k-NN 검색 및 k-NN 그래프 생성을 위한 고속 근사 알고리즘

학위논문 (박사)-- 서울대학교 대학원 : 전기·컴퓨터공학부, 2015. 2. 이상구.Finding k-nearest neighbors (k-NN) is an essential part of recommeder systems, information retrieval, and many data mining and machine learning algorithms. However, there are two main problems in finding k-nearest neighbors: 1) Existing approaches require a huge amount of time when the number of objects or dimensions is scale up. 2) The k-NN computation methods do not show the consistent performance over different search tasks and types of data. In this dissertation, we present fast and versatile algorithms for finding k-nearest neighbors in order to cope with these problems. The main contributions are summarized as follows: first, we present an efficient and scalable algorithm for finding an approximate k-NN graph by filtering node pairs whose large value dimensions do not match at all. Second, a fast collaborative filtering algorithm that utilizes k-NN graph is presented. The main idea of this approach is to reverse the process of finding k-nearest neighbors in item-based collaborative filtering. Last, we propose a fast approximate algorithm for k-NN search by selecting query-specific signatures from a signature pool to pick high-quality k-NN candidates.The experimental results show that the proposed algorithms guarantee a high level of accuracy while also being much faster than the other algorithms over different types of search tasks and datasets.Abstract i Contents iii List of Figures vii List of Tables xi Chapter 1 Introduction 1 1.1 Motivation and Challenges . . . . . . . . . . . . . . . . . . . . . . 2 1.1.1 Fast Approximation . . . . . . . . . . . . . . . . . . . . . 3 1.1.2 Versatility . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Our Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.1 Greedy Filtering . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.2 Signature Selection LSH . . . . . . . . . . . . . . . . . . . 7 1.2.3 Reversed CF . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.4 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Chapter 2 Background and Related Work 14 2.1 k-NN Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.1.1 Locality Sensitive Hashing . . . . . . . . . . . . . . . . . . 15 2.1.2 LSH-based k-NN Search . . . . . . . . . . . . . . . . . . . 16 2.2 k-NN Graph Construction . . . . . . . . . . . . . . . . . . . . . . 17 2.2.1 LSH-based Approach . . . . . . . . . . . . . . . . . . . . . 19 2.2.2 Clustering-based Approach . . . . . . . . . . . . . . . . . 19 2.2.3 Heuristic-based Approach . . . . . . . . . . . . . . . . . . 20 2.2.4 Similarity Join . . . . . . . . . . . . . . . . . . . . . . . . 21 2.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Chapter 3 Fast Approximate k-NN Graph Construction 26 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.3 Constructing a k-Nearest Neighbor Graph . . . . . . . . . . . . . 29 3.3.1 Greedy Filtering . . . . . . . . . . . . . . . . . . . . . . . 29 3.3.2 Prefix Selection Scheme . . . . . . . . . . . . . . . . . . . 32 3.3.3 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.4 Theoretical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.4.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.4.2 Graph Construction Time . . . . . . . . . . . . . . . . . . 39 3.4.3 Graph Accuracy . . . . . . . . . . . . . . . . . . . . . . . 40 3.5 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.5.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . 44 3.5.2 Performance Comparison . . . . . . . . . . . . . . . . . . 48 3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Chapter 4 Fast Collaborative Filtering 53 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.2 Related Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.3 Fast Collaborative Filtering . . . . . . . . . . . . . . . . . . . . . 58 4.3.1 Nearest Neighbor Graph Construction . . . . . . . . . . . 58 4.3.2 Fast Recommendation Algorithm . . . . . . . . . . . . . . 60 4.4 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 4.4.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . 64 4.4.2 Overall Comparison . . . . . . . . . . . . . . . . . . . . . 65 4.4.3 Effects of Parameter Changes . . . . . . . . . . . . . . . . 68 4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Chapter 5 Fast Approximate k-NN Search 72 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.2 Signature Selection LSH . . . . . . . . . . . . . . . . . . . . . . . 74 5.2.1 Data-dependent LSH . . . . . . . . . . . . . . . . . . . . . 75 5.2.2 Signature Pool Generation . . . . . . . . . . . . . . . . . . 76 5.2.3 Signature Selection . . . . . . . . . . . . . . . . . . . . . . 79 5.2.4 Optimization Techniques . . . . . . . . . . . . . . . . . . 83 5.3 S2LSH for Graph Construction . . . . . . . . . . . . . . . . . . . 84 5.3.1 Feature Selection . . . . . . . . . . . . . . . . . . . . . . . 84 5.3.2 Signature Selection . . . . . . . . . . . . . . . . . . . . . . 84 5.3.3 Optimization Techniques . . . . . . . . . . . . . . . . . . 85 5.4 Theoretical Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 86 5.5 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.5.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . 87 5.5.2 Experimental Results . . . . . . . . . . . . . . . . . . . . 91 5.5.3 Performance Analysis . . . . . . . . . . . . . . . . . . . . 97 5.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Chapter 6 Conclusion 103 Bibliography 105 초록 113Docto

