Fuzzy based emotional estimation system is one of the effective methods for estimation of speaker's emotion. Real-time processing and parallel processing are important for using emotion in practical communications. Therefore we try to implement the fuzzy based emotional estimation system into the Cell Broadband Engine which is a multi-core processor. In this paper, we investigate the performance and discuss the possibility of application to multi-modal systems.

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Recently, researches that aim to live together robot and human have been doing actively. In this research, we are developing communication system between human and robot. Therefore, robots have to recognize specific human in vision information. This paper proposes technique that partner robot pick up specific human in vision information.

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In the field of the pet robot and robot therapy, the creatural motion is important for the robots imitated the form of various animals. This paper presents the generation method of animal gait for quadrupedal robot. Here, we have employed AIBO as experimental quadrupedal robot and created the gait of AIBO in imitation of animal gait. At first, we have optimized the orbit of mono-leg, which can output propulsive force efficiently, by imitating dog gait and Genetic Algorithm. Moreover, we have generated the quadrupedal gait of AIBO using both the optimum orbit of mono-leg and "Trot" gait, which is classified the gait of walking dog based on the zoology.

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As robotics begin to have a more intimate relationship with people's lives, in contrast to the accurate and quick task management that has been demanded of manufacturing robots, the skills of adaptation to human behavior and to the surrounding environment have become key technologies. Based on the background described above, this study focuses on the formation and expression of emotion and proposes a method of acquiring in an autonomous fashion the behavior of appropriately expressing emotions that are formed via learning in unknown environments. This paper will execute the design of a system which considers the relationship between emotion, neuromodulators, and learning system meta parameters in order to make the proposed method a reality. Furthermore, we also report the results of an experiment by plural agent's computer simulation and Kansei evaluation to confirm the efficiency of proposed method.

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In this research, we construct an emotion measurement system by using information from the electroencephalogram of human.Generally, the measurement of electroencephalogram in human is complicated.Therefore, we propose a method of simple emotion measurement by using a cheap electroencephalograph in this research. The burden of an examinee is reduced by using this system. Then, we performed an experiment to confirm the efficiency of the proposed system in this research. In addition, we tested to compare this system with the system of body motion analysis with fuzzy emotion inference based on Laban's theory and also report the results of experiments.

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Generally, it is known that the engineering application simulated from the learning mechanism of animals is useful. Above all, the general idea of "Shaping" used by ethology, behavior analysis or animal training is a remarkable method recently. "Shaping" is a general idea that the learner is given a reinforcement signal step by step gradually and inductively forward the behavior from easy tasks to complicated tasks. In this paper, we propose a shaping reinforcement learning method took in a general idea of Shaping to the reinforcement learning that can acquire a desired behavior by the repeated search autonomously. Three different shaping reinforcement learning methods used Q-Learning, Profit Sharing, and Actor-Critic to check the efficiency of the Shaping were proposed at first. Furthermore, we proposed the Differential Reinforcement-type Shaping Q-Learning (DR-SQL) applied a general idea of "differential reinforcement" to reinforce a special behavior step by step such as real animal training, and confirmed the effectiveness of these methods by the simulation experiment of grid search problem.

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The paper presents new clustering algorithms which are based on fuzzy c-means. The algorithms can treat data with tolerance defined as hyper-rectangle. At first, the tolerance is introduced into optimization problems of clustering. This is generalization of calculation errors or missing values. Next, algorithms are constructed based on the results which are obtained by solving the optimization problems. Finally, usefulness of the proposed algorithms is verified through numerical examples.

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The present study discusses an algorithm that extracts clusters sequentially. An advantage of the proposed method is that the number of clusters need not be given beforehand. An algorithm for this method is described and compared with the mountain clustering that also extracts clusters sequentially. The present method is shown to perform better than the mountain clustering in higher dimensional spaces.

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Collaborative filtering is a technique for reducing information overload and the task is to predict missing values in a users vs. items matrix. GroupLens uses the weighted averages of ratings given by the "neighbors" considering similarities to the active user. It is also pointed out that the performance can be improved by item-based approach considering similarities among items. This paper proposes a linear fuzzy clustering model based on item partitioning and apply it to an item-based collaborative filtering system. Experimental results demonstrate that the model can be used for revealing mutual relation among variables and the item-based approach is useful for improving the performance of the model-based prediction model.

