Showing papers on "Euclidean distance published in 1998"
23 Feb 1998
TL;DR: This work proposes a modification of the so called "FastMap", to map sequences into points, with little compromise of "recall" (typically zero), and a fast linear test, to help to discard quickly many of the false alarms that FastMap will typically introduce.
Abstract: Fast similarity searching in large time sequence databases has typically used Euclidean distance as a dissimilarity metric. However, for several applications, including matching of voice, audio and medical signals (e.g., electrocardiograms), one is required to permit local accelerations and decelerations in the rate of sequences, leading to a popular, field tested dissimilarity metric called the "time warping" distance. From the indexing viewpoint, this metric presents two major challenges: (a) it does not lead to any natural indexable "features", and (b) comparing two sequences requires time quadratic in the sequence length. To address each problem, we propose to use: (a) a modification of the so called "FastMap", to map sequences into points, with little compromise of "recall" (typically zero); and (b) a fast linear test, to help us discard quickly many of the false alarms that FastMap will typically introduce. Using both ideas in cascade, our proposed method achieved up to an order of magnitude speed-up over sequential scanning on both real and synthetic datasets.
771 citations
23 May 1998
TL;DR: An approximation scheme for the plane that for any c > 0 produces a solution of cost at most 1+ 1/c times the optimum and runs in time O(n) and generalizes to some problems related to k-median.
Abstract: In the k-median problem we are given a set S of n points in a metric space and a positive integer k. We desire to locate k medians in space, such that the sum of the distances from each of the points of S to the nearest median is minimized. This paper gives an approximation scheme for the plane that for any c > 0 produces a solution of cost at most 1+ 1/c times the optimum and runs in time O(n). The approximation scheme also generalizes to some problems related to k-median. Our methodology is to extend Arora’s [1, 2] techniques for the TSP, which hitherto seemed inapplicable to problems such as the k-median problem.
391 citations
TL;DR: The authors developed tests for spatial-error correlation and methods of estimation in the presence of such correlation for discrete-choice models, which are based on the notion of a generalized residual, are a set of orthogonality conditions that should be satisfied under the null.
375 citations
Book•
01 Jan 1998
TL;DR: Subadditivity and superadditivity for euclidean functionals: Subadditive and super-additive Eulerian functionals are defined in this article, where the uniform case is assumed to be the case.
Abstract: Subadditivity and superadditivity.- Subadditive and superadditive euclidean functionals.- Asymptotics for euclidean functionals: The uniform case.- Rates of convergence and heuristics.- Isoperimetry and concentration inequalities.- Umbrella theorems for euclidean functionals.- Applications and examples.- Minimal triangulations.- Geometric location problems.- Worst case growth rates.
282 citations
Patent•
30 Jul 1998TL;DR: In this article, a method to measure channel quality in terms of signal to noise ratio for the transmission of coded signals over fading channels was proposed, where a Viterbi decoder metric for the Maximum Likelihood path was used as a channel quality measure.
Abstract: A system and method to measure channel quality in terms of signal to noise ratio for the transmission of coded signals over fading channels. A Viterbi decoder metric for the Maximum Likelihood path is used as a channel quality measure. This Euclidean distance metric is filtered in order to smooth out short term variations. The filtered or averaged metric is a reliable channel quality measure which remains consistent across different coded modulation schemes and at different mobile speeds. The filtered metric is mapped to the signal to noise ratio per symbol using a threshold based scheme. Use of this implicit signal to noise ratio estimate is used for the mobile assisted handoff and data rate adaptation in the transmitter.
159 citations
141 citations
TL;DR: An optimal redistribution algorithm, which minimises the Euclidean norm of the migrating load, is derived and the relationship between this algorithm and some existing algorithms is discussed and the convergence of the new algorithm is studied.
Abstract: The problem of redistributing the work load on parallel computers is considered. An optimal redistribution algorithm, which minimises the Euclidean norm of the migrating load, is derived. The relationship between this algorithm and some existing algorithms is discussed and the convergence of the new algorithm is studied. Finally, numerical results on randomly generated graphs as well as on graphs related to real meshes are given to demonstrate the effectiveness of the new algorithm. © 1998 John Wiley & Sons, Ltd.