Tree-Independent Dual-Tree Algorithms

Dual-tree algorithms are a widely used class of branch-and-bound algorithms. Unfortunately, developing dual-tree algorithms for use with different trees and problems is often complex and burdensome. We introduce a four-part logical split: the tree, the traversal, the point-to-point base case, and the pruning rule. We provide a meta-algorithm which allows development of dual-tree algorithms in a tree-independent manner and easy extension to entirely new types of trees. Representations are provided for five common algorithms; for k-nearest neighbor search, this leads to a novel, tighter pruning bound. The meta-algorithm also allows straightforward extensions to massively parallel settings.Comment: accepted in ICML 201

An Efficient Index for Visual Search in Appearance-based SLAM

Vector-quantization can be a computationally expensive step in visual bag-of-words (BoW) search when the vocabulary is large. A BoW-based appearance SLAM needs to tackle this problem for an efficient real-time operation. We propose an effective method to speed up the vector-quantization process in BoW-based visual SLAM. We employ a graph-based nearest neighbor search (GNNS) algorithm to this aim, and experimentally show that it can outperform the state-of-the-art. The graph-based search structure used in GNNS can efficiently be integrated into the BoW model and the SLAM framework. The graph-based index, which is a k-NN graph, is built over the vocabulary words and can be extracted from the BoW's vocabulary construction procedure, by adding one iteration to the k-means clustering, which adds small extra cost. Moreover, exploiting the fact that images acquired for appearance-based SLAM are sequential, GNNS search can be initiated judiciously which helps increase the speedup of the quantization process considerably

Fast k-means based on KNN Graph

In the era of big data, k-means clustering has been widely adopted as a basic processing tool in various contexts. However, its computational cost could be prohibitively high as the data size and the cluster number are large. It is well known that the processing bottleneck of k-means lies in the operation of seeking closest centroid in each iteration. In this paper, a novel solution towards the scalability issue of k-means is presented. In the proposal, k-means is supported by an approximate k-nearest neighbors graph. In the k-means iteration, each data sample is only compared to clusters that its nearest neighbors reside. Since the number of nearest neighbors we consider is much less than k, the processing cost in this step becomes minor and irrelevant to k. The processing bottleneck is therefore overcome. The most interesting thing is that k-nearest neighbor graph is constructed by iteratively calling the fast $k$-means itself. Comparing with existing fast k-means variants, the proposed algorithm achieves hundreds to thousands times speed-up while maintaining high clustering quality. As it is tested on 10 million 512-dimensional data, it takes only 5.2 hours to produce 1 million clusters. In contrast, to fulfill the same scale of clustering, it would take 3 years for traditional k-means

Conflict-free star-access in parallel memory systems

We study conflict-free data distribution schemes in parallel memories in multiprocessor system architectures. Given a host graph G, the problem is to map the nodes of G into memory modules such that any instance of a template type T in G can be accessed without memory conflicts. A conflict occurs if two or more nodes of T are mapped to the same memory module. The mapping algorithm should: (i) be fast in terms of data access (possibly mapping each node in constant time); (ii) minimize the required number of memory modules for accessing any instance in G of the given template type; and (iii) guarantee load balancing on the modules. In this paper, we consider conflict-free access to star templates. i.e., to any node of G along with all of its neighbors. Such a template type arises in many classical algorithms like breadth-first search in a graph, message broadcasting in networks, and nearest neighbor based approximation in numerical computation. We consider the star-template access problem on two specific host graphs-tori and hypercubes-that are also popular interconnection network topologies. The proposed conflict-free mappings on these graphs are fast, use an optimal or provably good number of memory modules, and guarantee load balancing. (C) 2006 Elsevier Inc. All rights reserved