A convolutional neural network based on quaternion, a four-dimensional hypercomplex number system, is proposed and evaluated in this paper. Called Quaternionic Convolutional Neural Networks (QCNNs), these networks can accept and operate three-dimensional signals by neurons in the networks. The performances of the proposed networks are investigated through classification of CIFAR-10 color images, and it is shown that the proposed QCNN outperforms a conventional (real-valued) CNN.

We propose a neural network model based on quantum information processing with quaternionic representation and operations, called Quaternionic Qubit Neural Network. The state of a neuron is represented by a point on the Bloch sphere with incorporating quaternionic representation. The operations for this neuron also follow the operations in quaternions. The proposed neural networks are evaluated through numerical experiments for predicting chaotic time series produced by a Lorentz system. They have better performances in predicting long-term series, as compared to conventional (real-valued) neural networks.

In this paper, we propose a Hopfield Associative Memory with Complex-valued and Real-valued neurons (CRHAM). CRHAM is an associative memory which can perform storing and recalling multi-valued patterns. A part of neurons in the network are complex-valued neurons, and the rest of neurons are conventional (real-valued) neurons. Spurious patterns that degrade the retrieval performance can be reduced by the combination of those two types of neurons. The experimental results show that high robustness for noisy inputs is achieved by CRHAM as compared with conventional complex-valued associative memories, such as Complex-valued Hopfield Associative Memory (CHAM) and Complex-valued Bipartite Auto-Associative Memory (CBAAM).

One of the approaches for improving quality of life of patients, undergoing hospitalization, is to improve hospital meals that are provided to them. It is a very cumbersome task to plan daily menus for hospital meals, which have many conditions for nutrition and allergies, and this task becomes difficult if patients' preferences of foods are also considered for enhancing patients' quality of life. This task can be formulated as an optimization problem with menu items as variables and specific nutritional and allergic as its constraints. We have proposed a menu creation scheme to satisfy these conditions with being incorporated patients' food preferences, and shows a preliminary result for creating menus for a patient. A genetic algorithm was utilized to better and more efficiently locate combinations of menu dishes for individual patients. This paper shows that a variety of menus can be produced for patients with several ranges of ages, three types of physical activities, and allergic conditions.

This paper presents Quaternionic Bidirectional Auto-Associative Memory (QBAAM) that is an associative memory network storing patterns with multiple levels. A part of neurons in the network are quaternionic neurons, where their states are encoded by quaternion, which is a four-dimensional hypercomplex number system. These neurons can represent three kinds of discretized phases, i.e., three-dimensional multilevel values. The rest of neurons are conventional (real-valued) neurons. QBAAM is expected to have a rich representation ability by employing quaternionic neurons, as well as to have fewer spurious patterns in the network by a combination of real-valued and quaternionic neurons. The experimental results show that high robustness of noisy inputs is achieved by QBAAM, as compared with Quaternionic Hopfield Associative Memory where all neurons in the network are quaternionic neurons.

The performance of layered neural networks with quaternionic encoding variables are investigated in this paper. The form of local analyticity with Wirtinger representation is adopted for a backpropagation learning algorithm in this network. A quaternionic version of tanh function is used for the activation function in neuron states' updates. As tasks of the performance evaluation of the presented networks, two types of three dimensional data processing problem are used; the prediction of the Lorentz attractor and affine transformations in three dimensional space.

Quantum-Inspired Particle Swarm Optimization (QPSO) is an extension of Particle Swarm Optimization (PSO) methods, in which the concept of quantum mechanics is adopted. The state of a particle in QPSO is described by a wave function derived from the Schrödinfer equation, whereas a particle in standard PSOs has its location and velocity as its state. The performances of QPSOs are demonstrated through the optimization problem for higher-dimensional functions, with comparison of the standard PSO. The experimental results show that QPSOs can find (near) optimal values much faster than the conventional PSO.

