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217
Waveletbased statistical signal processing using hidden Markov models
 IEEE Transactions on Signal Processing
, 1998
"... Abstract — Waveletbased statistical signal processing techniques such as denoising and detection typically model the wavelet coefficients as independent or jointly Gaussian. These models are unrealistic for many realworld signals. In this paper, we develop a new framework for statistical signal pr ..."
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Cited by 381 (53 self)
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Abstract — Waveletbased statistical signal processing techniques such as denoising and detection typically model the wavelet coefficients as independent or jointly Gaussian. These models are unrealistic for many realworld signals. In this paper, we develop a new framework for statistical signal processing based on waveletdomain hidden Markov models (HMM’s) that concisely models the statistical dependencies and nonGaussian statistics encountered in realworld signals. Waveletdomain HMM’s are designed with the intrinsic properties of the wavelet transform in mind and provide powerful, yet tractable, probabilistic signal models. Efficient expectation maximization algorithms are developed for fitting the HMM’s to observational signal data. The new framework is suitable for a wide range of applications, including signal estimation, detection, classification, prediction, and even synthesis. To demonstrate the utility of waveletdomain HMM’s, we develop novel algorithms for signal denoising, classification, and detection. Index Terms — Hidden Markov model, probabilistic graph, wavelets.
Difficulties in Simulating the Internet
 IEEE/ACM Transactions on Networking
, 2001
"... Simulating how the global Internet behaves is an immensely challenging undertaking because of the network's great heterogeneity and rapid change. The heterogeneity ranges from the individual links that carry the network's traffic, to the protocols that interoperate over the links, to the & ..."
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Cited by 334 (8 self)
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Simulating how the global Internet behaves is an immensely challenging undertaking because of the network's great heterogeneity and rapid change. The heterogeneity ranges from the individual links that carry the network's traffic, to the protocols that interoperate over the links, to the "mix" of different applications used at a site, to the levels of congestion seen on different links. We discuss two key strategies for developing meaningful simulations in the face of these difficulties: searching for invariants, and judiciously exploring the simulation parameter space. We finish with a brief look at a collaborative effort within the research community to develop a common network simulator. 1 Introduction Due to the network's complexity, simulation plays a vital role in attempting to characterize both the behavior of the current Internet and the possible effects of proposed changes to its operation. Yet modeling and simulating the Internet is not an easy task. The goal of this paper ...
Wavelet Analysis of Long Range Dependent Traffic
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A Wavelet based tool for the analysis of long range dependence is introduced and a related semiparametric estimator of the Hurst parameter. The estimator is shown to be unbiased under very general conditions, and efficient under Gaussian assumptions. It can be implemented very efficiently allowing t ..."
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Cited by 259 (22 self)
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A Wavelet based tool for the analysis of long range dependence is introduced and a related semiparametric estimator of the Hurst parameter. The estimator is shown to be unbiased under very general conditions, and efficient under Gaussian assumptions. It can be implemented very efficiently allowing the direct analysis of very large data sets, and is highly robust against the presence of deterministic trends, as well as allowing their detection and identification. Statistical, computational and numerical comparisons are made against traditional estimators including that of Whittle. The estimator is used to perform a thorough analysis of the long range dependence in Ethernet traffic traces. New features are found with important implications for the choice of valid models for performance evaluation. A study of mono vs multifractality is also performed, and a preliminary study of the stationarity with respect to the Hurst parameter and deterministic trends.
Why We Don't Know How to Simulate the Internet
, 1997
"... Simulating how the global Internet data network behaves is an immensely challenging undertaking because of the network's great heterogeneity and rapid change. The heterogeneity ranges from the individual links that carry the network's traffic, to the protocols that interoperate over the li ..."
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Cited by 228 (4 self)
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Simulating how the global Internet data network behaves is an immensely challenging undertaking because of the network's great heterogeneity and rapid change. The heterogeneity ranges from the individual links that carry the network's traffic, to the protocols that interoperate over the links, to the "mix" of different applications used at a site and the levels of congestion (load) seen on different links. We discuss two key strategies for developing meaningful simulations in the face of these difficulties: searching for invariants and judiciously exploring the simulation parameter space. We finish with a look at a collaborative effort to build a common simulation environment for conducting Internet studies.