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Possibilistic clustering method identify the membership function without probabilistic constraint. Because each cluster is independent, the cluster center will converge to the same point when initial points are close to each other. Therefore, completeness of cluster is assured by assuming all data the center of cluster in possibilistic clustering. But, in this algorithm, processing time increases in proportion to the number of the data. This paper shows a method to reduce a calculation cost with completeness of cluster.

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A fuzzy c-means (FCM) classifier derived from a generalized FCM clustering has been proposed. In this paper, the classifier is not initialized with random numbers, hence being deterministic. The parameters are optimized by cross validation (CV) protocol and the simple genetic algorithm. The FCM classifier outperforms well established methods such as the support vector machine and the k-nearest neighbor classifier in terms of generalization ability.

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We present in a series of papers an application of Hirano-Tsumoto's method of rough clustering to asymmetric similarity data. In the first report we considered its basic aspect using graph structures. In this second report we present several experimental results applied to two kinds of actual data.

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Cluster analysis of individual opinions given as decision tables is proposed in this paper. Each decision table is regarded as opinions of an individual given in terms of examples. In order to grasp major opinions in the whole group of individuals, we propose the application of an agglomerative hierarchical clustering to a set of decision tables. Major opinions are obtained as common decision rules included in the obtained clusters. Some similarities are defined to evaluate to what extent the members of two clusters agreed. The clustering results by different similarities are compared from the viewpoints of stability and group cohesiveness in clusters.

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This paper discusses kernelized functions used in support vector machines defined on fuzzy neighborhoods of a text sequence. We show that a family of functions for fuzzy neighborhoods which are used for text mining or Web information analysis define positive definite kernels under a certain sufficient condition. Accordingly, clustering algorithms using a kernel function, such as agglomerative hierarchical clustering, kernel hard c-means or kernel fuzzy c-means are proposed. Effectiveness of this method is investigated using artificially generated data, and moreover this method is applied to real data.

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This paper describes how the concepts of agglomerative clustering and c-means clustering are adapted to analyze information tables in rough set studies. Agglomerative clustering is generalized into poset-valued clustering and kernel based c-means algorithms are proposed with natural kernels for information tables.

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In this paper cluster validity measures are investigated and compared. The studied measures are the sum of the traces of the fuzzy covariances within clusters, Xie-Beni's index, Davies-Bouldin's index, and Fukuyama-Sugeno's measure. These measures are kernelized and applied to the determination of the number of clusters having nonlinear boundaries generated by kernel-based clustering algorithms. We also propose a clustering algorithm using Fukuyama-Sugeno's measure.

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Ordinal principal component analysis is based on the distance between objects and the orthogonal projection of objects into a low dimensional space. The distance between two objects in high dimensional space is larger than the distance between the projected objects. Even if we obtain a very small value of distance between two objects in the projected space the real value of distance between the objects in the observation space may be very large. In order to solve this problem, a weighted principal component analysis has been proposed considering the dissimilarity of objects in the observation space. In the weighted component analysis, a weight function is defined as degree of contribution of each object to a classification structure. In this paper, we propose various weight functions and investigate the features.

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In this study, we propose a graded possibilistic approach to fuzzy clustering for cooccurrence matrix (FCCM) using regularization technique with Kullback-Leibler divergences (K-L information). FCCM partitions individuals and items of the cooccurrence matrix by maximizing the degree of aggregation of each cluster. In FCCM, when the number of items is large, the values of memberships for them will become small and make it difficult to interpret the absolute responsibility of them. By applying the graded possibilistic approach using regularization with K-L information to FCCM, we can make the absolute responsibility of items clear and handle the cluster capacity.

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A fuzzy c-means (FCM) classifier is applied to the analysis of receiver operating characteristics of carbon monoxide emission in an incinerator. Together with the decisive performance of FCM classifier, the effectiveness of the fractal dimension computed from the time series of sensor data is revealed.

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Fuzzy c-Regression Models (FCRM) is a fuzzy clustering-based switching regression model where regression errors are also used for clustering criteria in a Fuzzy c-Means (FCM)-like iterative optimization procedure. In data mining applications, we often deal with databases consisting of mixed measurement levels. Optimal scaling is a technique for mixed measurement situations, in which nominal variables represented by categories are quantified so that they suit the current model and then the model is updated in a single numerical space using the current quantified scores. Honda et al. applied the technique to FCM-type fuzzy clustering in order to characterize each cluster considering mutual relation among categories. In this paper, we propose a new switching regression model that improves the interpretability of multiple regression models considering partition of categories. The new model uses a hybrid objective function of FCRM for numerical variables and FCM for categorical variables. The FCRM part is responsible for multiple regression model estimation while the FCM part tries to characterize each cluster by assigning corresponding categories.