In this paper, a method of determining examination groups is presented for new outpatients visiting the department of ophthalmology, using support vector machines (SVM's). Assuming that interview sheets are divided into four classes, the proposed method copes with the examination determination as the classification of the sheets. The data are generated from handwriting sentences in the sheets, and they are arranged in the form of a matrix. Some nouns and adjectives in the sentences are chosen as elements of the matrix, and are assigned to columns of the matrix. The sentences in the sheets are assigned to rows of the matrix. Frequencies of the chosen words appearing in the sentences are basically given as element values in the matrix, and weighting is applied to element values associated with the words having comparatively high frequencies for sentences belonging to two classes at most. Normal SVM learning constructs a discrimination model, and defines four discriminant functions associated with the model. Since one-versus-all approach is employed, the class of data to be examined is determined according to output values of the four functions. It is established that the determination made by the proposed method achieves as favorable accuracy as the first determination made by an average ophthalmologist.

Choosing an appropriate activation function is a challenging problem in quaternionic neural networks, due to the analyticity in quaternionic domain. This paper presents a Hopfield-type neural network with an activation function with quaternionic equivalent of tanh function. This activation function is obtained by incorporating so-called “local analyticity” on quaternionic domain and the recent results on complex-valued activation functions. The stability of the network is shown by proving monotonic decrease of energy with the changes of neuron states.

Properties and performances of associative memories, based on Complex-valued Synergetic Computer (CVSC), are explored in this paper. All the parameters of CVSC are encoded by complex values. CVSC is extended from the conventional Synergetic Computer (RVSC) in which the parameters are real values. Performances of associative memories in CVSC are investigated through a problem of image retrievals where the input images are partially occluded or noise-affected. From the experimental results concerning the retrieval performances related to various sizes of images and different levels of defectiveness of input images, we found that CVSC outperforms RVSC.

In this paper, methods of selecting formulas to calculate intraocular lens (IOL) power for a cataract patient are presented, using support vector machines (SVM's) and self-organizing maps (SOM's). Each of training data has measured values associated with axial length and corneal refractive power as element values. Three IOL power formulas have variables into which these values are substituted. The discrimination model constructed by SVM learning consists of three coordinate spaces having two regions corresponding to two formulas out of three. Each of the spaces provides a potential solution. The formula to be used for some patient is specified by a majority of the potential solutions. The SOM-based scheme determines the formula suitable to some patient, observing the label attached to the winner neuron for the presented data having the above element values associated with the patient. The experimental results finally establish that the proposed SVM-based scheme especially works well to select the formula.

Double contrast (DC) X-ray images are useful and cost-effective for the diagnosis of stomach tumors. However, it is difficult to automatically extract tumors from these images. This is due to the variations in the tumors appearing in the images as a result of the changes in stomach shapes and the distribution of barium meal in the stomach. In this paper, we propose an automated method for detecting tumors in DC X-ray images. Our method utilizes the distributions of contrast gradients in the images. The performance of our method is demonstrated by using actual DC X-ray images.

This paper explores two types of multistate Hopfield neural networks, based on commutative quaternions that are similar to Hamilton's quaternions but with commutative multiplication. In one type of the networks, the state of a neuron is represented by two kinds of phases and one real number. The other type of the networks adopts the decomposed form of commutative quaternion, i.e., the state of a neuron consists of a combination of two complex values. We have investigated the stabilities of these networks, i.e., the energies monotonically decreases with respect to the changes of the network states.

In this paper, a method of selecting one type out of three types of intraocular lens (IOL) power formulas for data of each individual cataract patient is presented, using self-organizing maps (SOM's). The proposed method employs three-dimensional vectors each of which has measured values of axial length, corneal refractive power and cylinder as training data for maps. The first two values are substituted into the power formulas, while the last value is associated with the astigmatism. This paper also proposes neuron labeling that depends on postoperative refractive errors occurring under the assumption that each of the three power formulas is applied. The proposed method determines the formula to be applied to some patient, observing the label attached to the winner neuron for the presented data with the above three element values associated with the patient. The experimental results finally establish that the proposed method adequately works to select the formula.

We propose a learning scheme for multistate complex-valued and quaternionic neural networks in order to store correlated patterns with respect to each other. This is an extension of the so-called local iterative scheme for real-valued Hopfield neural networks. We first show the stability of desired memory patterns for a multistate complex-valued network and also for the multistate quaternionic network.

This paper presents map-based data classification for hematopoietic tumor patients. A set of squarely arranged neurons in the map is defined as a block, and previously proposed block-matching-based learning constructs the map used for data classification. This paper incorporates pseudo-learning processes, which employ block reference vectors as quasi-training data, in the above training processes. Pseudo-learning improves the accuracy of classification. Experimental results establish that the percentage of missing the screening data of the tumor patients is very low.

