DOCSLIB.ORG

On the Difficulty of Nearest Neighbor Search

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
On the Difficulty of Nearest Neighbor Search On the Difficulty of Nearest Neighbor Search Junfeng He [email protected] Department of Electrical Engineering, Columbia University, New York, NY 10027, USA Sanjiv Kumar [email protected] Google Research, New York, NY 10011, USA Shih-Fu Chang [email protected] Department of Electrical Engineering, Columbia University, New York, NY 10027, USA Abstract Rapidly increasing data in many domains such as the Fast approximate nearest neighbor(NN) Web is posing new challenges on how to efficiently search in large databases is becoming popu- retrieve nearest neighbors of a query from massive lar. Several powerful learning-based formula- databases. Fortunately, in most applications, it is suf- tions have been proposed recently. However, ficient to return approximate nearest neighbors of a not much attention has been paid to a more query, which allows efficeint scalable search. fundamental question: how difficult is (ap- A large number of approximate Nearest Neighbor proximate) nearest neighbor search in a given (NN) search techniques have been proposed in the data set? And which data properties affect last decade including hashing and tree-based meth- the difficulty of nearest neighbor search and ods, to name a few, (Datar et al., 2004; Liu et al., how? This paper introduces the first concrete 2004; Weiss et al., 2008). However, the performance measure called Relative Contrast that can of all these techniques depends heavily on the data be used to evaluate the influence of several set characteristics. In fact, as a fundamental question, crucial data characteristics such as dimen- one would like to know how difficult is (approximate) sionality, sparsity, and database size simul- NN search in a given data set. And more broadly, taneously in arbitrary normed metric spaces. which data characteristics of the dataset affect the Moreover, we present a theoretical analysis ”difficulty” and how? The term ”difficulty” here has to prove how the difficulty measure (relative two different but related meanings: in the context of contrast) determines/affects the complexity NN search problem (independent of indexing meth- of Local Sensitive Hashing, a popular approx- ods), ”difficulty” represents ”meaningfulness”, i.e., for imate NN search method. Relative contrast a query, how differentiable is its NN point compared to also provides an explanation for a family of other points? In the context of approximate NN search heuristic hashing algorithms with good prac- methods like tree or hashing based indexing methods, tical performance based on PCA. Finally, we ”difficulty” represents ”complexity”, i.e., what is the show that most of the previous works in mea- time and space complexity to guarantee to find the NN suring NN search meaningfulness/difficulty point (with a high probability)? These questions have can be derived as special asymptotic cases not been paid much attention in the literature. for dense vectors of the proposed measure. In terms of ”meaningfulness” of NN search problem in a given dataset, most of the existing works have 1. Introduction focused on the effect of one data property: dimen- sionality, that too in an asymptotic sense, showing Finding nearest neighbors is a key step in many ma- that NN search will be meaningless when the num- chine learning algorithms such as spectral cluster- ber of dimensions goes to infinity (Beyer et al., 1999; ing, manifold learning and semi-supervised learning. Aggarwal et al., 2001; Francois et al., 2007). First, Appearing in Proceedings of the 29 th International Confer- non-asymptotic analysis has not been discussed, i.e., ence on Machine Learning, Edinburgh, Scotland, UK, 2012. when the number of dimensions is finite. Moreover, Copyright 2012 by the author(s)/owner(s). the effect of other crucial properties has not been stud- On the Difficulty of Nearest Neighbor Search d ied, for instance, the sparsity of data vectors. Since in where xi, q R are i.i.d samples from an unknown many applications, high-dimensional vectors tend to distribution p∈(x). Further, let D( , ) be the distance · · be sparse, it is important to study the two data prop- function for the d-dimensional data. We focus on Lp j j p 1/p erties e.g., dimensionality and sparsity together, along distances in this paper: D(x, q)=( j x q ) . with other factors such as database size and distance | − | metric. 