102 citations
23 Jun 1998
TL;DR: This paper proposes a novel pattern classification approach, called the nearest linear combination (NLC) approach, for eigenface based face recognition, using a linear combination of prototypical vectors to extend the representational capacity of the prototypes by generalization through interpolation and extrapolation.
Abstract: This paper proposes a novel pattern classification approach, called the nearest linear combination (NLC) approach, for eigenface based face recognition. Assume that multiple prototypical vectors are available per class, each vector being a point in an eigenface space. A linear combination of prototypical vectors belonging to a face class is used to define a measure of distance from the query vector to the class, the measure being defined as the Euclidean distance from the query to the linear combination nearest to the query vector (hence NLC). This contrasts to the nearest neighbor (NN) classification where a query vector is compared with each prototypical vector individually. Using a linear combination of prototypical vectors, instead of each of them individually, extends the representational capacity of the prototypes by generalization through interpolation and extrapolation. Experiments show that it leads to better results than existing classification methods.
98 citations
TL;DR: In this paper, it was shown that there are separated nets in the Euclidean plane which are not biLipschitz equivalent to the integer lattice, and the argument is based on the construction of a continuous function which is not the Jacobian of a bi-Lipschnitz map.
Abstract: We show that there are separated nets in the Euclidean plane which are not biLipschitz equivalent to the integer lattice. The argument is based on the construction of a continuous function which is not the Jacobian of a biLipschitz map.
86 citations
TL;DR: In this paper, the authors compute the number of summands in q-averages of norms needed to approximate an Euclidean norm and show that these numbers depend on the norm involved essentially only through the maximal ratio of the norm and the Euclideans norm.
Abstract: We compute the number of summands in q-averages of norms needed to approximate an Euclidean norm. It turns out that these numbers depend on the norm involved essentially only through the maximal ratio of the norm and the Euclidean norm. Particular attention is given to the case q = ∞ (in which the average is replaced with the maxima). This is closely connected with the behavior of certain families of projective caps on the sphere.
82 citations
TL;DR: In this article, an equivariant Bott periodicity theorem for infinite dimensional Euclidean vector spaces has been proved for amenable groups, and a non-commutative C *-algebra has been constructed to play the role of the algebra of functions on infinite dimensional vector spaces.
Patent•
19 Mar 1998TL;DR: In this paper, a Viterbi decoder metric for the Maximum Likelihood path is used as a channel quality measure for coherent and non-coherent transmission schemes, and the Euclidean distance metric is filtered in order to smooth out short term variations.
Abstract: A system and method to measure channel quality in terms of signal to interference plus noise ratio for the transmission of coded signals over fading channels in a communication system. A Viterbi decoder metric for the Maximum Likelihood path is used as a channel quality measure for coherent and non-coherent transmission schemes. This Euclidean distance metric is filtered in order to smooth out short term variations. The filtered or averaged metric is a reliable channel quality measure which remains consistent across different coded modulation schemes speeds. The filtered metric is mapped to the signal to interference plus noise ratio per symbol using a threshold based scheme. Use of this implicit signal to interference plus noise ratio estimate is used for the mobile assisted handoff in a cellular system, power control and data rate adaptation in the transmitter.
01 Aug 1998
TL;DR: This work gives a polynomial-time algorithm to compute the radius of stability in the Euclidean norm for a variety of stability domains and develops hybrid symbolic-numeric algorithms to constrain one root of a complex or realPolynomial to a curve in the complex plane.
Abstract: The location of polynomial roots is sensitive to perturbations of the coefficients. Continuous changes of the coefficients of a polynomial move the roots continuously. We consider the problem of finding the minimal perturbations to the coefficients to move one or several roots to given loci. We measure minimality in the Euclidean distance to the coefficient vector, as well as the maximal coefficient-wise change in absolute value (infinity norm), and in the Manhattan norm ($l\sp1$-norm). In the Euclidean norm the computational task reduces to a least squares problem, in the infinity norm and the $l\sp1$-norm it can be formulated as a linear program.