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In this paper, we use a cost-sensitive fuzzy system in a game environment. A cost-sensitive fuzzy system is generated so that the number of serious mistakes in decision making is minimized.Training data are generated from preliminary experiments.In computational experiments of this paper, cost-sensitive fuzzy systems are applied to a car-racing domain where two car agents compete for flags.We examine the performance of car agents with cost-sensitive fuzzy systems, standard fuzzy systems, and no fuzzy systems.Experimental results show the effectiveness of the cost-sensitive fuzzy systems for the game environment.

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A pursuit game is a multi-agents' benchmark problem, where 4 blue agents pursue and capture a red agent on a grid environment. In the previous research, we extended a grid environment to a real number one and proposed a method of fuzzy Q-learning with the state of fuzzy sets. In this research, we perform a numerical simulation with the environment and algorithm in the previous research. We have a result that we only need a small number of states to solve the problem in the previous research. We have reasons that the red agent with random movement does not get away from blue agents in spite that the red one has the same speed as blue ones, a blue agent has a large capture range and only 3 blue agents can often capture the red one.

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In order to apply the reinforcement learning to actual sized problem, the "curse of dimensionality" problem in partition of sensory states should be avoided maintaining computational efficiency. The paper describes a hierarchical modular reinforcement learning that Profit Sharing learning algorithm is combined with Q-Learning reinforcement learning algorithm hierarchically in multi-agent pursuit environment. As the model structure for such the huge problem, we propose a modular fuzzy model extending SIRMs architecture. Through numerical experiments, we found that the proposed method has good convergence property of learning compared with the conventional algorithms.

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As information technology advances, it has become possible for us to handle large amount of data. An agent is a computational entity such as a software program or a robot, and can be viewed as perceiving and acting upon its environment. This agent is autonomous in that its behavior at least partially depends on its own experience. The proposed support system applies multiagent techniques in order to improve the efficiency of information sharing and delivery. We examined what functionality is desirable or necessary for users. An experimental system is constructed to verify the validity of the proposed method.

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In this paper, we propose a model based on cognitive economy for the agent-based simulation about the formation of groups in social groups. The research about social balance regarded as a fundamental social process and formation of groups in social groups has a long and rich history. Heider, a founder of the theory of perceptual balance, defined the relations between three actors (P, O, X) as ``positive(+1)", ``negative(-1)"and judge the ``balance"or ``imbalance"of the group from using the product of these three signs in this cycle, and Cartwright et al extended Heider's balance theory to the groups consist of more than three actors to explain more realistic social problems. But in their researches, all the relations between each actors can be categorized only as ``positive (+1)", ``negative (-1)", ``no relation (0)". Then, we propose a model based on cognitive economy that can be categorized as more than three with using eigenvalue of adjacency matrix which represent actor's cognitive image in social groups. Moreover we study how the groups can be formed reaching balance under putting restrictions on the communications between each actors.

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A general aim of Kyushu Institute of Technology COE program is to create a new research field inspired by biological nervous systems and brain (Brain Information Technology). Since the research work on brain information technology extends over wide area of research fields, this program provides multi-disciplinary education so-called "Multi-talent Education" for young researchers. In the multi-talent education, the COE students, who are selected from ordinary students, can receive their education at four different research laboratories (from Neurophysiology, Psychology/Behavior, Modeling, Devices, Robotics section) for every six month during the master's course. In this presentation, the results of every research area and the impressions are reported in accordance with author's experience as COE student.

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Emotion Recognition Module from speech is proposed for Mascot Robot System to communicate with human being using speech content and minimum, maximum, and average fundamental frequency of each speech. It provides 6 output categories about speaker emotions which are employed for input of Eye Robot. Communication experimental results of the proposed module applied to Eye Robot show that the system communicates with user considering user's emotion and that recognition accuracy is 88%. The system is applied to Mascot Robot System which acts as information terminal in household environment.

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A trick art drawing system based on a torus type impossible figure generating algorithm is constructed. Proposed algorithm is based on the shapes and positions of corners of torus figures. Proposed system is able to generate an arbitrary n-bar torus type possible or impossible figure by interactive mouse-cricking operation on a figure generated only from initial n+1 inputs. It is possible to draw a trick art by painting each face of obtained figure. The proposed system aims a basic tool for experiments on visual psychology and an education support tool for discrete mathematics classes.

