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979
Independent Component Analysis
 Neural Computing Surveys
, 2001
"... A common problem encountered in such disciplines as statistics, data analysis, signal processing, and neural network research, is nding a suitable representation of multivariate data. For computational and conceptual simplicity, such a representation is often sought as a linear transformation of the ..."
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Cited by 1488 (93 self)
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A common problem encountered in such disciplines as statistics, data analysis, signal processing, and neural network research, is nding a suitable representation of multivariate data. For computational and conceptual simplicity, such a representation is often sought as a linear transformation of the original data. Wellknown linear transformation methods include, for example, principal component analysis, factor analysis, and projection pursuit. A recently developed linear transformation method is independent component analysis (ICA), in which the desired representation is the one that minimizes the statistical dependence of the components of the representation. Such a representation seems to capture the essential structure of the data in many applications. In this paper, we survey the existing theory and methods for ICA. 1
Hierarchical mixtures of experts and the EM algorithm
 Neural Computation
, 1994
"... We present a treestructured architecture for supervised learning. The statistical model underlying the architecture is a hierarchical mixture model in which both the mixture coefficients and the mixture components are generalized linear models (GLIM’s). Learning is treated as a maximum likelihood ..."
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Cited by 723 (19 self)
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We present a treestructured architecture for supervised learning. The statistical model underlying the architecture is a hierarchical mixture model in which both the mixture coefficients and the mixture components are generalized linear models (GLIM’s). Learning is treated as a maximum likelihood problem; in particular, we present an ExpectationMaximization (EM) algorithm for adjusting the parameters of the architecture. We also develop an online learning algorithm in which the parameters are updated incrementally. Comparative simulation results are presented in the robot dynamics domain. 1
ANFIS: AdaptiveNetworkBased Fuzzy Inference System
, 1993
"... This paper presents the architecture and learning procedure underlying ANFIS (AdaptiveNetwork based Fuzzy Inference System), a fuzzy inference system implemented in the framework of adaptive networks. By using a hybrid learning procedure, the proposed ANFIS can construct an inputoutput mapping bas ..."
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Cited by 432 (5 self)
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This paper presents the architecture and learning procedure underlying ANFIS (AdaptiveNetwork based Fuzzy Inference System), a fuzzy inference system implemented in the framework of adaptive networks. By using a hybrid learning procedure, the proposed ANFIS can construct an inputoutput mapping based on both human knowledge (in the form of fuzzy ifthen rules) and stipulated inputoutput data pairs. In our simulation, we employ the ANFIS architecture to model nonlinear functions, identify nonlinear components onlinely in a control system, and predict a chaotic time series, all yielding remarkable results. Comparisons with artificail neural networks and earlier work on fuzzy modeling are listed and discussed. Other extensions of the proposed ANFIS and promising applications to automatic control and signal processing are also suggested. 1 Introduction System modeling based on conventional mathematical tools (e.g., differential equations) is not well suited for dealing with illdefine...
Exponentiated Gradient Versus Gradient Descent for Linear Predictors
 Information and Computation
, 1995
"... this paper, we concentrate on linear predictors . To any vector u 2 R ..."
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Cited by 246 (12 self)
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this paper, we concentrate on linear predictors . To any vector u 2 R
Neurofuzzy modeling and control
 IEEE Proceedings
, 1995
"... Abstract  Fundamental and advanced developments in neurofuzzy synergisms for modeling and control are reviewed. The essential part of neurofuzzy synergisms comes from a common framework called adaptive networks, which uni es both neural networks and fuzzy models. The fuzzy models under the framew ..."
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Cited by 147 (1 self)
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Abstract  Fundamental and advanced developments in neurofuzzy synergisms for modeling and control are reviewed. The essential part of neurofuzzy synergisms comes from a common framework called adaptive networks, which uni es both neural networks and fuzzy models. The fuzzy models under the framework of adaptive networks is called ANFIS (AdaptiveNetworkbased Fuzzy Inference System), which possess certain advantages over neural networks. We introduce the design methods for ANFIS in both modeling and control applications. Current problems and future directions for neurofuzzy approaches are also addressed. KeywordsFuzzy logic, neural networks, fuzzy modeling, neurofuzzy modeling, neurofuzzy control, ANFIS. I.
Proper complex random processes with applications to information theory
 152 tel00906143, version 1  19 Nov 2013
, 1993
"... Abstract The “covariance ” of complex random variables and processes, when defined consistently with the corresponding notion for real random variables, is shown to be determined by the usual (complex) covariance together with a quantity called the pseudocovariance. A characterization of uncorrela ..."