A multifractal wavelet model with application to TCP network traffic
 IEEE TRANS. INFORM. THEORY
, 1999
"... In this paper, we develop a new multiscale modeling framework for characterizing positivevalued data with longrangedependent correlations (1=f noise). Using the Haar wavelet transform and a special multiplicative structure on the wavelet and scaling coefficients to ensure positive results, the mo ..."
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Cited by 206 (34 self)
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In this paper, we develop a new multiscale modeling framework for characterizing positivevalued data with longrangedependent correlations (1=f noise). Using the Haar wavelet transform and a special multiplicative structure on the wavelet and scaling coefficients to ensure positive results, the model provides a rapid O(N) cascade algorithm for synthesizing Npoint data sets. We study both the secondorder and multifractal properties of the model, the latter after a tutorial overview of multifractal analysis. We derive a scheme for matching the model to real data observations and, to demonstrate its effectiveness, apply the model to network traffic synthesis. The flexibility and accuracy of the model and fitting procedure result in a close fit to the real data statistics (variancetime plots and moment scaling) and queuing behavior. Although for illustrative purposes we focus on applications in network traffic modeling, the multifractal wavelet model could be useful in a number of other areas involving positive data, including image processing, finance, and geophysics.
Multiresolution markov models for signal and image processing
 Proceedings of the IEEE
, 2002
"... This paper reviews a significant component of the rich field of statistical multiresolution (MR) modeling and processing. These MR methods have found application and permeated the literature of a widely scattered set of disciplines, and one of our principal objectives is to present a single, coheren ..."
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Cited by 141 (18 self)
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This paper reviews a significant component of the rich field of statistical multiresolution (MR) modeling and processing. These MR methods have found application and permeated the literature of a widely scattered set of disciplines, and one of our principal objectives is to present a single, coherent picture of this framework. A second goal is to describe how this topic fits into the even larger field of MR methods and concepts–in particular making ties to topics such as wavelets and multigrid methods. A third is to provide several alternate viewpoints for this body of work, as the methods and concepts we describe intersect with a number of other fields. The principle focus of our presentation is the class of MR Markov processes defined on pyramidally organized trees. The attractiveness of these models stems from both the very efficient algorithms they admit and their expressive power and broad applicability. We show how a variety of methods and models relate to this framework including models for selfsimilar and 1/f processes. We also illustrate how these methods have been used in practice. We discuss the construction of MR models on trees and show how questions that arise in this context make contact with wavelets, state space modeling of time series, system and parameter identification, and hidden
A comparative study on contentbased music genre classification
 in Proc. SIGIR, 2003
"... Contentbased music genre classification is a fundamental component of music information retrieval systems and has been gaining importance and enjoying a growing amount of attention with the emergence of digital music on the Internet. Currently little work has been done on automatic music genre clas ..."
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Cited by 109 (15 self)
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Contentbased music genre classification is a fundamental component of music information retrieval systems and has been gaining importance and enjoying a growing amount of attention with the emergence of digital music on the Internet. Currently little work has been done on automatic music genre classification, and in addition, the reported classification accuracies are relatively low. This paper proposes a new feature extraction method for music genre classification, DWCHs 1. DWCHs capture the local and global information of music signals simultaneously by computing histograms on their Daubechies wavelet coefficients. Effectiveness of this new feature and of previously studied features are compared using various machine learning classification algorithms, including Support Vector Machines and Linear Discriminant Analysis. It is demonstrated that the use of DWCHs significantly improves the accuracy of music genre classification.
Fast Approximation of SelfSimilar Network Traffic
, 1995
"... Recent network traffic studies argue that network arrival processes are much more faithfully modeled using statistically selfsimilar processes instead of traditional Poisson processes [LTWW94a, PF94]. One difficulty in dealing with selfsimilar models is how to efficiently synthesize traces (sample ..."
