Harold H. Szu, "Neural network adaptive wavelets for signal representation and classification ", Optical Eng. v31, n9, pp1907-1916, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....function can be used to develop a learning algorithm for the neural network in Fig. 6. E 2 (s(t) s(t) #. 3.2) The value of E can be minimized by adaptively changing or learning the best possible values of the coe cients, w . One typical example is to use a conjugate gradient method [19,67] to achieve optimum approximation of the original signal s(t) Forming the column vectors [u(w) and [w] from the gradient analysis and coe cients w , the ith iteration for minimising E with respect to [w] proceeds according to the following two steps: i) if k is multiple of n then: ....

H. Szu, B. Telfer, S. Kadambe, Neural network adaptive wavelets for signal representation and classi"cation, Opt. Eng. 31 (September 1992.

....suggest that the wavelet layer exhibits superior performance than the conventional competitive neural layers when patterns exhibit a low signal to noise ratio. 1. Introduction Recently, important bridges have been established between the field of artificial neural networks (ANN s) and wavelets [1], 2] Wavelet Theory comprises a set of techniques aimed at developing efficient representations of signals through the use of elementary functions that are localized both in frequency and in time [3] A remarkable feature of wavelet based signal processing is that it mimics several natural ....

....pre processing [6] This paper proposes an algorithm for wavelet based clustering which employs a competitive training scheme. Unlike the majority of works in this field, the use of wavelets is not restricted to a pre processing stage. Instead, the representation capabilities of adaptive wavelets [1] are exploited to synthesize a typical element, or template for each cluster of signals. A brief introduction to adaptive wavelet representations is provided, in order to help the presentation of the key concepts. Initialization and training schemes are described, and some insight into the ....

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H. H. Szu, B. Telfer, and S. Kadambe. Neural network adaptive wavelets for signal representation and classification. Optical Engineering, 31(9):1907.

....accordingly to fit the new faces. The right images in Fig. 3 show the reconstruction of the deformed GWN of Fig. 1, now showing the same position, rotation and scale of the new faces (left) To formalize the idea, the reparameterization of a GWN is established by using a superwavelet [12]: Definition: Let (#, w) be a Gabor Wavelet Network with # = # n 1 , # nN ) w = w 1 , wN ) A superwavelet # n is defined to be a linear combination of the wavelets # n i such that # n (x) w i # n i (SR(x c) 9) where the parameters of vector n of superwavelet ....

H. Szu, B. Telfer, S. Kadambe, Neural network adaptive wavelets for signal representation and classification, Optical Engineering 31 (1992.

....for this can be seen in g. 2, where in the bottom right image the original positions of the wavelets are marked and in g. 5, where in new images the wavelet positions of the reparameterized wavelet network are marked. Parameterization of a wavelet net is established by using a superwavelet [24]. De nition: Let ( w) be a Gabor wavelet network with = n1 ; nN ) A superwavelet n is de ned to be a linear combination of the wavelets n i such that n (x) w i n i (SR(x c) 9) where the parameters of vector n of superwavelet de ne the dilation matrix S ....

.... combination of the wavelets n i such that n (x) w i n i (SR(x c) 9) where the parameters of vector n of superwavelet de ne the dilation matrix S = diag(s x ; s y ) the rotation matrix R, and the translation vector c = c x ; c y ) A superwavelet n is again a wavelet [24] and in particular a continuous function that has the wavelet parameters dilation, translation and rotation (see section 2) Therefore, we can handle it in the same way as we handled each single wavelet in the previous section. For a new image g we may arbitrarily deform the superwavelet by ....

H. Szu, B. Telfer, and S. Kadambe. Neural network adaptive wavelets for signal representation and classi cation. Optical Engineering, 31(9):1907-1961, 1992. 26

....example for this can be seen in fig. 1, where in the right image the original positions of the wavelets are marked and in fig. 4, where in new images the wavelet positions of the reparameterized wavelet network are marked. Parameterization of a wavelet net is established by using a superwavelet [12]. Definition: Let ( w) be a Gabor wavelet network with (11, 11N) T, w (Wl, WN) T. A superwavelet 11 is defined to be a linear combination of the wavelets 11 such that It11(X) y Wi11 i (SR(x c) 3) i where the parameters of vector n of superwavelet define the dilation ma ....

