Quaternionic neural networks are extensions of neural networks using quaternion algebra. 3-D and 4-D quaternionic MLPs have been studied. 3-D quaternionic neural networks are useful for handling 3-D objects, such as Euclidean transformation. As for Hopfield neural networks, only 4-D quaternionic Hopfield neural networks (QHNNs) have been studied. In this work, we propose the 3-D QHNNs. Moreover, we define the energy, and prove that it converges.

In this paper we present an analysis based on the indirect Lyapunov criteria, that is used to study the convergence of an infinite impulse response (IIR) adaptive digital filter (ADF) based on estimation of the allpass system. The analysis is then extended to investigate the necessity of directly estimating the transfer level of the unknown system. We consider two cases of modeling the ADF. In the first system, the allpass section of the ADF estimates only the real poles of the unknown system while in the second system, both real and complex poles the allpass section are estimated. From the analysis and computer simulation, we realize that the poles of the ADF converge selectively to the poles of the unknown system, depending on the sign of the step size of adaptation. Using these results we proposed a new method to control the convergence of the poles the IIR ADF based on estimation of the allpass system.

In camera-based object recognition and classification, surface color is one of the most important characteristics. However, apparent object color may differ significantly according to the illumination and surface conditions. Such a variation can be an obstacle in utilizing color features. Geusebroek et al.'s color invariants can be a powerful tool for characterizing the object color regardless of illumination and surface conditions. In this work, we analyze the estimation process of the color invariants from RGB images, and propose a novel invariant feature of color based on the elementary invariants to meet the circular continuity residing in the mapping between colors and their invariants. Experiments show that the use of the proposed invariant in combination with luminance, contributes to improve the retrieval performances of partial object image matching under varying illumination conditions.

Complex-valued Associative Memory (CAM) is an advanced model of Hopfield Associative Memory. The CAM is based on multi-state neurons and has the high ability of representation. Lee proposed gradient descent learning for the CAM to improve the storage capacity. It is based on only the phases of input signals. In this paper, we propose another type of gradient descent learning based on both the phases and the amplitude. The proposed learning method improves the noise robustness and accelerates the learning speed.

Recently, in the modem, the spread spectrum communication system and the software radio, Digital Signal Processor type Squaring Loop (DSP-squaring-loop) is employed in the demodulation of Binary Phase Shift Keying (BPSK) signal. The DSP-squaring-loop extracts the carrier signal that is used for the coherent detection. However, in case the Signal to Noise Ratio (SNR) is low, the DSP-Phase Locked Loop (DSP-PLL) can not pull in the frequency offset and the phase offset. In this paper, we propose a DSP-squaring-loop that is robust against noise and which uses the adaptive notch filter type frequency estimator and the adaptive Band Pass Filter (BPF). The proposed method can extract the carrier signal in the low SNR environment. The effectiveness of the proposed method is confirmed by the computer simulation results.

Learning for boltzmann machines deals with each state individually. If given data is categorized, the probabilities have to be distributed to each state, not to each catetory. We propose boltzmann machines identifying the states in the same categories. Boltzmann machines with hidden units are the special cases. Boltzmann learning and em algorithm are effective learning methods for boltzmann machines. We solve boltzmann learning and em algorithm for the proposed models.

Newton based adaptive algorithms are among the algorithms which are known to exhibit a higher convergence speed in comparison to the least mean square (LMS) algorithms. In this paper we propose a simplified Newton based adaptive algorithm for an adaptive infinite impulse response (IIR) filter implemented using cascades of second order allpass filters and a finite impulse response (FIR) filter. The proposed Newton based algorithm avoids the complexity that may arise in the direct differentiation of the mean square error. The analysis and simulation results presented for the algorithm, show that the property of convergence of the poles of the IIR ADF to those of the unknown system will be maintained for both white and colored input signal. Computer simulation results confirm an increase in convergence speed in comparison to the LMS algorithm.

In recent years, applications of neural networks with Clifford algebra have become widespread. Hyperbolic numbers are useful Clifford algebra to deal with hyperbolic geometry. It is difficult when Hopfield neural network is extended to hyperbolic versions, though several models have been proposed. Multistate or continuous hyperbolic Hopfield neural networks are promising models. However, the connection weights and domain of activation function are limited to the right quadrant of hyperbolic plane, and the learning algorithms are restricted. In this work, the connection weights and activation function are extended to the entire hyperbolic plane. In addition, the energy is defined and it is proven that the energy does not increase.

In this paper we propose a parallel composition based adaptive notch filter for eliminating sinusoidal signals whose frequencies are unknown. The proposed filter which is implemented using second order all-pass filter and a band-pass filter can achieve high convergence speed by using the output of an additional band-pass filter to update the coefficients of the notch filter. The high convergence speed of the proposed notch filter is obtained by reducing an effect that an updating term of coefficient for adaptation of a notch filter significantly increases when the notch frequency approaches the sinusoidal frequency. In this paper, we analyze such effect obtained by the additional band-pass filter. We also present an analysis of a convergence performance of cascaded system of the proposed notch filter for eliminating multiple sinusoids. Simulation results have shown the effectiveness of the proposed adaptive notch filter.

An adaptive infinite impulse response (IIR) filter implemented using an allpass and a minimum phase system has an advantage of its poles converging to the poles of the unknown system when the input is a white signal. However, when the input signal is colored, convergence speed deteriorates considerably, even to the point of lack of convergence for certain colored signals. Furthermore with a colored input signal, there is no guarantee that the poles of the adaptive digital filter (ADF) will converge to the poles of the unknown system. In this paper we propose a method which uses a linear predictor filter to whiten the input signal so as to improve the convergence characteristic. Computer simulation results confirm the increase in convergence speed and the convergence of the poles of the ADF to the poles of the unknown system even when the input is a colored signal.