A method of classifying interneurons of silkworm moths is presented in this paper. Self-organizing maps (SOM's) are employed as tools for the classification. The maps are trained by presenting the data, each of which has a fractal dimension value, a ratio of the number of voxels after applying the erosion operation compared to that after labeling voxels, and a degree of circularity, as three elements. The first and second elements quantify denseness of branching structures and thickness of main dendrites in neurons, respectively. The remaining element is provided for quantifying uniformity of branching structures. The classification result is given as unit clusters formed in the trained map. It is established that the proposed method allows us to obtain the favorable classification result. It is much close to the result manually classified by a neuroscientist, compared with that obtained by the previously proposed map-based method.

Associative memory networks based on quaternionic Hopfield neural network are investigated in this paper. These networks are composed of quaternionic neurons, and input, output, threshold, and connection weights are represented in quaternions, which is a class of hypercomplex number systems. The energy function of the network and the Hebbian rule for embedding patterns are introduced. The stable states and their basins are explored for the networks with three neurons and four neurons. It is clarified that there exist at most 16 stable states, called multiplet components, as the degenerated stored patterns, and each of these states has its basin in the quaternionic networks.

Associative memory by Hopfleld-type recurrent neural networks with quaternionic algebra, called quaternionic Hopfield neural network, is proposed in this paper. The variables in the network are represented by quaternions of four dimensional hypercomplex numbers. The neuron model, the energy function, and the Hebbian rule for embedding patterns into the network are introduced. The properties of this network are analyzed concretely through examples of the network with 3 and 4 quaternion neurons. It is demonstrated that there exist fixed attractors in the network, i.e., the pattern association from test pattern close to a stored pattern is possible in the quaternionic network, as in real-valued Hopfleld networks.

Neural networks have attracted much interest in the two decades for their potential to describe brain function realistically. Quantum computing is a likely candidate for improving the computational efficiency of neural networks, since it has been very successful in doing so for a selected set of computational problems. We have proposed Qubit neural network that is a multilayered neural network composed of Qubit inspired neurons with Quantum Back Propagation learning and confirmed the performance concerning basic benchmark problems such as 4-bit and 6-bit parity check problems. In this paper, we examine this Qubit neural network through more practical problems, for example, the Iris data classification and the night vision processing.

This paper proposes the scheme of detecting the screening data of hematopoietic tumor patients, using self-organizing maps. The data of an examinee frequently lacks several of the item values. In addition, there exist redundant common items that should be eliminated from all of the data because they have an unfavorable influence on classifying the data. The data imputation, which substitutes the averages of non-missing item values, and a genetic algorithm are adopted to overcome the above issues. It is basically judged, by observing a label of a winner neuron in a map, whether the data presented to the map belongs to the class of hematopoietic tumors. Quantitative evaluations show that the proposed scheme achieves the high probability of correctly identifying examinees as hematopoietic tumor patients.

Hopfield neural networks tolerating weight faults are presented. The network training is made on condition some faults occur. Statuses of such faults are evoked by intentionally injecting faults into the network. The learning using the single-fault injection is shown first. Learning schemes, which are based on the double-fault injection for a couple of weights within a neuron, are then proposed to improve the fault tolerance further. Experimental results show that the learning using the random-double-fault injection allows us to complete the reasonably dependable network with the acceptable length of the learning time. In addition, the proposed schemes make the network robust against the input noise.

In nonstationary environments, it is difficult to apply traditional genetic algorithms (GAs) because they use strong selection pressure and lose the diversity of individuals rapidly. We propose a GA with neutral variation that can track environmental changes. The idea of this GA is inspired by Kimura's neutral theory (1983). The scheme of this GA allows neutral characters, which do not directly affect the fitness with respect to environments, thus increasing the diversity of individuals. In order to demonstrate the properties of this GA, we apply it to a permutation problem called the ladder-network, of which the imposed alignment on the output changes regularly. We show that the GA with neutral variation can adapt better to environmental changes than a traditional GA.

This paper proposes feedforward neural networks (NNs) tolerating stuck-at faults of weights. To cope with faults having small false absolute values, the potential calculation of the neuron is modified, and the gradient of activation function is steepened. To cope with faults having large absolute values, the function working as filter sets products of inputs and faulty weights to allowable values. The experimental results show that the proposed NN is superior in fault tolerance, learning cycles and time to other NNs.