2.1. Definition P q In terms of the complexity of approximate NN Suppose Dmin = min D(xi, q) is the distance to the i=1,...n search methods like Locality Sensitive Hashing 1 q nearest database sample , and Dmean = Ex[D(x, q)] (LSH), some general bounds for (Gionis et al., 1999; is the expected distance of a random database sample Indyk & Motwani, 1998) have been presented. How- from the query q. We define the relative contrast for q ever, it has not been studied how the complexity of q Dmean the data set X for a query q as : Cr = Dq . It is approximate NN search methods is affected by the min difficulty of NN search problem on the dataset, and a very intuitive measure of separability of the nearest moreover, by various data properties like dimension, neighbor of q from the rest of the database points. sparsity, etc. Now, taking expectations with respect to queries, the relative contrast for the dataset X is given as, The main contributions of this paper are: q 1. We introduces a new concrete measure Relative Eq[Dmean] Dmean Cr = q = (1) Contrast for the meaningfulness/difficulty of nearest Eq[Dmin] Dmin neighbor search problem in a given data set (in- dependent of indexing methods). Unlike previous Intuitively, Cr captures the notion of difficulty of NN works that only provide asymptotic discussions for search in X. Smaller the Cr, more difficult the search. one or two data properties, we derive an explicitly If Cr is close to 1, then on average a query q will have computable function to estimate relative contrast in almost the same distance to its nearest neighbor as non-asymptotic case. It for the first time enables us to that to a random point in X. This will imply that NN analyze how the difficulty of nearest neighbor search search in database X is not very meaningful. is affected by different data properties simultaneously, In the following sections, we derive relative contrast as such as dimensionality, sparsity, database size, along a function of various important data characteristics. with the norm of Lp distance metric , for a given data set. (Sec. 2) 2.2. Estimation Suppose xj and qj are the jth dimensions of vectors x 2. We provide a theoretical analysis on how the and q. Let’s define, difficulty measure ”relative contrast” determines the complexity of LSH, a popular approximate NN d search method. This is the first work to relate the R = E [ xj qj p],R = R . (2) j q | − | j complexity of approximate NN search methods to j=1 the difficulty measure of a given dataset, allowing us X j to analyze how the complexity is affected by various Both Rj and R are random variables (because x is data properties simultaneously. For practitioners’ a random variable). Suppose each Rj has finite mean 2 benefits, relative contrast also provides insights on and variance denoted as µj = E[Rj ], σj = var[Rj]. how to choose parameters e.g., the number of hash Then, the mean and variance of R are given as, tables of LSH, and a principled explanation of why d d PCA-based methods perform well in practice. (Sec. 3) µ = µ , σ2 σ2. j ≤ j j=1 j=1 3. We reveal the relationship between relative X X contrast and previous studies on measuring NN search 2 2 Here, if dimensions are independent then σ = j σj . difficulty, and show that most existing works can be Without the loss of generality, we can scale the data P derived as special asymptotic cases for dense vectors such that the new mean µ′ is 1. The variance of the of the proposed relative contrast. (Sec. 4) scaled data, called normalized variance will be: 2 2. Relative Contrast (Cr) 2 σ σ′ = . (3) µ2 Suppose we are given a data set X containing n d- 1 dim points, X = xi, i = 1,...,n , and a query q Without loss of generality, we assume that the query { } q is distinct from the database samples, i.e., Dmin =6 0. On the Difficulty of Nearest Neighbor Search The normalized variance gives the spread of the dis- Moreover, after normalization, R follows a Gaus- tances from query to random points in the database sian distribution with mean 1. So, Rmean = 1, and 1 with the mean distance fixed at 1. If the spread is p Dmean Rmean = 1. Thus, the relative contrast can small, it is harder to separate the nearest neighbor be approximated≈ as: from the rest of the points. Next, we estimate the relative contrast for a given dataset as follows. Dmean 1 Cr = 1 Dmin ≈ 1 1 1 p [1 + φ− ( n + φ( −σ′ ))σ′] Theorem 2.1 If Rj, j=1,...d are independent and { 2 } satisfy Lindeberg’s condition , the relative contrast can which completes the proof. be approximated as, Dmean 1 Range of Cr: Note that when n is large enough C = 1 (4) 1 1 1 1 1 1 1 r φ( −′ ) +φ( −′ ) ,so0 1+φ− ( +φ( −′ ))σ′ Dmin ≈ 1 1 1 p σ n σ 2 n σ [1 + φ− ( n + φ( −σ′ ))σ′] ≤ ≤ ≤ ≤ 1 and hence Cr is always 1. And moreover, when 1 ≥ σ′ 0, φ( −′ ) 0, and Cr 1. where φ is the c.d.f of standard Gaussian, n is the → σ → → number of database samples, σ′ is normalized standard Generalization 1: The concept of relative contrast deviation, and p is the distance metric norm.
