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79
GTM: The generative topographic mapping
 Neural Computation
, 1998
"... Latent variable models represent the probability density of data in a space of several dimensions in terms of a smaller number of latent, or hidden, variables. A familiar example is factor analysis which is based on a linear transformations between the latent space and the data space. In this paper ..."
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Cited by 303 (5 self)
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Latent variable models represent the probability density of data in a space of several dimensions in terms of a smaller number of latent, or hidden, variables. A familiar example is factor analysis which is based on a linear transformations between the latent space and the data space. In this paper we introduce a form of nonlinear latent variable model called the Generative Topographic Mapping for which the parameters of the model can be determined using the EM algorithm. GTM provides a principled alternative to the widely used SelfOrganizing Map (SOM) of Kohonen (1982), and overcomes most of the significant limitations of the SOM. We demonstrate the performance of the GTM algorithm on a toy problem and on simulated data from flow diagnostics for a multiphase oil pipeline. Copyright c○MIT Press (1998). 1
A review of image denoising algorithms, with a new one
 Simul
, 2005
"... Abstract. The search for efficient image denoising methods is still a valid challenge at the crossing of functional analysis and statistics. In spite of the sophistication of the recently proposed methods, most algorithms have not yet attained a desirable level of applicability. All show an outstand ..."
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Cited by 297 (2 self)
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Abstract. The search for efficient image denoising methods is still a valid challenge at the crossing of functional analysis and statistics. In spite of the sophistication of the recently proposed methods, most algorithms have not yet attained a desirable level of applicability. All show an outstanding performance when the image model corresponds to the algorithm assumptions but fail in general and create artifacts or remove image fine structures. The main focus of this paper is, first, to define a general mathematical and experimental methodology to compare and classify classical image denoising algorithms and, second, to propose a nonlocal means (NLmeans) algorithm addressing the preservation of structure in a digital image. The mathematical analysis is based on the analysis of the “method noise, ” defined as the difference between a digital image and its denoised version. The NLmeans algorithm is proven to be asymptotically optimal under a generic statistical image model. The denoising performance of all considered methods are compared in four ways; mathematical: asymptotic order of magnitude of the method noise under regularity assumptions; perceptualmathematical: the algorithms artifacts and their explanation as a violation of the image model; quantitative experimental: by tables of L 2 distances of the denoised version to the original image. The most powerful evaluation method seems, however, to be the visualization of the method noise on natural images. The more this method noise looks like a real white noise, the better the method.
A Review and Empirical Evaluation of Feature Weighting Methods for a Class of Lazy Learning Algorithms
 ARTIFICIAL INTELLIGENCE REVIEW
, 1997
"... Many lazy learning algorithms are derivatives of the knearest neighbor (kNN) classifier, which uses a distance function to generate predictions from stored instances. Several studies have shown that kNN's performance is highly sensitive to the definition of its distance function. Many k ..."
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Cited by 126 (0 self)
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Many lazy learning algorithms are derivatives of the knearest neighbor (kNN) classifier, which uses a distance function to generate predictions from stored instances. Several studies have shown that kNN's performance is highly sensitive to the definition of its distance function. Many kNN variants have been proposed to reduce this sensitivity by parameterizing the distance function with feature weights. However, these variants have not been categorized nor empirically compared. This paper reviews a class of weightsetting methods for lazy learning algorithms. We introduce a framework for distinguishing these methods and empirically compare them. We observed four trends from our experiments and conducted further studies to highlight them. Our results suggest that methods which use performance feedback to assign weight settings demonstrated three advantages over other methods: they require less preprocessing, perform better in the presence of interacting features, and generally require less training data to learn good settings. We also found that continuous weighting methods tend to outperform feature selection algorithms for tasks where some features are useful but less important than others.
Local polynomial kernel regression for generalized linear models and quasilikelihood functions
 Journal of the American Statistical Association,90
, 1995
"... were introduced as a means of extending the techniques of ordinary parametric regression to several commonlyused regression models arising from nonnormal likelihoods. Typically these models have a variance that depends on the mean function. However, in many cases the likelihood is unknown, but the ..."