We can derive symbolic solutions in closed form for the Euclidean norm in the case of complex coefficients and a single complex root. Our new result is a formula for the minimum change in the infinity norm for the case of real coefficients and a single real root. Based on the principle of parametric minimization we develop hybrid symbolic-numeric algorithms to constrain one root of a complex or real polynomial to a curve in the complex plane.
As an application to robust control, we give a polynomial-time algorithm to compute the radius of stability in the Euclidean norm for a variety of stability domains.
TL;DR: Two new error-free sequential Euclidean distance transformations (EDT) for binary images in Z2are introduced: sufficientd1- Propagation and sufficientd∞-propagation, which are significantly faster than other well-known signed and unsigned EDTs.
TL;DR: It is shown that the Ungerboeck receiver requires additional channel prediction, degrading performance due to prediction uncertainty, and two alternative receiver forms are developed which do not require additional prediction, though the computational complexity is increased.
Abstract: Forney (1972) and Ungerboeck (1974) have each developed maximum-likelihood sequence estimation (MLSE) receivers for intersymbol interference (ISI) channels. The Forney receiver uses a whitened matched filter, followed by a sequence estimation algorithm using the Euclidean distance metric. The Ungerboeck receiver uses a matched filter, followed by a sequence estimation algorithm using a modified metric. A unified development of both receivers is given, in which each receiver is derived from the other. By deriving the Ungerboeck receiver from the Forney receiver, we show that the whitening operation is cancelled in the Euclidean distance metric, leaving the modified metric. In addition, the Ungerboeck receiver is extended to the case of a time-varying known channel. When the channel is unknown, decision-directed channel estimation is assumed, which requires channel prediction to account for the decision delay. It is shown that the Ungerboeck receiver requires additional channel prediction, degrading performance due to prediction uncertainty. To solve this problem, two alternative receiver forms are developed which do not require additional prediction, though the computational complexity is increased. Performance and complexity of the receiver forms are compared for the IS-136 digital cellular time-division multiple-access (TDMA) standard.
TL;DR: In this paper, the authors define a metric in the space of quantum states taking the Monge distance between corresponding Husimi distributions (Q-functions), which fulfils the axioms of a metric and satisfies the following semiclassical property: the distance between two coherent states is equal to the Euclidean distance between correspondences in the classical phase space.
Abstract: We define a metric in the space of quantum states taking the Monge distance between corresponding Husimi distributions (Q-functions). This quantity fulfils the axioms of a metric and satisfies the following semiclassical property: the distance between two coherent states is equal to the Euclidean distance between corresponding points in the classical phase space. We compute analytically distances between certain states (coherent, squeezed, Fock and thermal) and discuss a scheme for numerical computation of Monge distance for two arbitrary quantum states.
TL;DR: It is shown how the results for the Euclidean distance matrix completion problem can be derived from the corresponding results from the positive semidefinite completion problem, using a functional transform introduced by Schoenberg.
TL;DR: In this paper, an efficient Voronoi transform algorithm for constructing Voroni diagrams using segment lists of rows has been proposed, which takes segments rather than pixels as the basic units to represent and propagate the nearest neighbor information.
Abstract: We propose an efficient Voronoi transform algorithm for constructing Voronoi diagrams using segment lists of rows. A significant feature of the algorithm is that it takes segments rather than pixels as the basic units to represent and propagate the nearest neighbor information. The segment lists are dynamically updated as they are scanned. A distance map can then be easily computed from the segment list representation of the Voronoi diagram. Experimental results have demonstrated its high efficiency. Extension of the algorithm to higher dimensions is also discussed.
23 Feb 1998
TL;DR: A new algorithm for this subproblem is presented that computes shortest paths in a rectangular grid with respect to euclidean distance that achieves performance and memory requirements similar to fast line-search algorithms while still being optimal.
Abstract: Sequential routing algorithms using maze-running are very suitable for general Over-the-Cell-Routing but suffer often from the high memory or runtime requirements of the underlying path search routine. A new algorithm for this subproblem is presented that computes shortest paths in a rectangular grid with respect to euclidean distance. It achieves performance and memory requirements similar to fast line-search algorithms while still being optimal. An additional application for the computation of minimal rip-up sets will be presented. Computational results are shown for a detailed router based on these algorithms that is used for the design of high performance CMOS processors at IBM.