Load more

Recommended publications
  • Two Algorithms for Nearest-Neighbor Search in High Dimensions
    Two Algorithms for Nearest-Neighbor Search in High Dimensions Jon M. Kleinberg∗ February 7, 1997 Abstract Representing data as points in a high-dimensional space, so as to use geometric methods for indexing, is an algorithmic technique with a wide array of uses. It is central to a number of areas such as information retrieval, pattern recognition, and statistical data analysis; many of the problems arising in these applications can involve several hundred or several thousand dimensions. We consider the nearest-neighbor problem for d-dimensional Euclidean space: we wish to pre-process a database of n points so that given a query point, one can ef- ficiently determine its nearest neighbors in the database. There is a large literature on algorithms for this problem, in both the exact and approximate cases. The more sophisticated algorithms typically achieve a query time that is logarithmic in n at the expense of an exponential dependence on the dimension d; indeed, even the average- case analysis of heuristics such as k-d trees reveals an exponential dependence on d in the query time. In this work, we develop a new approach to the nearest-neighbor problem, based on a method for combining randomly chosen one-dimensional projections of the underlying point set. From this, we obtain the following two results. (i) An algorithm for finding ε-approximate nearest neighbors with a query time of O((d log2 d)(d + log n)). (ii) An ε-approximate nearest-neighbor algorithm with near-linear storage and a query time that improves asymptotically on linear search in all dimensions.
    [Show full text]
  • Rank-Approximate Nearest Neighbor Search: Retaining Meaning and Speed in High Dimensions
    Rank-Approximate Nearest Neighbor Search: Retaining Meaning and Speed in High Dimensions Parikshit Ram, Dongryeol Lee, Hua Ouyang and Alexander G. Gray Computational Science and Engineering, Georgia Institute of Technology Atlanta, GA 30332 p.ram@,dongryel@cc.,houyang@,agray@cc. gatech.edu { } Abstract The long-standing problem of efficient nearest-neighbor (NN) search has ubiqui- tous applications ranging from astrophysics to MP3 fingerprinting to bioinformat- ics to movie recommendations. As the dimensionality of the dataset increases, ex- act NN search becomes computationally prohibitive; (1+) distance-approximate NN search can provide large speedups but risks losing the meaning of NN search present in the ranks (ordering) of the distances. This paper presents a simple, practical algorithm allowing the user to, for the first time, directly control the true accuracy of NN search (in terms of ranks) while still achieving the large speedups over exact NN. Experiments on high-dimensional datasets show that our algorithm often achieves faster and more accurate results than the best-known distance-approximate method, with much more stable behavior. 1 Introduction In this paper, we address the problem of nearest-neighbor (NN) search in large datasets of high dimensionality. It is used for classification (k-NN classifier [1]), categorizing a test point on the ba- sis of the classes in its close neighborhood. Non-parametric density estimation uses NN algorithms when the bandwidth at any point depends on the ktℎ NN distance (NN kernel density estimation [2]). NN algorithms are present in and often the main cost of most non-linear dimensionality reduction techniques (manifold learning [3, 4]) to obtain the neighborhood of every point which is then pre- served during the dimension reduction.