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Cited by 65 (7 self)
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were introduced as a means of extending the techniques of ordinary parametric regression to several commonlyused regression models arising from nonnormal likelihoods. Typically these models have a variance that depends on the mean function. However, in many cases the likelihood is unknown, but the relationship between mean and variance can be specified. This has led to the consideration of quasilikelihood methods, where the conditionalloglikelihood is replaced by a quasilikelihood function. In this article we investigate the extension of the nonparametric regression technique of local polynomial fitting with a kernel weight to these more general contexts. In the ordinary regression case local polynomial fitting has been seen to possess several appealing features in terms of intuitive and mathematical simplicity. One noteworthy feature is the better performance near the boundaries compared to the traditional kernel regression estimators. These properties are shown to carryover to the generalized linear model and quasilikelihood model. The end result is a class of kernel type estimators for smoothing in quasilikelihood models. These estimators can be viewed as a straightforward generalization of the usual parametric estimators. In addition, their simple asymptotic distributions allow for simple interpretation
Nonparametric function induction in semisupervised learning
 In Proc. Artificial Intelligence and Statistics
, 2005
"... There has been an increase of interest for semisupervised learning recently, because of the many datasets with large amounts of unlabeled examples and only a few labeled ones. This paper follows up on proposed nonparametric algorithms which provide an estimated continuous label for the given unlabe ..."
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Cited by 43 (6 self)
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There has been an increase of interest for semisupervised learning recently, because of the many datasets with large amounts of unlabeled examples and only a few labeled ones. This paper follows up on proposed nonparametric algorithms which provide an estimated continuous label for the given unlabeled examples. First, it extends them to function induction algorithms that minimize a regularization criterion applied to an outofsample example, and happen to have the form of Parzen windows regressors. This allows to predict test labels without solving again a linear system of dimension n (the number of unlabeled and labeled training examples), which can cost O(n 3). Second, this function induction procedure gives rise to an efficient approximation of the training process, reducing the linear system to be solved to m ≪ n unknowns, using only a subset of m examples. An improvement of O(n 2 /m 2) in time can thus be obtained. Comparative experiments are presented, showing the good performance of the induction formula and approximation algorithm. 1
Feature preserving point set surfaces based on nonlinear kernel regression, Computer Graphics Forum 28 (2
, 2009
"... Moving least squares (MLS) is a very attractive tool to design effective meshless surface representations. However, as long as approximations are performed in a least square sense, the resulting definitions remain sensitive to outliers, and smoothout small or sharp features. In this paper, we addre ..."
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Cited by 33 (1 self)
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Moving least squares (MLS) is a very attractive tool to design effective meshless surface representations. However, as long as approximations are performed in a least square sense, the resulting definitions remain sensitive to outliers, and smoothout small or sharp features. In this paper, we address these major issues, and present a novel point based surface definition combining the simplicity of implicit MLS surfaces [SOS04,Kol05] with the strength of robust statistics. To reach this new definition, we review MLS surfaces in terms of local kernel regression, opening the doors to a vast and well established literature from which we utilize robust kernel regression. Our novel representation can handle sparse sampling, generates a continuous surface better preserving fine details, and can naturally handle any kind of sharp features with controllable sharpness. Finally, it combines ease of implementation with performance competing with other nonrobust approaches. 1.
Principal surfaces from unsupervised kernel regression
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2005
"... Abstract—We propose a nonparametric approach to learning of principal surfaces based on an unsupervised formulation of the NadarayaWatson kernel regression estimator. As compared with previous approaches to principal curves and surfaces, the new method offers several advantages: First, it provides ..."
