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Results 1 - 10
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4,852
Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
, 2003
"... One of the central problems in machine learning and pattern recognition is to develop appropriate representations for complex data. We consider the problem of constructing a representation for data lying on a low-dimensional manifold embedded in a high-dimensional space. Drawing on the correspondenc ..."
Abstract
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Cited by 1226 (15 self)
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on the correspondence between the graph Laplacian, the Laplace Beltrami operator on the manifold, and the connections to the heat equation, we propose a geometrically motivated algorithm for representing the high-dimensional data. The algorithm provides a computationally efficient ap-proach to nonlinear dimensionality
Analysis of Recommendation Algorithms for E-Commerce
, 2000
"... Recommender systems apply statistical and knowledge discovery techniques to the problem of making product recommendations during a live customer interaction and they are achieving widespread success in E-Commerce nowadays. In this paper, we investigate several techniques for analyzing large-scale pu ..."
Abstract
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Cited by 523 (22 self)
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-scale purchase and preference data for the purpose of producing useful recommendations to customers. In particular, we apply a collection of algorithms such as traditional data mining, nearest-neighbor collaborative ltering, and dimensionality reduction on two dierent data sets. The rst data set was derived from
Fastmap: A fast algorithm for indexing, data-mining and visualization of traditional and multimedia datasets
, 1995
"... A very promising idea for fast searching in traditional and multimedia databases is to map objects into points in k-d space, using k feature-extraction functions, provided by a domain expert [Jag91]. Thus, we can subsequently use highly fine-tuned spatial access methods (SAMs), to answer several ..."
Abstract
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Cited by 502 (22 self)
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easier for a domain expert to assess the similarity/distance of two objects. Given only the distance information though, it is not obvious how to map objects into points. This is exactly the topic of this paper. We describe a fast algorithm to map objects into points in some k-dimensional space (k
The Quickhull algorithm for convex hulls
- ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE
, 1996
"... The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull Algorithm with the general-dimension Beneath-Beyond Algorithm. It is similar to the randomized, incremental algo ..."
Abstract
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Cited by 713 (0 self)
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The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull Algorithm with the general-dimension Beneath-Beyond Algorithm. It is similar to the randomized, incremental
The particel swarm: Explosion, stability, and convergence in a multi-dimensional complex space
- IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTION
"... The particle swarm is an algorithm for finding optimal regions of complex search spaces through interaction of individuals in a population of particles. Though the algorithm, which is based on a metaphor of social interaction, has been shown to perform well, researchers have not adequately explained ..."
Abstract
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Cited by 852 (10 self)
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explained how it works. Further, traditional versions of the algorithm have had some dynamical properties that were not considered to be desirable, notably the particles’ velocities needed to be limited in order to control their trajectories. The present paper analyzes the particle’s trajectory as it moves
Laplacian eigenmaps and spectral techniques for embedding and clustering.
- Proceeding of Neural Information Processing Systems,
, 2001
"... Abstract Drawing on the correspondence between the graph Laplacian, the Laplace-Beltrami op erator on a manifold , and the connections to the heat equation , we propose a geometrically motivated algorithm for constructing a representation for data sampled from a low dimensional manifold embedded in ..."
Abstract
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Cited by 668 (7 self)
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in a higher dimensional space. The algorithm provides a computationally efficient approach to nonlinear dimensionality reduction that has locality preserving properties and a natural connection to clustering. Several applications are considered. In many areas of artificial intelligence, information
R-trees: A Dynamic Index Structure for Spatial Searching
- INTERNATIONAL CONFERENCE ON MANAGEMENT OF DATA
, 1984
"... In order to handle spatial data efficiently, as required in computer aided design and geo-data applications, a database system needs an index mechanism that will help it retrieve data items quickly according to their spatial locations However, traditional indexing methods are not well suited to data ..."
Abstract
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Cited by 2750 (0 self)
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to data objects of non-zero size located m multi-dimensional spaces In this paper we describe a dynamic index structure called an R-tree which meets this need, and give algorithms for searching and updating it. We present the results of a series of tests which indicate that the structure performs well
Power-Aware Routing in Mobile Ad Hoc Networks
, 1998
"... In this paper we present a case for using new power-aware metrics for determining routes in wireless ad hoc networks. We present five different metrics based on battery power consumption at nodes. We show that using these metrics in a shortest-cost routing algorithm reduces the cost/packet of rout ..."
Abstract
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Cited by 775 (5 self)
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In this paper we present a case for using new power-aware metrics for determining routes in wireless ad hoc networks. We present five different metrics based on battery power consumption at nodes. We show that using these metrics in a shortest-cost routing algorithm reduces the cost
Mixtures of Probabilistic Principal Component Analysers
, 1998
"... Principal component analysis (PCA) is one of the most popular techniques for processing, compressing and visualising data, although its effectiveness is limited by its global linearity. While nonlinear variants of PCA have been proposed, an alternative paradigm is to capture data complexity by a com ..."
Abstract
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Cited by 532 (6 self)
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of clustering, density modelling and local dimensionality reduction, and we demonstrate its applicat...
Fast subsequence matching in time-series databases
- PROCEEDINGS OF THE 1994 ACM SIGMOD INTERNATIONAL CONFERENCE ON MANAGEMENT OF DATA
, 1994
"... We present an efficient indexing method to locate 1-dimensional subsequences within a collection of sequences, such that the subsequences match a given (query) pattern within a specified tolerance. The idea is to map each data sequence into a small set of multidimensional rectangles in feature space ..."
Abstract
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Cited by 533 (24 self)
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space. Then, these rectangles can be readily indexed using traditional spatial access methods, like the R*-tree [9]. In more detail, we use a sliding window over the data sequence and extract its features; the result is a trail in feature space. We propose an ecient and eective algorithm to divide
Results 1 - 10
of
4,852