    [Show full text]
  • Nearest Neighbor Search in Google Correlate
    Nearest Neighbor Search in Google Correlate Dan Vanderkam Robert Schonberger Henry Rowley Google Inc Google Inc Google Inc 76 9th Avenue 76 9th Avenue 1600 Amphitheatre Parkway New York, New York 10011 New York, New York 10011 Mountain View, California USA USA 94043 USA [email protected] [email protected] [email protected] Sanjiv Kumar Google Inc 76 9th Avenue New York, New York 10011 USA [email protected] ABSTRACT queries are then noted, and a model that estimates influenza This paper presents the algorithms which power Google Cor- incidence based on present query data is created. relate[8], a tool which finds web search terms whose popu- This estimate is valuable because the most recent tradi- larity over time best matches a user-provided time series. tional estimate of the ILI rate is only available after a two Correlate was developed to generalize the query-based mod- week delay. Indeed, there are many fields where estimating eling techniques pioneered by Google Flu Trends and make the present[1] is important. Other health issues and indica- them available to end users. tors in economics, such as unemployment, can also benefit Correlate searches across millions of candidate query time from estimates produced using the techniques developed for series to find the best matches, returning results in less than Google Flu Trends. 200 milliseconds. Its feature set and requirements present Google Flu Trends relies on a multi-hour batch process unique challenges for Approximate Nearest Neighbor (ANN) to find queries that correlate to the ILI time series. Google search techniques. In this paper, we present Asymmetric Correlate allows users to create their own versions of Flu Hashing (AH), the technique used by Correlate, and show Trends in real time.
    [Show full text]
  • R-Trees with Voronoi Diagrams for Efficient Processing of Spatial
    VoR-Tree: R-trees with Voronoi Diagrams for Efficient Processing of Spatial Nearest Neighbor Queries∗ y Mehdi Sharifzadeh Cyrus Shahabi Google University of Southern California [email protected] [email protected] ABSTRACT A very important class of spatial queries consists of nearest- An important class of queries, especially in the geospatial neighbor (NN) query and its variations. Many studies in domain, is the class of nearest neighbor (NN) queries. These the past decade utilize R-trees as their underlying index queries search for data objects that minimize a distance- structures to address NN queries efficiently. The general ap- based function with reference to one or more query objects. proach is to use R-tree in two phases. First, R-tree's hierar- Examples are k Nearest Neighbor (kNN) [13, 5, 7], Reverse chical structure is used to quickly arrive to the neighborhood k Nearest Neighbor (RkNN) [8, 15, 16], k Aggregate Nearest of the result set. Second, the R-tree nodes intersecting with Neighbor (kANN) [12] and skyline queries [1, 11, 14]. The the local neighborhood (Search Region) of an initial answer applications of NN queries are numerous in geospatial deci- are investigated to find all the members of the result set. sion making, location-based services, and sensor networks. While R-trees are very efficient for the first phase, they usu- The introduction of R-trees [3] (and their extensions) for ally result in the unnecessary investigation of many nodes indexing multi-dimensional data marked a new era in de- that none or only a small subset of their including points veloping novel R-tree-based algorithms for various forms belongs to the actual result set.
