해 데이터를 이해하는 것은 필수적인 분석 방법 중 하나이다. 그러나, 최근 데이터의 크기가 폭발적으로 증가하면서 데이터 크기로 인해 발생하는 지연 시간이 인터랙티브한 시각적 분석에 큰 걸림돌이 되었다. 본 연구에서는 이러한 확장성 문제를 해결하기 위해 점진적 시각적 분석(Progressive Visual Analytics)을 지원하는 일련의 시스템을 디자인하고 개발한다. 이러한 점진적 시각적 분석 시스템은 데이터 처리가 완전히 끝나지 않더라도 중간 분석 결과를 사용자에게 제공함으로써 데이터의 크기로 인해 발생하는 지연 시간 문제를 완화할 수 있다. 첫째로, 수십억 건의 행을 가지는 데이터를 시각적으로 탐색할 수 있는 SwiftTuna 시스템을 제안한다. 데이터 처리 및 시각적 표현의 확장성을 목표로 개발된 이 시스템은, 약 40억 건의 행을 가진 데이터에 대한 시각화를 전처리 없이 수 초마다 업데이트할 수 있는 것으로 나타났다. 둘째로, 근사적 k-최근접점(Approximate k-Nearest Neighbor) 문제를 점진적으로 계산하는 PANENE 알고리즘을 제안한다. 근사적 k-최근접점 문제는 여러 기계 학습 기법에서 쓰임에도 불구하고 초기 계산 시간이 길어서 인터랙티브한 시스템에 적용하기 힘든 한계가 있었다. PANENE 알고리즘은 이러한 긴 초기 계산 시간을 획기적으로 개선하여 다양한 기계 학습 기법을 시각적 분석에 활용할 수 있도록 한다. 특히, 유용한 비선형적 차원 감소 기법인 t-분포 확률적 임베딩(t-Distributed Stochastic Neighbor Embedding)을 가속하여 수백 개의 차원을 가지는 데이터를 빠른 시간 내에 사영할 수 있다. 위의 두 시스템과 알고리즘이 데이터의 행 또는 열의 개수로 인한 확장성 문제를 해결하고자 했다면, 세 번째 시스템에서는 점진적 시각적 분석의 신뢰도 문제를 개선하고자 한다. 점진적 시각적 분석에서 사용자에게 주어지는 중간 계산 결과는 최종 결과의 근사치이므로 불확실성이 존재한다. 본 연구에서는 세이프가드를 이용한 점진적 시각적 분석(Progressive Visual Analytics with Safeguards)이라는 새로운 개념을 제안한다. 이 개념은 사용자가 점진적 탐색에서 마주하는 불확실한 중간 지식에 세이프가드를 남길 수 있도록 하여 탐색에서 얻은 지식의 정확도를 추후 검증할 수 있도록 한다. 또한, 이러한 개념을 실제로 구현하여 탑재한 ProReveal 시스템을 소개한다. ProReveal를 이용한 사용자 실험에서 사용자들은 세이프가드를 성공적으로 만들 수 있었을 뿐만 아니라, 중간 지식의 불확실성을 다루기 위해 세이프가드를 자발적으로 이용한다는 것을 알 수 있었다. 마지막으로, 위 세 가지 연구의 결과를 종합하여 점진적 시각적 분석 시스템을 구현할 때의 디자인적 난제와 향후 연구 방향을 모색한다.CHAPTER1. Introduction 2 1.1 Background and Motivation 2 1.2 Thesis Statement and Research Questions 5 1.3 Thesis Contributions 5 1.3.1 Responsive and Incremental Visual Exploration of Large-scale Multidimensional Data 6 1.3.2 ProgressiveComputation of Approximate k-Nearest Neighbors and Responsive t-SNE 7 1.3.3 Progressive Visual Analytics with Safeguards 8 1.4 Structure of Dissertation 9 CHAPTER2. Related Work 11 2.1 Progressive Visual Analytics 11 2.1.1 Definitions 11 2.1.2 System Latency and Human Factors 13 2.1.3 Users, Tasks, and Models 15 2.1.4 Techniques, Algorithms, and Systems. 17 2.1.5 Uncertainty Visualization 19 2.2 Approaches for Scalable Visualization Systems 20 2.3 The k-Nearest Neighbor (KNN) Problem 22 2.4 t-Distributed Stochastic Neighbor Embedding 26 CHAPTER3. SwiTuna: Responsive and Incremental Visual Exploration of Large-scale Multidimensional Data 28 3.1 The SwiTuna Design 31 3.1.1 Design Considerations 32 3.1.2 System Overview 33 3.1.3 Scalable Visualization Components 36 3.1.4 Visualization Cards 40 3.1.5 User Interface and Interaction 42 3.2 Responsive Querying 44 3.2.1 Querying Pipeline 44 3.2.2 Prompt Responses 47 3.2.3 Incremental Processing 47 3.3 Evaluation: Performance Benchmark 49 3.3.1 Study Design 49 3.3.2 Results and Discussion 52 3.4 Implementation 56 3.5 Summary 56 CHAPTER4. PANENE:AProgressive Algorithm for IndexingandQuerying Approximate k-Nearest Neighbors 58 4.1 Approximate k-Nearest Neighbor 61 4.1.1 A Sequential Algorithm 62 4.1.2 An Online Algorithm 63 4.1.3 A Progressive Algorithm 66 4.1.4 Filtered AKNN Search 71 4.2 k-Nearest Neighbor Lookup Table 72 4.3 Benchmark. 78 4.3.1 Online and Progressive k-d Trees 78 4.3.2 k-Nearest Neighbor Lookup Tables 83 4.4 Applications 85 4.4.1 Progressive Regression and Density Estimation 85 4.4.2 Responsive t-SNE 87 4.5 Implementation 92 4.6 Discussion 92 4.7 Summary 93 CHAPTER5. ProReveal: Progressive Visual Analytics with Safeguards 95 5.1 Progressive Visual Analytics with Safeguards 98 5.1.1 Definition 98 5.1.2 Examples 101 5.1.3 Design Considerations 103 5.2 ProReveal 105 5.3 Evaluation 121 5.4 Discussion 127 5.5 Summary 130 CHAPTER6. Discussion 132 6.1 Lessons Learned 132 6.2 Limitations 135 CHAPTER7. Conclusion 137 7.1 Thesis Contributions Revisited 137 7.2 Future Research Agenda 139 7.3 Final Remarks 141 Abstract (Korean) 155 Acknowledgments (Korean) 157Docto

The use of alternative data models in data warehousing environments

Data Warehouses are increasing their data volume at an accelerated rate; high disk space consumption; slow query response time and complex database administration are common problems in these environments. The lack of a proper data model and an adequate architecture specifically targeted towards these environments are the root causes of these problems. Inefficient management of stored data includes duplicate values at column level and poor management of data sparsity which derives from a low data density, and affects the final size of Data Warehouses. It has been demonstrated that the Relational Model and Relational technology are not the best techniques for managing duplicates and data sparsity. The novelty of this research is to compare some data models considering their data density and their data sparsity management to optimise Data Warehouse environments. The Binary-Relational, the Associative/Triple Store and the Transrelational models have been investigated and based on the research results a novel Alternative Data Warehouse Reference architectural configuration has been defined. For the Transrelational model, no database implementation existed. Therefore it was necessary to develop an instantiation of it’s storage mechanism, and as far as could be determined this is the first public domain instantiation available of the storage mechanism for the Transrelational model