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In the complex environment, the ordinary two-wheel type or four-wheel type locomotive mechanism (non-Horonomic vehicle) has the limited moving area and the restrained motion. On the contrary, the omni-directional locomotive mechanism (Horonomic vehicle) that can move for any direction instantly has been applied to various application fields owing to its high mobility.In addition, it is not easy to describe the if-then rule so that an autonomous mobile robot generates an action under complex environment.Therefore the fuzzy control technique including vagueness is often used.In this research, we designed and producted an autonomous soccer robot with omni-directional locomotive mechanism controlled by using the fuzzy reasoning.

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It is an important processing in the object recognition of robot vision to perform the color extraction processing by deciding the fittest threshold in real environment. In the dynamic environment, the color information of target object dynamically changes according to the locations and lighting conditions. It is not easy for human to obtain the fittest threshold values of a target object correctly and rapidly under such conditions. So, in the research, we propose an automatic threshold tuning method to be able to extract ellipse target selected by human with color static image taken by an omni-directional camera. In this method, the fittest threshold values are searched by using genetic algorithm based on the color information of target object. To confirm the effectiveness of this method, we performed the experiment for the performance comparison of color extraction process with and without GA. Further, we also report on comparing the extraction result by human to GA.

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Toward developing efficient algorithms of geometric data mining, we extract extreme phenomena with strong vortex of wind such as tropical cyclone (TC) from a meteorological database. The database consists of observational values of some attributes, including wind vectors, at altitudes of certain atmospheric pressure (17 levels) over circa 10,000 grid points on the earth. Conventional method regards a grid point which fulfills some empirical conditions defined for a part of the pressure levels as the center of a typhoon. So, it cannot detect extreme phenomenon with strong wind in another level than the ones for which the empirical conditions are defined. Moreover, because the conventional method checks all grid points, its computation costs enormously. In this study, we propose finding first centers of vortex by moving from random initial positions along streamlines. Next, we calculate intensity and both horizontal and vertical ranges of influence around each center of vortex, then, rank them in order of risk. Comparison experiments showed that the proposed method found and ranked all typhoons extracted by the conventional method as at high risk. Also, the proposed method detected some risky and possibly risky vortices which the conventional method could not find.

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The purpose of this paper is to reveal the picture quality tuning of choice for the ordinary people. The TV picture quality is tuned by a specialist in a TV maker, though its audience is the ordinary people. This is because the tuning is difficult for the ordinary people. However, if the ordinary people can tune the TV picture quality ideally, is the result the same to the specialist's one? Is the result reasonable form the perspective of image processing theory? And, what kind of subjective sense (Kansei) does make the ordinary people select the result? In order to answer these questions, we have performed an experiment and considered the ordinary people's preference.

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This paper proposes a system that analyzes corporate evaluation on bulletin board sites. The system downloads threads from bulletin board sites selected by a user and extracts articles from the threads. The system extracts both threads corresponding to the user's interests and expressions which represent the contents of the threads. The system shows analysis results to the user with three viewpoints. The paper evaluates the effect of the system through the user's trial operation. The paper improves the system by getting rid of the problem shown by the operation and verifies experimentally the effect of the improvement.

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We applied fractal-fuzzy control system for a gasification melting type municipal solid waste incinerator.Fractal dimensions for the time series data of the amount of solid waste at inlet position incinerator were sequentially calculated to measure the fluctuation of the data. We applied fuzzy rules using the fractal dimension size to control the amount of secondary air quantity, and the amount of waste feed quantity. Using the proposed fractal-fuzzy control we were able to improve the combustion state.The result of fractal-fuzzy control, CO concentration in flue gases is very low level achieved.

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In a petroleum refining plant with a large number of high-pressure facilities, high-pressure gas leaks resulting from equipment failures can engender disasters. By electro-chemical gas leak detectors, however, monitoring of gas concentration can identify leaks only long after they've accrued, sometimes 10 minutes or more. For immediate detection of high-pressure gas leak, we have developed a gas leak detection system based on the acoustic diagnosis. A previous work reported chaos information criteria (CIC) to analyze dynamics of acoustic time series data, method of calculating of the CIC threshold level for detecting gas leakage manually, and the usefulness of CIC on high-pressure gas leak detection. This paper shows ; (1) the CIC threshold level are calculated automatically, (2) the actual results of our proof experiment for gas leak detection in Idemitsu Chiba Refinery, where plant nitrogen gas and steam are expelled, (3) the usefulness of CIC ,comparing with FFT (Fast Fourier Transform) analysis.