    [Show full text]
  • Dimensional Testing for Reverse K-Nearest Neighbor Search
    University of Southern Denmark Dimensional testing for reverse k-nearest neighbor search Casanova, Guillaume; Englmeier, Elias; Houle, Michael E.; Kröger, Peer; Nett, Michael; Schubert, Erich; Zimek, Arthur Published in: Proceedings of the VLDB Endowment DOI: 10.14778/3067421.3067426 Publication date: 2017 Document version: Final published version Document license: CC BY-NC-ND Citation for pulished version (APA): Casanova, G., Englmeier, E., Houle, M. E., Kröger, P., Nett, M., Schubert, E., & Zimek, A. (2017). Dimensional testing for reverse k-nearest neighbor search. Proceedings of the VLDB Endowment, 10(7), 769-780. https://doi.org/10.14778/3067421.3067426 Go to publication entry in University of Southern Denmark's Research Portal Terms of use This work is brought to you by the University of Southern Denmark. Unless otherwise specified it has been shared according to the terms for self-archiving. If no other license is stated, these terms apply: • You may download this work for personal use only. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying this open access version If you believe that this document breaches copyright please contact us providing details and we will investigate your claim. Please direct all enquiries to [email protected] Download date: 05. Oct. 2021 Dimensional Testing for Reverse k-Nearest Neighbor Search Guillaume Casanova Elias Englmeier Michael E. Houle ONERA-DCSD, France LMU Munich, Germany NII, Tokyo,
    [Show full text]
  • Efficient Nearest Neighbor Searching for Motion Planning
    E±cient Nearest Neighbor Searching for Motion Planning Anna Atramentov Steven M. LaValle Dept. of Computer Science Dept. of Computer Science Iowa State University University of Illinois Ames, IA 50011 USA Urbana, IL 61801 USA [email protected] [email protected] Abstract gies of con¯guration spaces. The topologies that usu- ally arise are Cartesian products of R, S1, and projective We present and implement an e±cient algorithm for per- spaces. In these cases, metric information must be ap- forming nearest-neighbor queries in topological spaces propriately processed by any data structure designed to that usually arise in the context of motion planning. perform nearest neighbor computations. The problem is Our approach extends the Kd tree-based ANN algo- further complicated by the high dimensionality of con¯g- rithm, which was developed by Arya and Mount for Eu- uration spaces. clidean spaces. We argue the correctness of the algo- rithm and illustrate its e±ciency through computed ex- In this paper, we extend the nearest neighbor algorithm amples. We have applied the algorithm to both prob- and part of the ANN package of Arya and Mount [16] to abilistic roadmaps (PRMs) and Rapidly-exploring Ran- handle general topologies with very little computational dom Trees (RRTs). Substantial performance improve- overhead. Related literature is discussed in Section 3. ments are shown for motion planning examples. Our approach is based on hierarchically searching nodes in a Kd tree while handling the appropriate constraints induced by the metric and topology. We have proven the 1 Introduction correctness of our approach, and we have demonstrated the e±ciency of the algorithm experimentally.
    [Show full text]
  • A Fast All Nearest Neighbor Algorithm for Applications Involving Large Point-Clouds à Jagan Sankaranarayanan , Hanan Samet, Amitabh Varshney
    Best Journal Paper of 2007 Award ARTICLE IN PRESS Computers & Graphics 31 (2007) 157–174 www.elsevier.com/locate/cag A fast all nearest neighbor algorithm for applications involving large point-clouds à Jagan Sankaranarayanan , Hanan Samet, Amitabh Varshney Department of Computer Science, Center for Automation Research, Institute for Advanced Computer Studies, University of Maryland, College Park, MD - 20742, USA Abstract Algorithms that use point-cloud models make heavy use of the neighborhoods of the points. These neighborhoods are used to compute the surface normals for each point, mollification, and noise removal. All of these primitive operations require the seemingly repetitive process of finding the k nearest neighbors (kNNs) of each point. These algorithms are primarily designed to run in main memory. However, rapid advances in scanning technologies have made available point-cloud models that are too large to fit in the main memory of a computer. This calls for more efficient methods of computing the kNNs of a large collection of points many of which are already in close proximity. A fast kNN algorithm is presented that makes use of the locality of successive points whose k nearest neighbors are sought to reduce significantly the time needed to compute the neighborhood needed for the primitive operation as well as enable it to operate in an environment where the data is on disk. Results of experiments demonstrate an order of magnitude improvement in the time to perform the algorithm and several orders of magnitude improvement in work efficiency when compared with several prominent existing methods. r 2006 Elsevier Ltd. All rights reserved.
