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145
Traffic Matrix Estimation: Existing Techniques and New Directions
, 2002
"... Very few techniques have been proposed for estimating traffic matrices in the context of Internet traffic. Our work on POPtoPOP traffic matrices (TM) makes two contributions. The primary contribution is the outcome of a detailed comparative evaluation of the three existing techniques. We evaluate ..."
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Cited by 172 (13 self)
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Very few techniques have been proposed for estimating traffic matrices in the context of Internet traffic. Our work on POPtoPOP traffic matrices (TM) makes two contributions. The primary contribution is the outcome of a detailed comparative evaluation of the three existing techniques. We evaluate these methods with respect to the estimation errors yielded, sensitivity to prior information required and sensitivity to the statistical assumptions they make. We study the impact of characteristics such as path length and the amount of link sharing on the estimation errors. Using actual data from a Tier1 backbone, we assess the validity of the typical assumptions needed by the TM estimation techniques. The secondary contribution of our work is the proposal of a new direction for TM estimation based on using choice models to model POP fanouts. These models allow us to overcome some of the problems of existing methods because they can incorporate additional data and information about POPs and they enable us to make a fundamentally different kind of modeling assumption. We validate this approach by illustrating that our modeling assumption matches actual Internet data well. Using two initial simple models we provide a proof of concept showing that the incorporation of knowledge of POP features (such as total incoming bytes, number of customers, etc.) can reduce estimation errors. Our proposed approach can be used in conjunction with existing or future methods in that it can be used to generate good priors that serve as inputs to statistical inference techniques.
Wavelet transforms versus Fourier transforms
 Department of Mathematics, MIT, Cambridge MA
, 213
"... Abstract. This note is a very basic introduction to wavelets. It starts with an orthogonal basis of piecewise constant functions, constructed by dilation and translation. The "wavelet transform " maps each f(x) to its coefficients with respect to this basis. The mathematics is simple and the transfo ..."
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Cited by 71 (2 self)
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Abstract. This note is a very basic introduction to wavelets. It starts with an orthogonal basis of piecewise constant functions, constructed by dilation and translation. The "wavelet transform " maps each f(x) to its coefficients with respect to this basis. The mathematics is simple and the transform is fast (faster than the Fast Fourier Transform, which we briefly explain), but approximation by piecewise constants is poor. To improve this first wavelet, we are led to dilation equations and their unusual solutions. Higherorder wavelets are constructed, and it is surprisingly quick to compute with them — always indirectly and recursively. We comment informally on the contest between these transforms in signal processing, especially for video and image compression (including highdefinition television). So far the Fourier Transform — or its 8 by 8 windowed version, the Discrete Cosine Transform — is often chosen. But wavelets are already competitive, and they are ahead for fingerprints. We present a sample of this developing theory. 1. The Haar wavelet To explain wavelets we start with an example. It has every property we hope for, except one. If that one defect is accepted, the construction is simple and the computations are fast. By trying to remove the defect, we are led to dilation equations and recursively defined functions and a small world of fascinating new problems — many still unsolved. A sensible person would stop after the first wavelet, but fortunately mathematics goes on. The basic example is easier to draw than to describe: W(x)
Learning Hierarchical Object Maps Of NonStationary Environments With Mobile Robots
 In Proc. of the Conf. on Uncertainty in Artificial Intelligence (UAI
, 2002
"... Building models, or maps, of robot environments is a highly active research area; however, most existing techniques construct unstructured maps and assume static environments. In this paper, we present an algorithm for learning object models of nonstationary objects found in officetype enviro ..."
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Cited by 45 (6 self)
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Building models, or maps, of robot environments is a highly active research area; however, most existing techniques construct unstructured maps and assume static environments. In this paper, we present an algorithm for learning object models of nonstationary objects found in officetype environments. Our algorithm exploits the fact that many objects found in office environments look alike (e.g., chairs, trash bins).