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This paper aims at the construction of a cooperative partner system that plays a seven-card stud poker game with a human partner against a computer opponent player. At each situation, the partner system gives a presentation to a human player about which action to take the game and the grounds for that action. If a human player makes another action, a human player and the partner system discuss which action to take by presenting their grounds for the action to each other as follows. (1) A human player selects the grounds for his/her action. (2) If the partner system accepts the player's grounds, they take the action which a player chooses, Otherwise, the partner system asks whether the player has other grounds or not. Through discussion, a human player and the partner system play a poker game cooperating with each other This paper also performs comparative experiments to confirm the usefulness of the presented partner system. In the experiments each subject plays games with/without the partner system.

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This study aims to construct a new framework for conceptual design support system in the field of Industrial Design. In the system, the Interactive Genetic Algorithm is introduced to generate the tableware which reflect users' conceptual feeling. Users evaluate pairs of tableware, which are generated as chromosomes by the system. Then the system re-generates next generation candidates based on the evaluation results. Repeating the interaction, users acquire pair of tableware which reflects users' feeling. In the chromosome of GA, "Feature Expressing Rules," which generate shapes of parts from linguistic feature, are used. In this paper, in order to reflect the users' feeling more effectively, the system saves and uses the rules which are common among the users' good evaluated shape.

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In this paper, we analyze a dialogue corpus between a user and an instructor toward the realization of smart help for novices who have some difficulty in operating a computer well. An experiment is conducted concerning the question and answer. The user asks a question to the instructor in another room by only his/her voice during operating word-processing software. The instructor also answers the question by only his/her voice. We construct the transcribed corpus based on the dialogues collected from the experiment. The speakers, the kind of task, the corresponding title of help, the kind of question, and the phase of dialogue are tagged. We analyze the corpus on the following contents: 1) the feature of each knowledge level, 2) the feature of each task, 3) the kind of question type. We show an example of scenario of smart help for novice based on the result of the analysis.

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This paper proposes a music/lyrics composing system consisting of two sections, a lyric composing section and a music composing section, which reflects user's impressions of theme of songs to lyrics/music. Love and nature are considered as theme in this paper. First of all, a user has a theme and image of lyrics to compose. The lyric composing section presents initial lyrics selected at random from database that is generated using existent lyrics and Markov Chain. If presented lyrics do not fit user's image, a part of lyrics not fitting user's image is changed by some other lyrics. When satisfied four lines lyrics are obtained, the music composition section starts. This section composes music fitting lyrics generated by the lyric composing section with the music composition system. The section presents combinations of four lines lyrics and 16 measures music. A subject evaluates each combination of lyrics and music whether they fit his/her image of a song. According to subject's evaluation music melody is changed by Genetic Algorithms and a part of lyrics are changed. These procedures are repeated until satisfied combination of lyrics and music melody is generated. In order to verify the validity of the presented system, subject experiments are performed.

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Currently, universities in the United States begin to consider on-line advising services in order to promote E-learning programs. In response to this trend, we are developing a web-based advising system that incorporates standard expert system technologies: symbolic reasoning and fuzzy reasoning. We studied that symbolic reasoning by itself may enable advices based on many factors, such as degree requirements, prerequisites, student transcript, course announcements, course catalog, seat availability, and student weekly schedule. We further studied that the reasoning based on fuzzy logic increases the quality of the generated advice by using additional factors with uncertainties, such as possible future course offering, course preferences, and course priority. Web technologies make this system better accessible to students who live remotely, and to those who only take correspondence or on-line courses. A logic programming engine and Apache Tomcat are used for this implementation.

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This research aims at developing a system to specify a phenomenon occured in observable space by the system with multiple-sensors. In this paper, observation based on image processing is used for feature-points are extracted. The proposed system performs pattern-matching with the pattern of the known observation-subject assumed from the dynamic pattern of the feature-points. Based on the result, it can be considered among the dynamic patterns of details that is the same observation subject is clustered, and system can determine known-subject based on DP matching for feature patterns in principal component space.