    [Show full text]
  • Fast Algorithm for Nearest Neighbor Search Based on a Lower Bound Tree
    in Proceedings of the 8th International Conference on Computer Vision, Vancouver, Canada, Jul. 2001, Volume 1, pages 446–453 Fast Algorithm for Nearest Neighbor Search Based on a Lower Bound Tree Yong-Sheng Chen†‡ Yi-Ping Hung†‡ Chiou-Shann Fuh‡ †Institute of Information Science, Academia Sinica, Taipei, Taiwan ‡Dept. of Computer Science and Information Engineering, National Taiwan University, Taiwan Email: [email protected] Abstract In the past, Bentley [2] proposed the k-dimensional bi- nary search tree to speed up the the nearest neighbor search. This paper presents a novel algorithm for fast nearest This method is very efficient when the dimension of the data neighbor search. At the preprocessing stage, the proposed space is small. However, as reported in [13] and [3], its algorithm constructs a lower bound tree by agglomeratively performance degrades exponentially with increasing dimen- clustering the sample points in the database. Calculation of sion. Fukunaga and Narendra [8] constructed a tree struc- the distance between the query and the sample points can be ture by repeating the process of dividing the set of sam- avoided if the lower bound of the distance is already larger ple points into subsets. Given a query point, they used than the minimum distance. The search process can thus a branch-and-bound search strategy to efficiently find the be accelerated because the computational cost of the lower closest point by using the tree structure. Djouadi and Bouk- bound, which can be calculated by using the internal node tache [5] partitioned the underlying space of the sample of the lower bound tree, is less than that of the distance.
    [Show full text]
  • Efficient Similarity Search in High-Dimensional Data Spaces
    New Jersey Institute of Technology Digital Commons @ NJIT Dissertations Electronic Theses and Dissertations Spring 5-31-2004 Efficient similarity search in high-dimensional data spaces Yue Li New Jersey Institute of Technology Follow this and additional works at: https://digitalcommons.njit.edu/dissertations Part of the Computer Sciences Commons Recommended Citation Li, Yue, "Efficient similarity search in high-dimensional data spaces" (2004). Dissertations. 633. https://digitalcommons.njit.edu/dissertations/633 This Dissertation is brought to you for free and open access by the Electronic Theses and Dissertations at Digital Commons @ NJIT. It has been accepted for inclusion in Dissertations by an authorized administrator of Digital Commons @ NJIT. For more information, please contact [email protected]. Copyright Warning & Restrictions The copyright law of the United States (Title 17, United States Code) governs the making of photocopies or other reproductions of copyrighted material. Under certain conditions specified in the law, libraries and archives are authorized to furnish a photocopy or other reproduction. One of these specified conditions is that the photocopy or reproduction is not to be “used for any purpose other than private study, scholarship, or research.” If a, user makes a request for, or later uses, a photocopy or reproduction for purposes in excess of “fair use” that user may be liable for copyright infringement, This institution reserves the right to refuse to accept a copying order if, in its judgment, fulfillment
    [Show full text]
  • A Cost Model for Nearest Neighbor Search in High-Dimensional Data Space
    A Cost Model For Nearest Neighbor Search in High-Dimensional Data Space Stefan Berchtold Christian Böhm University of Munich University of Munich Germany Germany [email protected] [email protected] Daniel A. Keim Hans-Peter Kriegel University of Munich University of Munich Germany Germany [email protected] [email protected] Abstract multimedia indexing [9], CAD [17], molecular biology (for In this paper, we present a new cost model for nearest neigh- the docking of molecules) [24], string matching [1], etc. Most bor search in high-dimensional data space. We first analyze applications use some kind of feature vector for an efficient different nearest neighbor algorithms, present a generaliza- access to the complex original data. Examples of feature vec- tion of an algorithm which has been originally proposed for tors are color histograms [23], shape descriptors [16, 18], Quadtrees [13], and show that this algorithm is optimal. Fourier vectors [26], text descriptors [15], etc. Nearest neigh- Then, we develop a cost model which - in contrast to previous bor search on the high-dimensional feature vectors may be models - takes boundary effects into account and therefore defined as follows: also works in high dimensions. The advantages of our model Given a data set DS of d-dimensional points, find the data are in particular: Our model works for data sets with an arbi- point NN from the data set which is closer to the given query trary number of dimensions and an arbitrary number of data point Q than any other point in the data set.