14 Jul 1998
TL;DR: The work described demonstrates that texture analysis is a useful tool for writer identification based on handwriting, and uses multichannel spatial filtering techniques to extract texture features from a nonuniformly skewed and nonskewed handwriting image.
Abstract: This paper describes a text-independent writer identification method. The difficulties with writer identification are discussed. These include the sensitivity of the identification algorithm to variations in the size of the training samples, in the words, line and character spacing, point sizes, and scanner resolutions. The work described demonstrates that texture analysis is a useful tool for writer identification based on handwriting. We use multichannel spatial filtering techniques to extract texture features from a nonuniformly skewed and nonskewed handwriting image. There are many available tilters in the multichannel technique. We use Gabor filters, since they have proven to be successful in extracting features for similar applications. We also use grey-scale co-occurrence matrices (GSCM) for feature extraction (for comparison purposes). Two classification techniques are adopted here, namely the weighted Euclidean distance (WED) and the k-NN classifiers. Our algorithm achieves a classification accuracy of 95.3% using 300 test images from 20 writers.
11 Oct 1998
TL;DR: To display individuals of interactive evolutionary computations in an evaluation order, two prediction methods-the first using neural networks, and the second using Euclidean distance measure-are proposed.
Abstract: This paper proposes to display individuals of interactive evolutionary computations in an evaluation order to reduce the burden on human operators. To display an evaluation order, two prediction methods-the first using neural networks, and the second using Euclidean distance measure-are proposed. We evaluate their predictive performance through simulation experiments and subjective tests.
01 Feb 1998
TL;DR: In this article, a multiple criterion updating method which minimizes the Euclidean norm of the error vector obtained by adding the normalised eigenproblem equation and equation of motion with equal weighting functions is proposed.
Abstract: A multiple criterion updating method which minimises the Euclidean norm of the error vector obtained by adding the normalised eigenproblem equation and equation of motion with equal weighting functions is proposed. The method is applied to detecting damage in structures and is tested on an unsymmetrical H-shaped structure. It is found that the multiple criterion updating method predicts the presence, the position and the extent of damage. The multiple criterion method is compared to the frequency response function method and the modal property based method by using the co-ordinate modal assurance criterion and the modal assurance criterion. It is found that the proposed method gives results that are on average consistent with the results given by the two methods individually. Furthermore, it is postulated that the method gives an updated model which has a higher probability of being unique than using when the individual methods are used.
Journal Article•
TL;DR: An object-oriented constraint solving toolkit, QOCA, designed for interactive graphical applications that provides three solvers, all of which rely on keeping the constraints in solved form and relies on novel algorithms for efficient resolving of constraints during direct manipulation.
Abstract: We describe an object-oriented constraint solving toolkit, QOCA, designed for interactive graphical applications. It has a simple yet powerful interface based on the metric space model for constraint manipulation. Currently QOCA supports linear arithmetic constraints and two different metrics: the square of the Euclidean distance and the Manhattan distance. It provides three solvers, all of which rely on keeping the constraints in solved form and relies on novel algorithms for efficient resolving of constraints during direct manipulation. We provide a thorough empirical evaluation of QOCA, both of the interface design and the speed of constraint solving.
01 Jan 1998
TL;DR: Polynomial time approximation schemes for geometric optimization problems in euclidean metric spaces and Semidefinite programming and its applications to approximation algorithms.
Abstract: to the theory of complexity and approximation algorithms.- to randomized algorithms.- Derandomization.- Proof checking and non-approximability.- Proving the PCP-Theorem.- Parallel repetition of MIP(2,1) systems.- Bounds for approximating MaxLinEq3-2 and MaxEkSat.- Deriving non-approximability results by reductions.- Optimal non-approximability of MaxClique.- The hardness of approximating set cover.- Semidefinite programming and its applications to approximation algorithms.- Dense instances of hard optimization problems.- Polynomial time approximation schemes for geometric optimization problems in euclidean metric spaces.
TL;DR: In this paper, the best constant involving the L2 norm in Wente's inequality is shown to be universal for any Riemannian surface with boundary and without boundary, and the existence of a non-trivial critical point for a plan domain with small holes is established.
