Mark A. Aizerman, Emmanuel M. Braverman, and Lev I. Rozono er. Theoretical foundations of the potential function method in pattern recognition and learning. Automation and Remote Control, 25:821--837, 1964.  Home/Search Document Not in Database Summary Related Articles Check |
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A Tutorial on ν-Support Vector Machines - Chen, Lin, Schölkopf (Correct)
....different. For the former, we require a similarity measure k : X X # R, x, x # ) k(x, x # ) 2) i.e. a function that, given two examples x and x # , returns a real number characterizing their similarity. For reasons that will become clear later, the function k is called a kernel ( 24] [1], 8] A type of similarity measure that is of particular mathematical appeal are dot products. For instance, given two vectors x, x # , the canonical dot product is defined Parts of the present article are based on [31] as x # ) x) i (x # ) i . 3) Here, x) i denotes the ....
.... Portrait hyperplane classifier [41] to nonlinear Support Vector machines [8] Aizerman et al. called the linearization space, and used in the context of the potential function classification method to express the dot product between elements of in terms of elements of the input space [1]. What does k look like for the case of polynomial features We start by giving an example ( 38] for N = d = 2. For the map # 2 : x] 1 , x] 2 ) 2 , x] 1 [x] 2 , x] 2 [x] 1 ) 48) dot products in take the form (# 2 (x) # 2 (x # ) x] 1 [x] 2 2[x] 1 [x] 2 [x # ] 1 ....
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M. A. Aizerman, E.. M. Braverman, and L. I. Rozono er. Theoretical foundations of the potential function method in pattern recognition learning. Automation and Remote Control, 25:821--837, 1964.
Statistical Mechanics of Neural Networks: Enhancement by.. - Dietrich (Correct)
....the power and note that the double integral in (3.21) factorises. The separating surface is a polynomial surface of degree d. Radial basis function (RBF) classifiers, K (# ) exp [ # #] with student classification S exp # . The proof has been stated in [1]. Two layer neural networks, K (# ) tanh [c # d] implementing the classification rule S tanh [c # d] In this case, 3.21) holds only for some range of values of c and d, cf. 70, p. 141] All three types of kernels have been successfully applied to the real ....
M. Aizerman, E. Braverman, and L. Rozonoer. Theoretical foundations of the potential function method in pattern recognition learning. Automation and Remote Control, 25:821--837, 1964.
Technical documentation of the multi-class SVM - Guermeur (2003) (Correct)
....set of functions h from R into R given by : 8x 2 X ; h(x) Wx b = 6 6 6 6 6 6 . 7 7 7 7 7 7 x 6 6 6 6 6 6 . 7 7 7 7 7 7 5 The second is nonlinear. Il directly springs from the preceding one, by introduction of a kernel k satisfying Mercer s conditions [1]. This kernel can be expressed as the l 2 dot product in a feature space image of R by a nonlinear function . This can be written as : 8(x 1 ; x 2 ) 2 R ; k(x 1 ; x 2 ) x 1 ) x 2 ) The model can thus be expressed as follows : 8x 2 X ; h(x) W (x) b = 6 6 6 6 6 6 . ....
M. Aizerman, E. Braverman, and L. Rozonoer. Theoretical foundations of the potential function method in pattern recognition learning. Automation and Remote Control, 25:821-837, 1964.
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Mark A. Aizerman, Emmanuel M. Braverman, and Lev I. Rozono er. Theoretical foundations of the potential function method in pattern recognition and learning. Automation and Remote Control, 25:821--837, 1964.
Journal of Machine Learning Research 6 (2005) 1579--1619.. - With Online And (2005) (Correct)
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M. A. Aizerman, E. M. Braverman, and L. I. Rozono er. Theoretical foundations of the potential function method in pattern recognition learning. Automation and Remote Control, 25:821--837, 1964.
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M. Aizerman, E. Braverman, and L. Rozonoer. Theoretical foundations of the potential function method in pattern recognition learning. Automation and Remote Control, 25:821--837, 1964.
Merl -- A Mitsubishi Electric Research Laboratory - Http Www Merl (2002) (Correct)
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M. Aizerman, E. Braverman, and L. Rozonoer. Theoretical foundations of the potential function method in pattern recognition learning. Automation and Remote Control, 25:821--837, 1964.
