Optimized Cartesian KK-Means

Product quantization-based approaches are effective to encode high-dimensional data points for approximate nearest neighbor search. The space is decomposed into a Cartesian product of low-dimensional subspaces, each of which generates a sub codebook. Data points are encoded as compact binary codes using these sub codebooks, and the distance between two data points can be approximated efficiently from their codes by the precomputed lookup tables. Traditionally, to encode a subvector of a data point in a subspace, only one sub codeword in the corresponding sub codebook is selected, which may impose strict restrictions on the search accuracy. In this paper, we propose a novel approach, named Optimized Cartesian $K$-Means (OCKM), to better encode the data points for more accurate approximate nearest neighbor search. In OCKM, multiple sub codewords are used to encode the subvector of a data point in a subspace. Each sub codeword stems from different sub codebooks in each subspace, which are optimally generated with regards to the minimization of the distortion errors. The high-dimensional data point is then encoded as the concatenation of the indices of multiple sub codewords from all the subspaces. This can provide more flexibility and lower distortion errors than traditional methods. Experimental results on the standard real-life datasets demonstrate the superiority over state-of-the-art approaches for approximate nearest neighbor search.Comment: to appear in IEEE TKDE, accepted in Apr. 201

Survey of Vector Database Management Systems

There are now over 20 commercial vector database management systems (VDBMSs), all produced within the past five years. But embedding-based retrieval has been studied for over ten years, and similarity search a staggering half century and more. Driving this shift from algorithms to systems are new data intensive applications, notably large language models, that demand vast stores of unstructured data coupled with reliable, secure, fast, and scalable query processing capability. A variety of new data management techniques now exist for addressing these needs, however there is no comprehensive survey to thoroughly review these techniques and systems. We start by identifying five main obstacles to vector data management, namely vagueness of semantic similarity, large size of vectors, high cost of similarity comparison, lack of natural partitioning that can be used for indexing, and difficulty of efficiently answering hybrid queries that require both attributes and vectors. Overcoming these obstacles has led to new approaches to query processing, storage and indexing, and query optimization and execution. For query processing, a variety of similarity scores and query types are now well understood; for storage and indexing, techniques include vector compression, namely quantization, and partitioning based on randomization, learning partitioning, and navigable partitioning; for query optimization and execution, we describe new operators for hybrid queries, as well as techniques for plan enumeration, plan selection, and hardware accelerated execution. These techniques lead to a variety of VDBMSs across a spectrum of design and runtime characteristics, including native systems specialized for vectors and extended systems that incorporate vector capabilities into existing systems. We then discuss benchmarks, and finally we outline research challenges and point the direction for future work.Comment: 25 page

Relative NN-Descent: A Fast Index Construction for Graph-Based Approximate Nearest Neighbor Search

Approximate Nearest Neighbor Search (ANNS) is the task of finding the database vector that is closest to a given query vector. Graph-based ANNS is the family of methods with the best balance of accuracy and speed for million-scale datasets. However, graph-based methods have the disadvantage of long index construction time. Recently, many researchers have improved the tradeoff between accuracy and speed during a search. However, there is little research on accelerating index construction. We propose a fast graph construction algorithm, Relative NN-Descent (RNN-Descent). RNN-Descent combines NN-Descent, an algorithm for constructing approximate K-nearest neighbor graphs (K-NN graphs), and RNG Strategy, an algorithm for selecting edges effective for search. This algorithm allows the direct construction of graph-based indexes without ANNS. Experimental results demonstrated that the proposed method had the fastest index construction speed, while its search performance is comparable to existing state-of-the-art methods such as NSG. For example, in experiments on the GIST1M dataset, the construction of the proposed method is 2x faster than NSG. Additionally, it was even faster than the construction speed of NN-Descent.Comment: Accepted by ACMMM 202

Fast Neighbor Search By Using Revised K-D Tree

We present two new neighbor query algorithms, including range query (RNN) and nearest neighbor (NN) query, based on revised k-d tree by using two techniques. The first technique is proposed for decreasing unnecessary distance computations by checking whether the cell of a node is inside or outside the specified neighborhood of query point, and the other is used to reduce redundant visiting nodes by saving the indices of descendant points. We also implement the proposed algorithms in Matlab and C. The Matlab version is to improve original RNN and NN which are based on k-d tree, C version is to improve k-Nearest neighbor query (kNN) which is based on buffer k-d tree. Theoretical and experimental analysis have shown that the proposed algorithms significantly improve the original RNN, NN and kNN in low dimension, respectively. The tradeoff is that the additional space cost of the revised k-d tree is approximately O(αnlog (n))

Vector Quantization Techniques for Approximate Nearest Neighbor Search on Large-Scale Datasets

The technological developments of the last twenty years are leading the world to a new era. The invention of the internet, mobile phones and smart devices are resulting in an exponential increase in data. As the data is growing every day, finding similar patterns or matching samples to a query is no longer a simple task because of its computational costs and storage limitations. Special signal processing techniques are required in order to handle the growth in data, as simply adding more and more computers cannot keep up.Nearest neighbor search, or similarity search, proximity search or near item search is the problem of finding an item that is nearest or most similar to a query according to a distance or similarity measure. When the reference set is very large, or the distance or similarity calculation is complex, performing the nearest neighbor search can be computationally demanding. Considering today’s ever-growing datasets, where the cardinality of samples also keep increasing, a growing interest towards approximate methods has emerged in the research community.Vector Quantization for Approximate Nearest Neighbor Search (VQ for ANN) has proven to be one of the most efficient and successful methods targeting the aforementioned problem. It proposes to compress vectors into binary strings and approximate the distances between vectors using look-up tables. With this approach, the approximation of distances is very fast, while the storage space requirement of the dataset is minimized thanks to the extreme compression levels. The distance approximation performance of VQ for ANN has been shown to be sufficiently well for retrieval and classification tasks demonstrating that VQ for ANN techniques can be a good replacement for exact distance calculation methods.This thesis contributes to VQ for ANN literature by proposing five advanced techniques, which aim to provide fast and efficient approximate nearest neighbor search on very large-scale datasets. The proposed methods can be divided into two groups. The first group consists of two techniques, which propose to introduce subspace clustering to VQ for ANN. These methods are shown to give the state-of-the-art performance according to tests on prevalent large-scale benchmarks. The second group consists of three methods, which propose improvements on residual vector quantization. These methods are also shown to outperform their predecessors. Apart from these, a sixth contribution in this thesis is a demonstration of VQ for ANN in an application of image classification on large-scale datasets. It is shown that a k-NN classifier based on VQ for ANN performs on par with the k-NN classifiers, but requires much less storage space and computations

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