Abstract: In the first part of this paper, we study the best constant involving the L2 norm in Wente's inequality. We prove that this best constant is universal for any Riemannian surface with boundary, or respectively, for any Riemannian surface without boundary. The second part concerns the study of critical points of the associate energy functional, whose Euler equation corresponds to H-surfaces. We will establish the existence of a non-trivial critical point for a plan domain with small holes.
TL;DR: A recognition system using displacement extraction based on directional features is proposed for handwritten Chinese characters and an improvement in recognition performance is achieved as compared with the method without displacement extraction.
TL;DR: The multiple-criterion method was found to be better able to detect damage on the structure than the modal property method and gave results that were less noisy, i.e., less updating to undamaged elements, than the frequency-response method.
Abstract: A new multiple-criterion updating method that minimizes the Euclidean norm of the error vector obtained by adding the normalized eigenproblem equation and equation of motion with equal weighting functions is proposed. The method is applied to detecting damage in structures and is tested on an unsymmetrical H-shaped structure. It is found that the multiple-criterion updating method predicts the presence, the position, and the extent of damage. The multiple-criterion method is compared to the frequency-response function method and the modal property-based method by using the coordinate modal assurance criterion and the modal assurance criterion. The multiple-criterion method was found to give better results than the other two methods. This is because it was better able to detect damage on the structure than the modal property method (which failed to detect multiple-damage cases) and gave results that were less noisy, i.e., less updating to undamaged elements, than the frequency-response method.
26 Oct 1998
TL;DR: QOCA as discussed by the authors is an object-oriented constraint solving toolkit for interactive graphical applications that supports linear arithmetic constraints and two different metrics: the square of the Euclidean distance and the Manhattan distance.
Abstract: We describe an object-oriented constraint solving toolkit, QOCA, designed for interactive graphical applications. It has a simple yet powerful interface based on the metric space model for constraint manipulation. Currently QOCA supports linear arithmetic constraints and two different metrics: the square of the Euclidean distance and the Manhattan distance. It provides three solvers, all of which rely on keeping the constraints in solved form and relies on novel algorithms for efficient resolving of constraints during direct manipulation. We provide a thorough empirical evaluation of QOCA, both of the interface design and the speed of constraint solving.
TL;DR: In this article, the mutual distances of points in a Euclidean space satisfying the ultrametric inequality (A;B) maxf (A,C); (C,B)g for all points in S are investigated and geometrically characterized.
Abstract: Finite sets S of points in a Euclidean space the mutual distances of which satisfy the ultrametric inequality (A;B) maxf (A;C); (C;B)g for all points in S are investigated and geometrically characterized. Inspired by results on ultrametric matrices and previous results on simplices, connections with so-called centered metric trees as well as with strongly isosceles right simplices are found. AMS subject classi cations. 51K05, 05C12.
TL;DR: This paper relates to the application method of channel state information (CSI) to the Viterbi (maximum likelihood) decoder in the digital terrestrial television broadcasting system and simulated this method in Rayleigh fading defined in the ETSI standard.
Abstract: This paper relates to the application method of channel state information (CSI) to the Viterbi (maximum likelihood) decoder in the digital terrestrial television broadcasting system. The proposed Viterbi decoder uses the CSI derived from the pilots inserted in the transmitter of the COFDM (coded orthogonal frequency division multiplexing) system. The CSI is calculated by interpolation using the pilots in the receiver. The active real (I) and imaginary (Q) data after equalization are transferred to the branch metric calculation block that decides the euclidean distance for soft decision decoding and also the estimated CSI values are transferred to the same block. After calculating the euclidean distance for the soft decision decoding, the euclidean distance of the branch metric is multiplied by CSI. To do so, new branch metric values that consider each carrier state information are obtained. We simulated this method in Rayleigh fading defined in the ETSI standard. From the simulation, this method has better performance of about 0.15 dB to 0.7 dB and 2.2 dB to 2.9 dB in the Rayleigh channel than that of conventional soft decision Viterbi decoding with or without a bit interleaver where the constellation is QPSK, l6-QAM and 64-QAM.