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Recently various kinds of systems based on electronics such as cars, computers, mobile phones and even robots have been widespread across our daily life. However, at the same time, these electronic systems could burden elderly or disabled people with its asymmetry postulate. To balance the asymmetry between human and electronic systems various problems have to be solved. Authors term the electronics to solve these problems "Humatronics". In our social life we see a lot of information concerned with our personality. Authors can support human actively to obtain and share the information as "Personal Property" through networked robots. Then authors proposed to construct the system where the networked robots with Personal Property can offer various services according to many kinds of circumstances. This indicates that the system can understand human. The system is based on Humatronics. In the end we show how capable the system is through the demonstration on television reception support service system.

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Recently, Robots have various sensors for environmental perception. Therefore, robots can get huge information. However, robots have to interpret information to work in real environment among huge physical information. In this paper, we discuss the environmental perception for mobile robot based on human perception.

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Household robots need to communicate with human beings in a friendly fashion. To achieve better understanding of displayed information, an importance and a certainty of the information should be communicated together with the main information. The proposed intent expression system aims to convey this additional information using an eye robot. The eye motions are represented as states in a pleasure-arousal space model. Change of the model state is calculated by fuzzy inference according to the importance and certainty of the displayed information. This change influences the arousal-sleep coordinate in the space which corresponds to activeness in communication. The eye robot provides a basic interface for the mascot robot system which is an easy to understand information terminal for home environments in a humatronics society.

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We are studying and developing automatic wheelchair robot DREAM-3 for the purpose of burden reduction for caregivers and independent support of a senior citizen and the person with disabilities. Several sensor systems for environment recognition are equipped with DREAM-3, and the traveling environment is recognized using the sensor systems. The environmental information obtained from this sensor system beforehand, is drawn on the environment map. Based on the environment map, the behavior choice is performed using the fuzzy inference. In this paper, semi-automatic wheelchair robot DREAM-4 with a learning function is proposed. A driver operates DREAM-4 by a joystick. And when the wheelchair meets with obstacles and senses danger, it travels slowly and avoids obstacles automatically. And DREAM-4 is to learn according to the operational feature of the driver, so that to make the steering easy.

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A new self-organizing map which includes winner afterglow layer for spatio-temporal pattern processing is proposed. In the proposed method, information of past winner is embedded in the additional competitive layer called winner afterglow layer, not in the usual competitive layer, thus it is expected that spatial topology is preciously preserved on the competitive layer. It facilitates understanding of map information. The effectiveness is verified by applying it to some spatio-temporal pattern classification problems.

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Kohonen's self-organizing map (SOM) is an architecture that generates a map of a given dataset. In this paper, a novel extension of SOM called SOM2 is proposed. The mapping objects of SOM2 are SOMs themselves, each of which represents a set of data vectors. Thus, the entire SOM2 represents a set of data distributions. SOM2 is expected to be a powerful tool for the classification, estimation and recognition tasks relevant to nonlinear manifolds. In this paper, we applied SOM2 to the face image classification task.

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The self-organizing relationship (SOR) network was proposed in order to extract a desirable input-output relationship of a target system by using input-output data pairs with their evaluations. In the execution mode, the SOR network can be used as a fuzzy inference engine. The output of the SOR network is calculated by using reference vectors and matching parameters, which correspond to the standard deviation of the Gaussian membership function used in fuzzy inference. However, the issue of the optimization of the matching parameters has not yet been treated in previous works. In this paper, we introduce an energy function to the SOR network in order to tune the matching parameters. The energy function can be used not only to tune the matching parameters but also to fine-tune the reference vectors with a gradient descent method. The proposed method is applied to a function approximation problem and the improvement of the approximation ability is confirmed.

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The U-matrix method is usually used well as for clustering of a self-organizing maps. However, the U-matrix method is effective only when data forms the cluster in the space. In the case of the pulse wave map of a subtitle, input data space has the continuous distribution. Therefore, it has become clear that the boundary of the U-matrix method differs from the class classification to which data belongs. When it had such data distribution, the labels for clustering needed to be manually created by the expert. In this report, labeling is automatically carried out based on special wave data points, and the technique of creating a cluster automatically using the label is proposed.

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A cluster analysis method is proposed in this paper. As benchmark data, the Fisher's iris dataset and Wine recognition data were used. As a result of the numerical experiment, a clustering method by the dendrogram took 97 % in accuracy. It is difficult to display a multi-dimensional data by the dendrogram in the one dimension. The ultimate of the visualization is 3 dimensional expressions. We can conclude that it should be the best way that a multi-dimensional data is expressed by a sphere where the phase relationship is smooth.

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