Fast iterative alignment of pose graphs with poor initial estimates
 In IEEE Intl. Conf. on Robotics and Automation (ICRA
, 2006
"... Abstract — A robot exploring an environment can estimate its own motion and the relative positions of features in the environment. Simultaneous Localization and Mapping (SLAM) algorithms attempt to fuse these estimates to produce a map and a robot trajectory. The constraints are generally nonlinear ..."
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Cited by 43 (5 self)
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Abstract — A robot exploring an environment can estimate its own motion and the relative positions of features in the environment. Simultaneous Localization and Mapping (SLAM) algorithms attempt to fuse these estimates to produce a map and a robot trajectory. The constraints are generally nonlinear, thus SLAM can be viewed as a nonlinear optimization problem. The optimization can be difficult, due to poor initial estimates arising from odometry data, and due to the size of the state space. We present a fast nonlinear optimization algorithm that rapidly recovers the robot trajectory, even when given a poor initial estimate. Our approach uses a variant of Stochastic Gradient Descent on an alternative statespace representation that has good stability and computational properties. We compare our algorithm to several others, using both real and synthetic data sets.
kPlane Clustering
 Journal of Global Optimization
, 2000
"... A finite new algorithm is proposed for clustering m given points in ndimensional real space into k clusters by generating k planes that constitute a local solution to the nonconvex problem of minimizing the sum of squares of the 2norm distances between each point and a nearest plane. The key to th ..."
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Cited by 42 (3 self)
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A finite new algorithm is proposed for clustering m given points in ndimensional real space into k clusters by generating k planes that constitute a local solution to the nonconvex problem of minimizing the sum of squares of the 2norm distances between each point and a nearest plane. The key to the algorithm lies in a formulation that generates a plane in ndimensional space that minimizes the sum of the squares of the 2norm distances to each of m1 given points in the space. The plane is generated by an eigenvector corresponding to a smallest eigenvalue of an n \Theta n simple matrix derived from the m1 points. The algorithm was tested on the publicly available Wisconsin Breast Prognosis Cancer database to generate well separated patient survival curves. In contrast, the kmean algorithm did not generate such wellseparated survival curves. 1 Introduction There are many approaches to clustering such as statistical [2, 9, 6], machine learning [7, 8] and mathematical programming [15...
Neighborhood formation and anomaly detection in bipartite graphs
 In ICDM
, 2005
"... Many real applications can be modeled using bipartite graphs, such as users vs. files in a P2P system, traders vs. stocks in a financial trading system, conferences vs. authors in a scientific publication network, and so on. We introduce two operations on bipartite graphs: 1) identifying similar nod ..."
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Cited by 41 (11 self)
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Many real applications can be modeled using bipartite graphs, such as users vs. files in a P2P system, traders vs. stocks in a financial trading system, conferences vs. authors in a scientific publication network, and so on. We introduce two operations on bipartite graphs: 1) identifying similar nodes (Neighborhood formation), and 2) finding abnormal nodes (Anomaly detection). And we propose algorithms to compute the neighborhood for each node using random walk with restarts and graph partitioning; we also propose algorithms to identify abnormal nodes, using neighborhood information. We evaluate the quality of neighborhoods based on semantics of the datasets, and we also measure the performance of the anomaly detection algorithm with manually injected anomalies. Both effectiveness and efficiency of the methods are confirmed by experiments on several real datasets. 1
Robust rangeonly beacon localization
 In Proceedings of Autonomous Underwater Vehicles
, 2004
"... Abstract — Most Autonomous Underwater Vehicle (AUV) systems rely on prior knowledge of beacon locations for localization. We present a system capable of navigating without prior beacon locations. Noise and outliers are major issues; we present a powerful outlier rejection method that imposes geometr ..."
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Cited by 40 (8 self)
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Abstract — Most Autonomous Underwater Vehicle (AUV) systems rely on prior knowledge of beacon locations for localization. We present a system capable of navigating without prior beacon locations. Noise and outliers are major issues; we present a powerful outlier rejection method that imposes geometric constraints on measurements. We have successfully applied our algorithm to realworld data and have demonstrated navigation performance comparable to that of systems that assume known beacon locations. I.