Complex-valued Hopfield associative memory (CHAM) is one of the most promising neural network models to deal with multilevel information. CHAM has an inherent property of rotational invariance. Rotational invariance is a factor that reduces a network's robustness to noise, which is a critical problem. Here, we proposed complex-valued bipartite auto-associative memory (CBAAM) to solve this reduction in noise robustness. CBAAM consists of two layers, a visible complex-valued layer and an invisible real-valued layer. The invisible real-valued layer prevents rotational invariance and the resulting reduction in noise robustness. In addition, CBAAM has high parallelism, unlike CHAM. By computer simulations, we show that CBAAM is superior to CHAM in noise robustness. The noise robustness of CHAM decreased as the resolution factor increased. On the other hand, CBAAM provided high noise robustness independent of the resolution factor.

Several models of feed-forward complex-valued neural networks have been proposed, and those with split and polar-represented activation functions have been mainly studied. Neural networks with split activation functions are relatively easy to analyze, but complex-valued neural networks with polar-represented functions have many applications but are difficult to analyze. In previous research, Nitta proved the uniqueness theorem of complex-valued neural networks with split activation functions. Subsequently, he studied their critical points, which caused plateaus and local minima in their learning processes. Thus, the uniqueness theorem is closely related to the learning process. In the present work, we first define three types of reducibility for feed-forward complex-valued neural networks with polar-represented activation functions and prove that we can easily transform reducible complex-valued neural networks into irreducible ones. We then prove the uniqueness theorem of complex-valued neural networks with polar-represented activation functions.

In recent years, applications of complex-valued neural networks have become wide spread. Quaternions are an extension of complex numbers, and neural networks with quaternions have been proposed. Because quaternion algebra is non-commutative algebra, we can consider two orders of multiplication to calculate weighted input. However, both orders provide almost the same performance. We propose hybrid quaternionic Hopfield neural networks, which have both orders of multiplication. Using computer simulations, we show that these networks outperformed conventional quaternionic Hopfield neural networks in noise tolerance. We discuss why hybrid quaternionic Hopfield neural networks improve noise tolerance from the standpoint of rotational invariance.

In this paper we propose a new simplified algorithm for cascaded second order adaptive notch filters implemented using an allpass filter, for elimination of multiple sinusoids. Each of the stages of the notch filter is implemented using direct form second order allpass filter. We also present an analysis which compares the proposed algorithm with the conventional simplified algorithm, and which indicates that the proposed algorithm has a reduced bias in the estimation of the multiple input sinusoids. Simulation results that have been provided confirm this analysis.

In this study, expressions were compared with reference material using the coaxial feed-type open-ended cut-off circular waveguide reflection method to support simple and instantaneous evaluation of dielectric constants in small amounts of scarce liquids over a broad frequency range. S11 values were determined via electromagnetic analysis for individual jig structure conditions and dielectric property values without actual S11 measurement under the condition that the tip of the measurement jig with open and short-ended conditions and with the test material inserted. Next, information on the relationships linking jig structure, dielectric properties and S11 properties was stored on a database to simplify the procedure and improve accuracy in reference material evaluation. The accuracy of the estimation formula was first theoretically verified for cases in which values indicating the dielectric properties of the reference material and the actual material differed significantly to verify the effectiveness of the proposed method. The results indicated that dielectric property values for various liquids measured at 0.5 and 1.0GHz using the proposed method corresponded closely to those obtained using the method previously proposed by the authors. The effectiveness of the proposed method was evaluated by determining the dielectric properties of certain liquids at octave-range continuous frequencies between 0.5 and 1.0GHz based on interpolation from limited data of several frequencies. The results indicated that the approach enables quicker and easier measurement to establish the complex permittivity of liquids over a broad frequency range than the previous method.

This paper describes a digital filter realization method by simulating an LCR filter. Having the node equation of an original LCR filter the frequency variable s is transformed into a z one using the bilinear transformation. The resulting network equation can be digitally realized with the same transfer function as the original LCR filter. Using such a method, the circuit either has a large error in the transfer response near zero frequencies or causes oscillations. A technique to avoid this problem by a simple modification of the multiplier coefficients is shown. A fifth order elliptic filter is presented with illustrative comparison to classical cascade structure.

Conventional adaptive notch filter based on an infinite impulse response (IIR) filter is well known. However, this kind of adaptive notch filter has a problem of stability due to its adaptive IIR filter. In addition, tap coefficients of this notch filter converge to solutions with bias error. In order to solve these problems, an adaptive notch filter using Fourier sine series (ANFF) is proposed. The ANFF is stable because an adaptive IIR filter is not used as an all-pass filter. Further, the proposed adaptive notch filter is robust enough to overcome effects of a disturbance signal, due to a structure of the notch filter based on an exponential filter and line symmetry of auto correlation.

Adaptive infinite impulse response (IIR) digital filter implemented using a cascade of second order direct form allpass filters and a finite impulse response (FIR) filter, has the property of its poles converging to those of the unknown system. In this paper we implement the adaptive allpass-FIR digital filter using a lattice allpass filter with minimum number of multipliers. We then derive a simple adaptive algorithm, which does not increase the overall number of multipliers of the proposed adaptive digital filter (ADF) in comparison to the ADF that uses the direct form allpass filter. The proposed structure and algorithm exhibit a kind of orthogonality, which ensures convergence of the poles of the ADF to those of the unknown system. Simulation results confirm this convergence.