As a sort of MINs (Multistage Interconnection Networks), we propose the 2-dilated baseline network whose performance in the faulty case degrades as gracefully as possible. All the available paths established between an input terminal and an output one via an identical input of SE (Switching Element) in some stage never pass through an identical SE in the next stage. The loads on SEs, therefore, are shared efficiently. Extra links added to enhance the performance never complicate the routing scheme. There is no difference between our MIN and other ones in hardware overhead. Besides our MIN is superior to other ones in performance, especially in robustness against concentrated SE faults in an identical stage.

In recent years, some researchers have been exploring quantum computers in view of neural networks to realize a distributed and strongly connectionist system that achieves parallel and fast information processing. We (1998) have proposed and investigated a qubit neuron model based on quantum mechanics, and constructed the quantum backpropagation learning rule (QBP). In this paper, we show an improved QBP neural network model and discuss its performance on solving the 4 bit parity check problem and the function identification problem. Then, we conclude that our model is more effective than the conventional one in information processing efficiency.

We describe the results of computer simulations of the dynamical behavior of a neural network model based on BP learning incorporated with stochastic resonance (SR neural network). This model is effective in solving the XOR problem, as reported in our previous work. This network is a small scale network for practical engineering. In this study, therefore we apply 4 bits parity problem and investigate learning abilities in the enhanced network to establish our SR method. From the results of experiments, we see the learning abilities of our network is improve more than the limited abilities of the traditional BP learning network. We also observe the stochastic resonance in our network.

This paper proposes a method for extracting the human hippocampus based on multiscale structure matching scheme. Focusing on the feature that an overextraction occurs on anatomically specific place, the method detects the redundancy by comparing with given desired models. Since each of the desired models has information about locations of their redundant segments, the place of corresponding redundancy can be specified on the overextracted object. Then, subtle intensity difference around their connecting place is investigated to separate the hippocampus and redundancy. The matching process can proceed in parallel for various types of redundancy and individual variances. Qualitative evaluation of a physician shows that our method can detect the redundancies and extract hippocampus correctly.

We propose a learning algorithm to enhance the fault tolerance of feedforward neural networks (NNs for short) by manipulating the gradient of sigmoid activation function of the neuron. For the output layer, we employ the function with the relatively gentle gradient. For the hidden layer we steepen the gradient of function after convergence. The experimental results show that our NNs are superior to NNs trained with other algorithms employing fault injection and the calculation of relevance of each weight to the output error in fault tolerance, learning cycles and time. The gradient manipulation never spoils the generalization ability.

Proposes a method of reconfiguring 2D meshes embedded in hypercubes. Our reconfiguration for link failures consists of two stages. The first stage assigns the d dimensions of the hypercubes to two directions with respect to rows and columns in the mesh, so that the number of disconnected pairs with adjacent rows and columns becomes smaller. The second stage re-establishes the mesh communication by assigning the Cartesian product of two Gray code sequences, which represent the order of healthy rows and columns to every node. We introduce graphs with edges corresponding to connections between rows or columns, and search the sequences. Then either an approach based on the depth-first search or one based on a genetic algorithm is applied to the graphs. The approach is made valid for node failures by regarding a faulty node as a node without healthy links. Simulation results show that our method reconfigures embedded meshes efficiently with relatively short computation time.

The paper presents the state of the art of motion systems particularly emphasizing both estimation and identification of parameters and control variables of an electric-motor-driven motion system. In a modern electrical drive system, it is required to take not only the electrical aspect but also the mechanical phase into total system consideration. Improvement in electrical aspect needs a variety of information pertaining to electrical machines and power electronic circuits for improving AC variable-speed drives. Important techniques of identification or estimation of parameters and control variables in AC drives are explained. Such information includes machine parameters, flux, speed, position, and so on. Also, the paper shows that there is some theoretical limit of performance. For improvement of the mechanical phase, the disturbance torque is the most important variable to be identified. It is used in motion control systems, for example, in the feedback loop. Various applications are possible by modification of such a basic approach. As a conclusion, the paper shows that the total robustness is attained by integrating advances of control technique on the electrical aspect and the mechanical aspect. There are numerous variations of controller by possible combinations of these two aspects according to applications.>