    [Show full text]
  • Improving K-Nearest Neighbor Approaches for Density-Based Pixel Clustering in Hyperspectral Remote Sensing Images
    remote sensing Article Improving K-Nearest Neighbor Approaches for Density-Based Pixel Clustering in Hyperspectral Remote Sensing Images Claude Cariou 1,*, , Steven Le Moan 2 and Kacem Chehdi 1 1 Institut d’Électronique et des Technologies du numéRique, CNRS, Univ Rennes, UMR 6164, Enssat, 6 rue de Kerampont, F22300 Lannion, France; [email protected] 2 Centre for Research in Image and Signal Processing, Massey University, Palmerston North 4410, New Zealand; [email protected] * Correspondence: [email protected] Received: 30 September 2020; Accepted: 12 November 2020; Published: 14 November 2020 Abstract: We investigated nearest-neighbor density-based clustering for hyperspectral image analysis. Four existing techniques were considered that rely on a K-nearest neighbor (KNN) graph to estimate local density and to propagate labels through algorithm-specific labeling decisions. We first improved two of these techniques, a KNN variant of the density peaks clustering method DPC, and a weighted-mode variant of KNNCLUST, so the four methods use the same input KNN graph and only differ by their labeling rules. We propose two regularization schemes for hyperspectral image analysis: (i) a graph regularization based on mutual nearest neighbors (MNN) prior to clustering to improve cluster discovery in high dimensions; (ii) a spatial regularization to account for correlation between neighboring pixels. We demonstrate the relevance of the proposed methods on synthetic data and hyperspectral images, and show they achieve superior overall performances in most cases, outperforming the state-of-the-art methods by up to 20% in kappa index on real hyperspectral images. Keywords: clustering methods; density estimation; nearest neighbor search; deterministic algorithm; unsupervised learning 1.
    [Show full text]
  • Very Large Scale Nearest Neighbor Search: Ideas, Strategies and Challenges
    Int. Jnl. Multimedia Information Retrieval, IJMIR, vol. 2, no. 4, 2013. The final publication is available at Springer via http://dx.doi.org/10.1007/s13735-013-0046-4 Very Large Scale Nearest Neighbor Search: Ideas, Strategies and Challenges Erik Gast, Ard Oerlemans, Michael S. Lew Leiden University Niels Bohrweg 1 2333CA Leiden The Netherlands {gast, aoerlema, mlew} @liacs.nl Abstract Web-scale databases and Big Data collections are computationally challenging to analyze and search. Similarity or more precisely nearest neighbor searches are thus crucial in the analysis, indexing and utilization of these massive multimedia databases. In this work, we begin by reviewing the top approaches from the research literature in the past decade. Furthermore, we evaluate the scalability and computational complexity as the feature complexity and database size vary. For the experiments we used two different data sets with different dimensionalities. The results reveal interesting insights regarding the index structures and their behavior when the data set size is increased. We also summarized the ideas, strategies and challenges for the future. 1. Introduction Very large scale multimedia databases are becoming common and thus searching within them has become more important. Clearly, one of the most frequently used searching paradigms is k-nearest neighbor(k- NN), where the k objects that are most similar to the query are retrieved. Unfortunately, this k-NN search is also a very expensive operation. In order to do a k-NN search efficiently, it is important to have an index structure that can efficiently handle k-NN searches on large databases. From a theoretical and technical point of view, finding the k nearest neighbors is less than linear time is challenging and largely 1 unsolved.
    [Show full text]