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Cited by 114 (0 self)
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Abstract The “covariance ” of complex random variables and processes, when defined consistently with the corresponding notion for real random variables, is shown to be determined by the usual (complex) covariance together with a quantity called the pseudocovariance. A characterization of uncorrelatedness and widesense stationarity in terms of covariance and pseudocovariance is given. Complex random variables and processes with a vanishing pseudocovariance are called proper. It is shown that properness is preserved under affine transformations and that the complexmultivariate Gaussian density assumes a natural form only for proper random variables. The maximumentropy theorem is generalized to the complexmultivariate case. The differential entropy of a complex random vector with a fixed correlation matrix is shown to be maximum, if and only if the random vector is proper, Gaussian and zeromean. The notion of circular stutionarity is introduced. For the class of proper complex random processes, a discrete Fourier transform correspondence is derived relating circular stationarity in the time domain to uncorrelatedness in the frequency domain. As an application of the theory, the capacity of a discretetime channel with complex inputs, proper complex additive white Gaussian noise, and a finite complex unitsample response is determined. This derivation is considerably simpler than an earlier derivation for the real discretetime Gaussian channel with intersymbol interference, whose capacity is obtained as a byproduct of the results for the complex channel. Znder TermsProper complex random processes, circular stationarity, intersymbol interference, capacity. T I.
Equalization Using the Constant Modulus Criterion: A
 Review,” Proccedings of the IEEE, Invited
, 1997
"... This paper provides a tutorial introduction to the constant modulus (CM) criterion for blind fractionally spaced equalizer (FSE) design via a (stochastic) gradient descent algorithm such as the constant modulus algorithm (CMA). The topical divisions utilized in this tutorial can be used to help cata ..."
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Cited by 100 (21 self)
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This paper provides a tutorial introduction to the constant modulus (CM) criterion for blind fractionally spaced equalizer (FSE) design via a (stochastic) gradient descent algorithm such as the constant modulus algorithm (CMA). The topical divisions utilized in this tutorial can be used to help catalog the emerging literature on the CM criterion and on the behavior of (stochastic) gradient descent algorithms used to minimize it.
Basis Expansion Models and Diversity Techniques for Blind Identification and Equalization of TimeVarying Channels
 PROC. IEEE
, 1998
"... ..."
RateDistortion Optimized Mode Selection for Very Low Bit Rate Video Coding and the Emerging H.263 Standard
, 1995
"... This paper addresses the problem of encoder optimization in a macroblockbased multimode video compression system. An efficient solution is proposed in which, for a given image region, the optimum combination of macroblock modes and the associated mode parameters are jointly selected so as to minim ..."
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Cited by 76 (12 self)
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This paper addresses the problem of encoder optimization in a macroblockbased multimode video compression system. An efficient solution is proposed in which, for a given image region, the optimum combination of macroblock modes and the associated mode parameters are jointly selected so as to minimize the overall distortion for a given bitrate budget. Conditions for optimizing the encoder operation are derived within a rateconstrained product code framework using a Lagrangian formulation. The instantaneous rate of the encoder is controlled by a single Lagrange multiplier that makes the method amenable to mobile wireless networks with timevarying capacity. When rate and distortion dependencies are introduced between adjacent blocks (as is the case when the motion vectors are differentially encoded and/or overlapped block motion compensation is employed), the ensuing encoder complexity is surmounted using dynamic programming. Due to the generic nature of the algorithm, it can be succ...
Beyond streams and graphs: Dynamic tensor analysis
 In KDD
, 2006
"... How do we find patterns in authorkeyword associations, evolving over time? Or in DataCubes, with productbranchcustomer sales information? Matrix decompositions, like principal component analysis (PCA) and variants, are invaluable tools for mining, dimensionality reduction, feature selection, rule ..."
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Cited by 70 (11 self)
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How do we find patterns in authorkeyword associations, evolving over time? Or in DataCubes, with productbranchcustomer sales information? Matrix decompositions, like principal component analysis (PCA) and variants, are invaluable tools for mining, dimensionality reduction, feature selection, rule identification in numerous settings like streaming data, text, graphs, social networks and many more. However, they have only two orders, like author and keyword, in the above example. We propose to envision such higher order data as tensors, and tap the vast literature on the topic. However, these methods do not necessarily scale up, let alone operate on semiinfinite streams. Thus, we introduce the dynamic tensor analysis (DTA) method, and its variants. DTA provides a compact summary for highorder and highdimensional data, and it also reveals the hidden correlations. Algorithmically, we designed DTA very carefully so that it is (a) scalable, (b) space efficient (it does not need to store the past) and (c) fully automatic with no need for user defined parameters. Moreover, we propose STA, a streaming tensor analysis method, which provides a fast, streaming approximation to DTA. We implemented all our methods, and applied them in two real settings, namely, anomaly detection and multiway latent semantic indexing. We used two real, large datasets, one on network flow data (100GB over 1 month) and one from DBLP (200MB over 25 years). Our experiments show that our methods are fast, accurate and that they find interesting patterns and outliers on the real datasets. 1.