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| 1.
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Miyoshi, Seiji ; Nakayama, Kenji
概要:
In this paper, the geometric learning algorithm (GLA) is proposed for an elementary perceptron which includes a single output neuron. The GLA is a modified version of the affine projection algorithm (APA) for adaptive filters.
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The weights update vector is determined geometrically towards the intersection of the k hyperplanes which are perpendicular to patterns to be classified. k is the order of the GLA. In the case of the APA, the target of the coefficients update is a single point which corresponds to the best identification of the unknown system. On the other hand, in the case of the GLA, the target of the weights update is an area, in which all the given patterns are classified correctly. Thus, their convergence conditions are different. In this paper, the convergence condition of the 1st order GLA for 2 patterns is theoretically derived. The new concept `the angle of the solution area' is introduced. The computer simulation results support that this new concept is a good estimation of the convergence properties.
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| 2.
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Tokui, N. ; Nakayama, Kenji ; Hirano, Akihiro
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In order to achieve fast convergence and less computation for adaptive filters, a joint method combining a whitening process and the NLMS algorithm is a hopeful approach. However, updating the filter coefficients is not synchronized with the
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reflection coefficient updating resulting in unstable behavior. We analyzed effects of this, and proposed the Synchronized Learning Algorithm to solve this problem. Asynchronous error between them is removed, and fast convergence and small residual error were obtained. This algorithm, however, requires O(ML) computations, where M is an adaptive filter length, and L is a lattice predictor length. It is still large compared with the NLMS algorithm. In order to achieve less computation while the fast convergence is maintained, a block implementation method is proposed. The reflection coefficients are updated at some period, and are fixed during this interval. The proposed block implementation can be effectively applied to parallel form adaptive filters, such as sub-band adaptive filters. Simulation using speech signal shows that a learning curve of the proposed block implementation a little slower than the our original algorithm, but can save the computational complexity.
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| 3.
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Nakayama, Kenji ; Hirano, Akihiro ; Nishiwaki, Takayuki
概要:
A network structure and its learning algorithm have been proposed for blind source separation applied to nonlinear mixtures. The network has a cascade form consists of a source separation block and a linearization block in this order.
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The conventional learning algorithm is employed for the separation block. A new learning algorithm is proposed for the linearization block assuming 2nd-order nonlinearity. After, source separation, the outputs include the nonlinear components for the same signal source. This nonlinearity is suppressed through the linearization block. Parameters in this block are iteratively adjusted based on a process of solving a 2nd-order equation of a single variable. Simulation results, using 2-channel speech signals and an instantaneous nonlinear mixing process, show good separation performance.
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| 4.
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Nakayama, Kenji ; Hirano, Akihiro ; Fusakawa, M.
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In multilayer neural networks, network size reduction and fast convergence are important. For this purpose, trainable activation functions and nonlinear synapses have been proposed. When high-order polynomials are used for
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nonlinearity, the number of terms in the polynomial becomes a very large for a high-dimensional input. It causes very complicated networks and slow convergence. In this paper, a method to select the useful terms in the polynomial in a learning process is proposed. This method is based on the genetic algorithm (GA), and combines the internal information, magnitude of connection weihgts, to select the gene in the next generation. A mechanism of pruning the terms is inherently included. Many examples demonstrate usefulness of the proposed method compared with the ordinary GA method. Convergence is stable and the number of the selected terms is well reduced.
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| 5.
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Kobori, Hideki ; Ikeda, Kazushi ; Nakayama, Kenji
概要:
金沢大学理工研究域電子情報学系<br />A model of dynamic associative memories is proposed in this paper. The aim is to find all stored pa
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tterns, and to distinguish the stored and the spurious patterns. Aihara used chaotic neurons and showed that his model has a nonperiodic associative dynamics. In his model, however, it is difficult to distinguish the stored patterns from the others, because the state of the network changes continually. We propose such a new model of neurons that each neuron changes its output to the other when the accumulation of its internal state exceeds a certain threshold. By computer experiments, we show that the state of the network stays at the stored pattern for a while and then travels around to another pattern, and so on. Furthermore, when the number of the stored patterns is small, the stored and the spurious patterns can be distinguished using interval of the network staying these patterns.