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Aizerman, M. A., Braveman, E. M. and Rozoner, L. I. Theoretical foundations of the potential function method in pattern recognition learning. Automation and Remote Control, 25:821--837, 1964.
Fisher Discriminant Analysis with Kernels - Mika, Rätsch, Weston.. (1999) (65 citations) (Correct)
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M. Aizerman, E. Braverman and L. Rozonoer, \Theoretical foundations of the potential function method in pattern recognition learning." Automation and Remote Control, vol. 25, pp. 821 - 837, 1964.
Input Space vs. Feature Space in Kernel-Based Methods - Schölkopf, Mika, Burges.. (1999) (2 citations) (Correct)
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M. Aizerman, E. Braverman, and L. Rozonoer, \Theoretical foundations of the potential function method in pattern recognition learning.," Automation and Remote Control, vol. 25, pp. 821 - 837, 1964.
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M. Aizerman, E. Braverman, and L. Rozonoer. Theoretical foundations of the potential function method in pattern recognition learning. Automation and Remote Control, 25:821-837, 1964.
Support Vector Committee Machines - Dominique Martinez And (2000) (Correct)
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Aizerman, M.A., Braverman E.M. & Rozonoer, L.I. (1964) Theoretical foundations of the potential function method in pattern recognition learning, A utomation and remote control, 25, pp. 821-837.
Entropy Numbers, Operators and - Support Vector Kernels (1998) (Correct)
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M. A. Aizerman, E. M. Braverman, and L. I. Rozonoer. Theoretical foundations of the potential function method in pattern recognition learning. Automation and Remote Control, 25:821--837, 1964.
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M. A. Aizerman, E. M. Braverman, and L. I. Rozonoer. Theoretical foundations of the potential function method in pattern recognition learning. Automation an Remote Cone ol, 25:821--837, 1964.
Merl -- A Mitsubishi Electric Research Laboratory - Http Www Merl (2002) (Correct)
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M. Aizerman, E. Braverman, and L. Rozonoer. Theoretical foundations of the potential function method in pattern recognition learning. Automation and Remote Control, 25:821--837, 1964.
Convolution Kernels for Natural Language - Collins, Duffy (2001) (13 citations) (Correct)
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Aizerman, M., Braverman, E., and Rozonoer, L. (1964). Theoretical Foundations of the Potential Function Method in Pattern Recognition Learning. Automation and Remote Control, 25:821--837.
Generalization Performance of Regularization - Networks And Support (Correct)
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M. A. Aizerman, E. M. Braverman, and L. I. Rozonor, "Theoretical foundations of the potential function method in pattern recognition learning," Autom. Remote Contr., vol. 25, pp. 821--837, 1964.
Input Space Versus Feature Space in Kernel-Based Methods - Schölkopf, Mika, Burges, .. (1999) (1 citation) (Correct)
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M. Aizerman, E. Braverman, and L. Rozonoer, "Theoretical foundations of the potential function method in pattern recognition learning," Automat. Remote Contr., vol. 25, pp. 821--837, 1964.
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M. Aizerman, E. Braverman, and L. Rozonoer. Theoretical foundations of the potential function method in pattern recognition learning. Automation and Remote Control, 25:821837, 1964.
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M. A. Aizerman, E. M. Braverman, and L. I. Rozono'er. Theoretical foundations of the potential function method in pattern recognition learning. Automation and Remote Control, 25:821--837, 1964.
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M. A. Aizerman, E. M. Braverman, and L. I. Rozonoer. Theoretical foundations of the potential function method in pattern recognition learning. Automation and Remote Control, 25:821--837, 1964.
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M.A. Aizerman, E.M. Braverman, and L.I. Roeznoer. Theoretical foundations of the potential function method in pattern recognition learning. Avtomatika i Telemekhanika,(25):' 1964.
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Aizerman, M., Braverman, E. and Rozoner, L. I. (1964) Theoretical foundations of the potential function method in pattern recognition, Automation and Remote Control, 15, 821-837.
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M. Aizerman, E. Braverman, and L. Rozonoer. Theoretical foundations of the potential function method in pattern recognition learning. Automation and Remote Control, 25:821837, 1964.
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M. A. Aizerman, E. M. Braverman, and L. I. Rozonoer. Theoretical foundations of the potential function method in pattern recognition learning. Automation and Remote Control, 25:821--837, 1964.
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