Construction of Multiscaling Functions with Approximation and Symmetry
, 1998
"... . This paper presents a new and e#cient way to create multiscaling functions with given approximation order, regularity, symmetry, and short support. Previous techniques were operating in time domain and required the solution of large systems of nonlinear equations. By switching to the frequency dom ..."
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Cited by 36 (10 self)
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. This paper presents a new and e#cient way to create multiscaling functions with given approximation order, regularity, symmetry, and short support. Previous techniques were operating in time domain and required the solution of large systems of nonlinear equations. By switching to the frequency domain and employing the latest results of the multiwavelet theory we are able to elaborate a simple and e#cient method of construction of multiscaling functions. Our algorithm is based on a recently found factorization of the refinement mask through the twoscale similarity transform (TST). Theoretical results and new examples are presented. Key words. approximation order, symmetry, multiscaling functions, multiwavelets AMS subject classifications. 41A25, 42A38, 39B62 PII. S0036141096297182 1. Introduction. This paper discusses the construction of multiscaling functions which generate a multiresolution analysis (MRA) and lead to multiwavelets. A standard (scalar) MRA assumes that there is ...
Fast Counting of Triangles in Large Real Networks: Algorithms and Laws
"... How can we quickly find the number of triangles in a large graph, without actually counting them? Triangles are important for real world social networks, lying at the heart of the clustering coefficient and of the transitivity ratio. However, straightforward and even approximate counting algorithms ..."
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Cited by 36 (9 self)
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How can we quickly find the number of triangles in a large graph, without actually counting them? Triangles are important for real world social networks, lying at the heart of the clustering coefficient and of the transitivity ratio. However, straightforward and even approximate counting algorithms can be slow, trying to execute or approximate the equivalent of a 3way database join. In this paper, we provide two algorithms, the EigenTriangle for counting the total number of triangles in a graph, and the EigenTriangleLocal algorithm that gives the count of triangles that contain a desired node. Additional contributions include the following: (a) We show that both algorithms achieve excellent accuracy, with up to ≈ 1000x faster execution time, on several, real graphs and (b) we discover two new power laws ( DegreeTriangle and TriangleParticipation laws) with surprising properties. Figure 1. Speedup ratio versus accuracy for the Wikipedia web graph ( ≈ 3, 1M nodes, ≈ 37M edges). Proposed method achieves 1021x faster time, for 97.4 % accuracy, compared to a typical competitor, the Node Iterator method. 1
Multiwavelets: Theory and Applications
, 1996
"... A function OE(t) is refinable if it satisfies a dilation equation OE(t) = P k C k OE(2t \Gamma k). A refinable function (scaling function) generates a multiresolution analysis (MRA): Set of nested subspaces : : : V \Gamma1 ae V 0 ae V 1 : : : such that S 1 j=\Gamma1 V j = L 2 (R), T 1 j=\Gam ..."
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Cited by 35 (4 self)
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A function OE(t) is refinable if it satisfies a dilation equation OE(t) = P k C k OE(2t \Gamma k). A refinable function (scaling function) generates a multiresolution analysis (MRA): Set of nested subspaces : : : V \Gamma1 ae V 0 ae V 1 : : : such that S 1 j=\Gamma1 V j = L 2 (R), T 1 j=\Gamma1 V j = f0g, and translates OE(t \Gamma k) constitute a basis of V 0 . Then a basis fw jk : w jk = w(2 j t \Gamma k) j; k 2 Zg of L 2 (R) is generated by a wavelet w(t), whose translates w(t \Gamma k) form a basis of W 0 , V 1 = V 0 \Phi W 0 . A standard (scalar) MRA assumes that there is only one scaling function. We make a step forward and allow several scaling functions OE 0 (t); : : : ; OE r\Gamma1 (t) to generate a basis of V 0 . The vector OE(t) = [OE 0 (t) : : : OE r\Gamma1 (t)] T satisfies a dilation equation with matrix coefficients C k . Associated with OE(t) is a multiwavelet w(t) = [w 0 (t) : : : w r\Gamma1 (t)] T . Unlike the scalar case, construction of a multiwave...