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| 6.
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Khalaf, Ashraf A.M. ; Nakayama, Kenji
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Time series prediction is a very important technology in a wide variety of field. The actual time series contains both linear and nonlinear properties. The amplitude of the time series to be predicted is usually continuous value. For
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this reason, we combine nonlinear and linear predictors in a cascade form. In order to estimate the minimum size of the proposed predictor, we propose a nonlinearity analysis for the time series of interest. Computer simulations using the sunspot data have demonstrated the efficiency of the proposed predictor and the nonlinearity analysis.
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| 7.
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Wang, Youhua ; Ikeda, Kazushi ; Nakayama, Kenji
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金沢大学大学院自然科学研究科情報システム<br />金沢大学工学部<br />The numerical property of an adaptive filter algorithm is the most important prob
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lem in practical applications. Most fast adaptive filter algorithms have the numerical instability problem and the fast Newton transversal filter (FNTF) algorithms are no exception. In this paper, we propose a numerically stable fast Newton type adaptive filter algorithm. Two problems are dealt with in the paper. First, we derive the proposed algorithm from the order-update fast least squares (FLS) algorithm. This derivation is direct and simple to understand. Second, we give the stability analysis using a linear time-variant state-space method. The transition matrix of the proposed algorithm is given. The eigenvalues of the ensemble average of the transition matrix are shown to be asymptotically all less than unity. This results in a much improved numerical performance compared with the FNTF algorithms. The computer simulations implemented by using a finite-precision arithmetic have confirmed the validity of our analysis.
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| 8.
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Hara, Kazuyuki ; Nakayama, Kenji
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A training data selection method for multi-class data is proposed. This method can be used for multilayer neural networks (MLNN). The MLNN can be applied to pattern classification, signal process, and other problems that can be
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considered as the classification problem. The proposed data selection algorithm selects the important data to achieve a good classification performance. However, the training using the selected data converges slowly, so we also propose an acceleration method. The proposed training method adds the randomly selected data to the boundary data. The validity of the proposed methods is confirmed through the computer simulation.
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| 9.
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9. A blind source separation cascading separation and linearization for low-order nonlinear mixtures
Nishiwaki, Takayuki ; Nakayama, Kenji ; Hirano, Akihiro
概要:
A network structure and its learning algorithm have been proposed for blind source separation applied to nonlinear mixtures. Nonlinearity is expressed by low-order polynomials, which are acceptable in many practical applications. A
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separation block and a linearization block are cascaded. In the separation block, the cross terms are suppressed, and the signal sources are separated in each group, which include its high-order components. The high-order components are further suppressed through the linearization block. A learning algorithm minimizing the mutual information is applied to the separation block. A new learning algorithm is proposed for the linearization block. Simulation results, using 2-channel speech signals, instantaneous mixtures, and 2nd-order post nonlinear functions, show good separation performance.
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| 10.
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Nakayama, Kenji ; Hirano, Akihiro ; Kourin, Makoto
概要:
In this paper, a synthesis and learning method for the neural network with embedded gate units and a multi-dimensional input is proposed. When the input is multi-dimensional, gate functions are controlled in a multi-dimensional space.
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In this case, a hypersurface, on which the gate function is formed should be optimized. Furthermore, the switching points should be considered on the unit input. An initialization and a control methods for gate functions, which optimize the hypersurface, the switching point and the inclination, are proposed. The stabilization methods, already proposed, are further modified to be applied to the multi-dimensional environment. The gate functions can be trained together with the connection weights. Discontinuous function approximation is demonstrated to confirm usefulness of the proposed method.
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