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64
A tutorial on support vector regression
, 2004
"... In this tutorial we give an overview of the basic ideas underlying Support Vector (SV) machines for function estimation. Furthermore, we include a summary of currently used algorithms for training SV machines, covering both the quadratic (or convex) programming part and advanced methods for dealing ..."
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Cited by 473 (2 self)
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In this tutorial we give an overview of the basic ideas underlying Support Vector (SV) machines for function estimation. Furthermore, we include a summary of currently used algorithms for training SV machines, covering both the quadratic (or convex) programming part and advanced methods for dealing with large datasets. Finally, we mention some modifications and extensions that have been applied to the standard SV algorithm, and discuss the aspect of regularization from a SV perspective.
An introduction to kernelbased learning algorithms
 IEEE TRANSACTIONS ON NEURAL NETWORKS
, 2001
"... This paper provides an introduction to support vector machines (SVMs), kernel Fisher discriminant analysis, and ..."
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Cited by 373 (48 self)
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This paper provides an introduction to support vector machines (SVMs), kernel Fisher discriminant analysis, and
Regularization Theory and Neural Networks Architectures
 Neural Computation
, 1995
"... We had previously shown that regularization principles lead to approximation schemes which are equivalent to networks with one layer of hidden units, called Regularization Networks. In particular, standard smoothness functionals lead to a subclass of regularization networks, the well known Radial Ba ..."
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Cited by 309 (31 self)
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We had previously shown that regularization principles lead to approximation schemes which are equivalent to networks with one layer of hidden units, called Regularization Networks. In particular, standard smoothness functionals lead to a subclass of regularization networks, the well known Radial Basis Functions approximation schemes. This paper shows that regularization networks encompass a much broader range of approximation schemes, including many of the popular general additive models and some of the neural networks. In particular, we introduce new classes of smoothness functionals that lead to different classes of basis functions. Additive splines as well as some tensor product splines can be obtained from appropriate classes of smoothness functionals. Furthermore, the same generalization that extends Radial Basis Functions (RBF) to Hyper Basis Functions (HBF) also leads from additive models to ridge approximation models, containing as special cases Breiman's hinge functions, som...
Smoothness in Layers: Motion segmentation using nonparametric mixture estimation
, 1997
"... Grouping based on common motion, or "common fate" provides a powerful cue for segmenting image sequences. Recently a number of algorithms have been developed that successfully perform motion segmentation by assuming that the motion of each group can be described by a low dimensional parametric model ..."
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Cited by 160 (5 self)
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Grouping based on common motion, or "common fate" provides a powerful cue for segmenting image sequences. Recently a number of algorithms have been developed that successfully perform motion segmentation by assuming that the motion of each group can be described by a low dimensional parametric model (e.g. affine). Typically the assumption is that motion segments correspond to planar patches in 3D undergoing rigid motion. Here we develop an alternative approach, where the motion of each group is described by a smooth dense flow field and the stability of the estimation is ensured by means of a prior distribution on the class of flow fields. We present a variant of the EM algorithm that can segment image sequences by fitting multiple smooth flow fields to the spatiotemporal data. Using the method of Green's functions, we show how the estimation of a single smooth flow field can be performed in closed form, thus making the multiple model estimation computationally feasible. Furthermore, t...
Trainable Videorealistic Speech Animation
 PROCEEDINGS OF SIGGRAPH 2002, SAN ANTONIO TEXAS
, 2002
"... We describe how to create with machine learning techniques a generative, videorealistic, speech animation module. A human subject is first recorded using a videocamera as he/she utters a predetermined speech corpus. After processing the corpus automatically, a visual speech module is learned from th ..."
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Cited by 156 (5 self)
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We describe how to create with machine learning techniques a generative, videorealistic, speech animation module. A human subject is first recorded using a videocamera as he/she utters a predetermined speech corpus. After processing the corpus automatically, a visual speech module is learned from the data that is capable of synthesizing the human subject's mouth uttering entirely novel utterances that were not recorded in the original video. The synthesized utterance is recomposited onto a background sequence which contains natural head and eye movement. The final output is videorealistic in the sense that it looks like a video camera recording of the subject. At run time, the input to the system can be either real audio sequences or synthetic audio produced by a texttospeech system, as long as they have been phonetically aligned. The two key
The Connection between Regularization Operators and Support Vector Kernels
, 1998
"... In this paper a correspondence is derived between regularization operators used in Regularization Networks and Support Vector Kernels. We prove that the Green's Functions associated with regularization operators are suitable Support Vector Kernels with equivalent regularization properties. Moreover ..."