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Cited by 104 (0 self)
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Recent network traffic studies argue that network arrival processes are much more faithfully modeled using statistically selfsimilar processes instead of traditional Poisson processes [LTWW94a, PF94]. One difficulty in dealing with selfsimilar models is how to efficiently synthesize traces (sample paths) corresponding to selfsimilar traffic. We present a fast Fourier transform method for synthesizing approximate selfsimilar sample paths and assess its performance and validity. We find that the method is as fast or faster than existing methods and appears to generate a closer approximation to true selfsimilar sample paths than the other known fast method (Random Midpoint Displacement). We then discuss issues in using such synthesized sample paths for simulating network traffic, and how an approximation used by our method can dramatically speed up evaluation of Whittle's estimator for H, the Hurst parameter giving the strength of longrange dependence present in a selfsimilar time s...
Connectionlevel Analysis and Modeling of Network Traffic
 in ACM SIGCOMM Internet Measurement Workshop
, 2001
"... Abstract — Most network traffic analysis and modeling studies lump all connections together into a single flow. Such aggregate traffic typically exhibits longrangedependent (LRD) correlations and nonGaussian marginal distributions. Importantly, in a typical aggregate traffic model, traffic bursts ..."
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Cited by 97 (5 self)
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Abstract — Most network traffic analysis and modeling studies lump all connections together into a single flow. Such aggregate traffic typically exhibits longrangedependent (LRD) correlations and nonGaussian marginal distributions. Importantly, in a typical aggregate traffic model, traffic bursts arise from many connections being active simultaneously. In this paper, we develop a new framework for analyzing and modeling network traffic that moves beyond aggregation by incorporating connectionlevel information. A careful study of many traffic traces acquired in different networking situations reveals (in opposition to the aggregate modeling ideal) that traffic bursts typically arise from just a few highvolume connections that dominate all others. We term such dominating connections alpha traffic. Alpha traffic is caused by large file transmissions over high bandwidth links and is extremely bursty (nonGaussian). Stripping the alpha traffic from an aggregate trace leaves a beta traffic residual that is Gaussian, LRD, and shares the same fractal scaling exponent as the aggregate traffic. Beta traffic is caused by both small and large file transmissions over low bandwidth links. In our alpha/beta traffic model, the heterogeneity of the network resources give rise to burstiness and heavytailed connection durations give rise to LRD. Queuing experiments suggest that the alpha component dictates the tail queue behavior for large queue sizes, whereas the beta component controls the tail queue behavior for small queue sizes. Keywords—network traffic modeling, animal kingdom I.
Multiscale Representations of Markov Random Fields
 IEEE TRANSACTIONS ON SIGNAL PROCESSING. VOL 41. NO 12. DECEMBER 1993
, 1993
"... Recently, a framework for multiscale stochastic modeling was introduced based on coarsetofine scalerecursive dynamics defined on trees. This model class has some attractive characteristics which lead to extremely efficient, statistically optimal signal and image processing algorithms. In this pap ..."
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Cited by 93 (26 self)
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Recently, a framework for multiscale stochastic modeling was introduced based on coarsetofine scalerecursive dynamics defined on trees. This model class has some attractive characteristics which lead to extremely efficient, statistically optimal signal and image processing algorithms. In this paper, we show that this model class is also quite rich. In particular, we describe how 1D Markov processes and 2D Markov random fields (MRF’s) can be represented within this framework. The recursive structure of 1D Markov processes makes them simple to analyze, and generally leads to computationally efficient algorithms for statistical inference. On the other hand, 2D MRF’s are well known to be very difficult to analyze due to their noncausal structure, and thus their use typically leads to computationally intensive algorithms for smoothing and parameter identification. In contrast, our multiscale representations are based on scalerecursive models and thus lead naturally to scalerecursive algorithms, which can be substantially more efficient computationally than those associated with MRF models. In 1D, the multiscale representation is a generalization of the midpoint deflection construction of Brownian motion. The representation of 2D MRF’s is based on a further generalization to a “midline ” deflection construction. The exact representations of 2D MRF’s are used to motivate a class of multiscale approximate MRF models based on onedimensional wavelet transforms. We demonstrate the use of these latter models in the context of texture representation and, in particular, we show how they can be used as approximations for or alternatives to wellknown MRF texture models.