S. Bannour and M. R. Azimi-Sadjadi. Principal component extraction using recursive least squares learning method. IEEE transactions on neural networks, 6:457-469, March 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....specifically RRLSA [3] with the Gram Schmidt method, exploiting the fact that the orthonormalization works on vectors that were obtained by applying a learning rule to already orthonormal vectors. RRLSA was chosen as the learning mechanism since like other recursive least square methods [1] it is fast and not su#ering from accuracy speed trade o#s like least mean square methods, and proved to be robust in several applications. Section 2 describes the method where learning and orthonormalization are separated, section 3 introduces the method where both steps are interlocked, ....

S. Bannour, M.R. Azimi-Sadjadi, Principal component extraction using recursive least squares learning, IEEE Trans. Neural Netw. 6(2), March (1995) 457-469

....PCA network [9] since it includes a tapped delay line. This temporal PCA network can be viewed as a static PCA network for multiple input vectors, so its convergence will be guaranteed. The training algorithm adopted here is the recursive estimation based on Kalman filter, which has the form of [1]: where X(n) denotes the signal vector at the tapped delay line, is the weight vector of the PCA network connected to the output , and Notice that in Eq. 2) a controlling factor is put before the gain ,j=1, M. This makes the adaptation rule slightly different from the original Kalman filter ....

....vector at the tapped delay line, is the weight vector of the PCA network connected to the output , and Notice that in Eq. 2) a controlling factor is put before the gain ,j=1, M. This makes the adaptation rule slightly different from the original Kalman filter approach proposed by Bannour [1]. The step size controlling factor is incorporated so that the search then convergence idea is integrated into the learning [2] namely, where and are constants. Due to the fact that the eigenvectors of the PCA converge sequentially from the W i n ( D 2e i n ( V i n ( 1) W 2 W N W 1 yn( ....

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Bannour, S., and Azimi-Sadjadi, M., "Principal components extraction using recursive least square learning," IEEE Trans. on Neural Networks, Vol.6, No.2, 1995.

....of x(t) are statistically correlated. This second order redundancy may be partially (or completely) removed by computing a linear operator Q such that the new random signal defined by y(t) def = Q T (x(t) Gamma Ex [x] 2 R m has uncorrelated components, with m p arbitrarily selected [1, 2, 3, 4, 9, 10, 12, 14, 15]. The data stream can then be reconstructed by the simple synthesis formula x(t) Qy(t) Ex [x] Among others, Kung and Diamantaras proposed in [11] a principal component analyzer, implemented by means of a laterally connected linear neural network having the topology shown in Figure 1, termed ....

S. BANNOUR AND M.R. AZIMI-SADJADI, Principal Component extraction using recursive least squares learning, IEEE Trans. on Neural Networks, Vol.6, No.2, March 1995

....results To show the behavior of the proposed class of APEX like learning rules, several experiments have been performed. The aim of these experiments is to compare, in terms of performance on real world signals, the proposed algorithms with the original APEX and with other known PCA methods [1] [2], 3] 12] The considered signals consist of gray scale images, 8 bit per pixel, normalized to have zero mean (the true mean value is removed) A 8 Theta 8 pixel sliding window is taken without overlap from left to right and from top to bottom of these images and constitutes the input pattern ....

....j) th pixel of the original N r Theta N c image whose principal components are to be extracted, and I ij denotes the corresponding value of the reconstructed image. Table I shows the performance of the tested algorithms (APEX, y 2 APEX, jyj APEX, 0 APEX, GHA [12] CRLS [3] RLS PCA [2], SAMH [1] when the first 8 PCs of the standard image Lena (512 Theta 512 pixels) are sequentially extracted. The maximum number of epochs per each PC has been fixed to 40 while a threshold on the DeltaW (2 Theta 10 Gamma4 ) allows the algorithm to jump to the next PC when a reasonable ....

S. Bannour and M.R. Azimi-Sadjadi, Principal component extraction using recursive least squares learning, IEEE Trans. on Neural Networks, Vol. 6, No. 2, March 1995

....of singular value decomposition (SVD) and in eigenvalue problems. 1 Introduction Principal Component Analysis (PCA) is a powerful data analysis tool in multivariate statistics and it has been videly used in image compression, signal restoration and classification and feature extraction [5 14, 21]. Most known adaptive unsupervised learning algorithms for PCA are developed for real valued data or signals [1 24] These methods are optimal in the least square sense [1 4] In many signal processing problems signals are rather complex valued [25] and or are distorted by outliers or spiky ....

S. Bannour and M.R. Azimi-Sadjadi, "Principal component extraction using recursive least squares learning ", IEEE Tran. on Neural Networks, vol.6 pp. 456--469, 1995.

....digit recognition using LPCA (Local Principal Component Analysis) the time of training by Oja RLS rule is about ten times faster than by classical Oja rule. The iterative scheme (1) with the function f defined by (3) and gains by (2) was defined without specifying fi 0 ; by several authors [1, 3, 2]. Its derivation was based on the concept of Recursive Least Square (RLS) method, however no correct convergence analysis was given so far. The convergence proof for classical Oja rule was attempted to be shown by reducing the stochastic difference equation to the corresponding deterministic ....

Bannour S., Azimi-Sadjadi M.R. (1995): Principal component extraction using recursive least squares learning, IEEE Transactions on Neural Networks, 6, 457-469.

....that the training set can be reduced even to 10 of the total number of pixels, for high resolution images, without substantial loss of accuracy. 1. Introduction Adaptive feature extraction is useful in many information processing systems. One of such tools for feature extraction is PCA and PSA [1, 2, 3, 4, 5]. Unfortunately, most of the known adaptive algorithms for PSA PCA are relatively slow [2] In this paper we propose an extension of learning algorithms which improves the convergence speed, especially for image compression. 2. Problem formulation The Principal Component Analysis (PCA) problem ....

....speed is controlled by the learning rate j k 0 which generally can be changed at every learning step. Usually many epochs are required to reach the solution (see e.g. Cichocki,Unbehanen [3] In order to improve the convergence speed we can apply recursive least squares (RLS) technique ([5, 6]) as follows: j 0 0 = E[kxk 2 ] y k = w T k x k j 0 k = j 0 k01 y 2 k 1w k = y k =j 0 k ) x k 0 y k w k ) w k 1 = w k 1w k (3) where j 0 = 1=j: As our experiments show, for images of natural scenes this scheme finds the solution in one learning epoch with the error less ....

Bannour S., Azimi-Sadjadi M.R., Principal component extraction using recursive least squares learning, IEEE Trans. Neural Networks, 6, 1995, 457-469.

.... components of a complex data set, such as those encountered in radar and sonar systems or communication systems[6, 7] We use a complex valued artificial neural network with a single layer of linear neurons trained according to a Hebbian learning rule to perform Principal Components Analysis (PCA) [2, 3, 8, 10, 15]. The learning rule has been extended to accommodate complex values. The data and the synapse weights are also complex valued. After the convergence of the Complex Generalized Hebbian Algorithm (CGHA) each neuron of This work was in part supported by a grant from Conselho Nacional de ....

S. Bannour e M. R. Azimi-Sadjadi. Principal component extraction using recursive least squares learning. IEEE Trans. Neural Net., 6(2), 1995.

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S. Bannour and M. R. Azimi-Sadjadi. Principal component extraction using recursive least squares learning method. IEEE transactions on neural networks, 6:457-469, March 1995.

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Bannour, S., and Azimi-Sadjadi, M., "Principal components extraction using recursive least square learning," IEEE Trans. on Neural Networks, Vol.6, No.2, 1995.

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