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Cited by 146 (43 self)
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In this paper a correspondence is derived between regularization operators used in Regularization Networks and Support Vector Kernels. We prove that the Green's Functions associated with regularization operators are suitable Support Vector Kernels with equivalent regularization properties. Moreover the paper provides an analysis of currently used Support Vector Kernels in the view of regularization theory and corresponding operators associated with the classes of both polynomial kernels and translation invariant kernels. The latter are also analyzed on periodical domains. As a byproduct we show that a large number of Radial Basis Functions, namely conditionally positive definite functions, may be used as Support Vector kernels.
Kernel partial least squares regression in reproducing kernel hilbert space
 Journal of Machine Learning Research
, 2001
"... A family of regularized least squares regression models in a Reproducing Kernel Hilbert Space is extended by the kernel partial least squares (PLS) regression model. Similar to principal components regression (PCR), PLS is a method based on the projection of input (explanatory) variables to the late ..."
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Cited by 106 (5 self)
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A family of regularized least squares regression models in a Reproducing Kernel Hilbert Space is extended by the kernel partial least squares (PLS) regression model. Similar to principal components regression (PCR), PLS is a method based on the projection of input (explanatory) variables to the latent variables (components). However, in contrast to PCR, PLS creates the components by modeling the relationship between input and output variables while maintaining most of the information in the input variables. PLS is useful in situations where the number of explanatory variables exceeds the number of observations and/or a high level of multicollinearity among those variables is assumed. Motivated by this fact we will provide a kernel PLS algorithm for construction of nonlinear regression models in possibly highdimensional feature spaces. We give the theoretical description of the kernel PLS algorithm and we experimentally compare the algorithm with the existing kernel PCR and kernel ridge regression techniques. We will demonstrate that on the data sets employed kernel PLS achieves the same results as kernel PCR but uses significantly fewer, qualitatively different components. 1.
A nonparametric approach to pricing and hedging derivative securities via learning networks
 Journal of Finance
, 1994
"... http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, noncom ..."
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Cited by 104 (4 self)
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http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, noncommercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at
Example Based Image Analysis and Synthesis
, 1993
"... Image analysis and graphics synthesis can be achieved with learning techniques using directly image examples without physicallybased, 3D models. We describe here novel techniques for the analysis and the synthesis of new greylevel (and color) images. With the first technique, ffl the mapping from ..."
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Cited by 101 (26 self)
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Image analysis and graphics synthesis can be achieved with learning techniques using directly image examples without physicallybased, 3D models. We describe here novel techniques for the analysis and the synthesis of new greylevel (and color) images. With the first technique, ffl the mapping from novel images to a vector of "pose" and "expression" parameters can be learned from a small set of example images using a function approximation technique that we call an analysis network; ffl the inverse mapping from input "pose" and "expression" parameters to output greylevel images can be synthesized from a small set of example images and used to produce new images under realtime control using a similar learning network, called in this case a synthesis network. This technique relies on (i) using a correspondence algorithm that matches corresponding pixels among pairs of greylevel images and effectively "vectorizes" them, and (ii) exploiting a class of multidimensional interpolation n...
On a Kernelbased Method for Pattern Recognition, Regression, Approximation, and Operator Inversion
, 1997
"... We present a Kernelbased framework for Pattern Recognition, Regression Estimation, Function Approximation and multiple Operator Inversion. Previous approaches such as ridgeregression, Support Vector methods and regression by Smoothing Kernels are included as special cases. We will show connection ..."
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Cited by 77 (25 self)
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We present a Kernelbased framework for Pattern Recognition, Regression Estimation, Function Approximation and multiple Operator Inversion. Previous approaches such as ridgeregression, Support Vector methods and regression by Smoothing Kernels are included as special cases. We will show connections between the costfunction and some properties up to now believed to apply to Support Vector Machines only. The optimal solution of all the problems described above can be found by solving a simple quadratic programming problem. The paper closes with a proof of the equivalence between Support Vector kernels and Greene's functions of regularization operators.