.... 11 is defined to be a linear combination of the wavelets 11 such that It11(X) y Wi11 i (SR(x c) 3) i where the parameters of vector n of superwavelet define the dilation ma trix S = diag(sz,Sy) the rotation matrix R, and the translation vector A superwavelet 11 is again a wavelet [12] and in particular a continuous function that has the wavelet parameters dilation, translation and rotation (see section 2) Therefore, we can handle it in the same way as we handled each single wavelet in the previous section. For a new image g we may arbitrarily deform the superwavelet by ....

H. Szu, B. Teller, and S. Kadambe. Neural network adaptive wavelets for signal representation and classification. Optical Engineering, 31(9):1907-1961, 1992.

....From this, the local spectrum is said to represent the formant of the speech signal. 2. 3 Phoneme and Speaker Classification using Adaptive Wavelets The adaptive wavelet transform and the concept of the super wavelet were developed as an alternative to existing wavelet representation schemes [8]. Given a wavelet function of the form shown in (2) the idea is to iteratively find the translation and dilation parameters, t and a respectively such that some application dependent energy function is minimised. With respect to the classification problem, a set of wavelet coefficients would ....

Szu, H; Telfer, B; Kadambe, S. "Neural network adaptive wavelets for signal representation and classification," Optical Engineering, vol.31 No.9 pp.

....An increasing amount of evidence has been gathered showing that chaos and other nonlinear phenomena are actually ubiquitous in this class of dynamical systems. The best known paradigm for chaos in electronic circuits, the Chua circuit, is itself characterized by a piecewise linear component [8]. Over the years various mathematical methods have been proposed to investigate the dynamics of nonsmooth dynamical systems. Traditionally, engineers have looked at appropriate linearized, average models of switching circuits; and the so called averaging technique has been used successfully to ....

....SIAM and IEEE. Since July 1999, he has been associate editor of the IEEE Transactions on Circuits and Systems I. Complex Behavior . continued from Page 11 have been shown essential in determining behavior . Border collision and grazing bifurcations, as well as sliding motion, 13 [8] L. O. Chua, M. Komuro, and T. Matsumoto, The Double Scroll Family: I and II , IEEE Transactions on Circuits and Systems, vol. 33, pp. 1072 1118, 1986. 9] M. di Bernardo, M. I. Feigin, S. J. Hogan, and M. E. Homer, Local Analysis of CBifurcations in n Dimensional Piecewise Smooth Dynamical ....

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H. Szu, B. A.Telfer, and S. Kadame, "Neural Network Adaptive Wavelets for Signal Representation and Classification", Optical Engineering, vol.31, pp.

....w h are frozen (i.e. they do not depend on the function f(x) Let us call such neural networks, for which s(x) is a wavelet, w h = 2 j , and b h = Gammak, wavelet neural networks. Remark. The relationship between wavelets and neural networks has been explored in [18] 24] 19] 25] [20], 21] C. Wavelet Neural Network as an Approximation Scheme We have already mentioned that an arbitrary smooth function f(x) on (0,1) can be represented by a series f(x) P j;k C jk e jk (x) with C jk = R f(x)e jk (x) dx. We can use the coefficients C jk as a record from which we can ....

H. Szu, B. Telfer, and S. Kadambe, "Neural Network Adaptive Wavelets for Signal Representation and Classification," Opt. Eng., Vol. 31, pp.

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Harold H. Szu, "Neural network adaptive wavelets for signal representation and classification ", Optical Eng. v31, n9, pp1907-1916, 1992.

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H. H. Szu, B. A. Telfer, and S. Kadambe, "Neural Network Adaptive Wavelets for Signal Representation and Classificaiton," Optical Enginering, v31, n9, pp 1907-16, Sept. 1992.

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H. H. Szu, B. Telfer, and S. Kadambe, Neural Network Adaptive Wavelets for Signal Representation and Classification, Optical Engineering, Vol. 31, No. 9, September 1992, pages 1907-1916.

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H. Szu, B. Telfer, and S. Kadambe. Neural network adaptive wavelets for signal representation and classi cation. Optical Engineering, 31:1907-1961, 1992.

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