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Cited by 22 (13 self)
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Abstract—We propose a nonparametric approach to learning of principal surfaces based on an unsupervised formulation of the NadarayaWatson kernel regression estimator. As compared with previous approaches to principal curves and surfaces, the new method offers several advantages: First, it provides a practical solution to the model selection problem because all parameters can be estimated by leaveoneout crossvalidation without additional computational cost. In addition, our approach allows for a convenient incorporation of nonlinear spectral methods for parameter initialization, beyond classical initializations based on linear PCA. Furthermore, it shows a simple way to fit principal surfaces in general feature spaces, beyond the usual data space setup. The experimental results illustrate these convenient features on simulated and real data. Index Terms—Dimensionality reduction, principal curves, principal surfaces, density estimation, model selection, kernel methods. æ 1
Visual exploration of high dimensional scalar functions
 IEEE TRANS. VISUALIZATION AND COMPUTER GRAPHICS
, 2010
"... An important goal of scientific data analysis is to understand the behavior of a system or process based on a sample of the system. In many instances it is possible to observe both input parameters and system outputs, and characterize the system as a highdimensional function. Such data sets arise, ..."
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Cited by 13 (8 self)
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An important goal of scientific data analysis is to understand the behavior of a system or process based on a sample of the system. In many instances it is possible to observe both input parameters and system outputs, and characterize the system as a highdimensional function. Such data sets arise, for instance, in large numerical simulations, as energy landscapes in optimization problems, or in the analysis of image data relating to biological or medical parameters. This paper proposes an approach to analyze and visualizing such data sets. The proposed method combines topological and geometric techniques to provide interactive visualizations of discretely sampled highdimensional scalar fields. The method relies on a segmentation of the parameter space using an approximate MorseSmale complex on the cloud of point samples. For each crystal of the MorseSmale complex, a regression of the system parameters with respect to the output yields a curve in the parameter space. The result is a simplified geometric representation of the MorseSmale complex in the high dimensional input domain. Finally, the geometric representation is embedded in 2D, using dimension reduction, to provide a visualization platform. The geometric properties of the regression curves enable the visualization of additional information about each crystal such as local and global shape, width, length, and sampling densities. The method is illustrated on several synthetic examples of two dimensional functions. Two use cases, using data sets from the UCI machine learning repository, demonstrate the utility of the proposed approach on real data. Finally, in collaboration with domain experts the proposed
Dirichlet Process Mixtures of Generalized Linear Models
"... We propose Dirichlet Process mixtures of Generalized Linear Models (DPGLMs), a new method of nonparametric regression that accommodates continuous and categorical inputs, models a response variable locally by a generalized linear model. We give conditions for the existence and asymptotic unbiasedne ..."
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Cited by 13 (1 self)
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We propose Dirichlet Process mixtures of Generalized Linear Models (DPGLMs), a new method of nonparametric regression that accommodates continuous and categorical inputs, models a response variable locally by a generalized linear model. We give conditions for the existence and asymptotic unbiasedness of the DPGLM regression mean function estimate; we then give a practical example for when those conditions hold. We evaluate DPGLM on several data sets, comparing it to modern methods of nonparametric regression including regression trees and Gaussian processes. 1
Modeling and Integrating Background Knowledge in Data Anonymization
"... Abstract — Recent work has shown the importance of considering the adversary’s background knowledge when reasoning about privacy in data publishing. However, it is very difficult for the data publisher to know exactly the adversary’s background knowledge. Existing work cannot satisfactorily model ba ..."
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Abstract — Recent work has shown the importance of considering the adversary’s background knowledge when reasoning about privacy in data publishing. However, it is very difficult for the data publisher to know exactly the adversary’s background knowledge. Existing work cannot satisfactorily model background knowledge and reason about privacy in the presence of such knowledge. This paper presents a general framework for modeling the adversary’s background knowledge using kernel estimation methods. This framework subsumes different types of knowledge (e.g., negative association rules) that can be mined from the data. Under this framework, we reason about privacy using Bayesian inference techniques and propose the skyline (B, t)privacy model, which allows the data publisher to enforce privacy requirements to protect the data against adversaries with different levels of background knowledge. Through an extensive set of experiments, we show the effects of probabilistic background knowledge in data anonymization and the effectiveness of our approach in both privacy protection and utility preservation. I.