JP2007164704A - Apparatus using self-organizing map, and method and program thereof - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an apparatus capable of actualizing high-versatility control from among few training cases. <P>SOLUTION: In this apparatus, a control object is controlled by using the control signal of a controller related to a unit, containing a prediction device which most accurately predicts the prediction state of the control object at the next time among a plurality of units consisting of neural network modules present within the apparatus. Consequently, control with high immediacy can be actualized, and a self-organization map can be formed. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to an apparatus using a self-organizing map, and more particularly to an apparatus optimal for control requiring immediacy.

  As a background art of the present invention, there is an agent learning device disclosed in Japanese Patent Laid-Open No. 2000-35956.

  This background art agent learning device is composed of a combination of a reinforcement learning system that works on the environment and determines an action output for maximizing a reward obtained as a result, and an environment prediction system that predicts a change in the environment. Multiple learning modules are provided, and the responsibility signal that takes a larger value is required as the prediction error of the environment prediction system of each learning module is smaller, and the action output by the reinforcement learning system is weighted in proportion to this responsibility signal, and the environment It is the structure where the action for is given.

According to the agent learning device of this background art, in a non-stationary / non-stationary controlled object or system environment, a specific teacher signal is not given, and an action that is optimal for various environmental states and operation modes It is possible to perform behavioral learning flexibly without switching or combining them and without using foresight knowledge.
JP 2000-35956 A Wolpert, DM, Kawato, M .: Multiple paired forward and inverse models for motor control.Neural Networks 11, 1317-1329, 1998

The agent learning apparatus of the background art cannot solve the problem in the real world, in which the supervised learning framework cannot be applied and what is the correct output is unknown.
However, even the background art agent learning device has a problem that it may not be possible to solve the problem promptly and appropriately when there are few training cases. In particular, when environment 1, environment 2, and environment 3 are assumed and environment 2 is an environment where environment 1 and environment 3 are compromised, environment 1 is sufficiently trained and environment 3 is sufficiently trained. When the environment 2 is trained, the learning module corresponding to the environment 1 and the learning module corresponding to the environment 3 correspond to each other in the form of walking up to the environment 2, so that it takes a considerable amount of time to sufficiently cope with the environment 2. It takes. That is, there is a problem that it is impossible to take immediate action on a new environment by using an already learned environment.

  The present invention has been made to solve the above-described problems, and an object of the present invention is to provide an apparatus that can realize highly generalized control from a few training cases.

  That is, an object of the present invention is to realize an apparatus that can deal with a sudden change in the characteristics of a controlled object and can acquire generalized control capability from as few samples as possible. Therefore, we propose a self-organizing adaptive controller (SOC) that introduces the concept of a self-organizing map. The development of SOAC is related to the theme of adaptive control in control engineering, but adaptive control basically assumes that the characteristics of a controlled object change slowly with time, and is different in that respect.

  The SOAC was devised for the purpose of self-organizing the controller, and has two main characteristics. The first feature is that an architecture based on mnSOM (modular network SOM), which has the features of both a self-organizing map (SOM) and a modular network, is used. That is, the SOAC has a structure in which a large number of functional modules of a neural network are gathered, and these are learned according to the SOM algorithm. The second feature is that each functional module of the SOAC is composed of a pair of a controller and a predictor. That is, the SOAC has a structure in which many controllers and predictors having different characteristics are arranged (FIG. 1). Here, FIG. 1 is a diagram showing a basic configuration of the SOAC of the present invention.

  First, mnSOM, which is a first feature, is obtained by replacing each vector unit of a conventional SOM with a functional module of a neural network. For example, in mnSOM, modules such as MLP (Multi-Layer Perceptron) and RNN (Recurrent Neural Network) can be used instead of SOM vector units. By doing so, it is possible to map a set of data vectors and time series data that could not be handled by the conventional SOM. Note that if a Heb learning neuron is selected as the functional module of the mnSOM, the mnSOM becomes a normal SOM, so that the mnSOM can be regarded as a generalization of the SOM. Since the mnSOM function module can be freely designed by the user, the application range of the SOM can be greatly expanded. Accordingly, the inventor has come up with mnSOM with a controller using a neural network as a functional module after diligent efforts. This is the first feature of SOAC. That is, the SOAC is a collection of a large number of neural network controllers, and the functions are divided and coordinated by the SOM algorithm. When a certain control object is given, the module that best controls the control object is selected as the best matching controller (BMC), and the object is controlled using the BMC module. If the characteristics of the controlled object suddenly change, the BMC is immediately changed to another module, so that adaptive control can be performed (FIG. 2). Here, FIG. 2 is an explanatory diagram of module switching according to the present invention.

The second feature of SOAC is a modular structure in which a controller and a predictor are paired. The need arises from the fact that control tasks must be performed in real time. When the characteristics of the controlled object change, the optimum controller, that is, the BMC must be switched immediately correspondingly. Therefore, in the SOAC, a predictor that is paired with all the controllers is prepared, and the predictor that best estimates the state of the next time to be controlled and the paired controller are the BMC at that time. In other words, the predictor functions as a system identifier, and the paired controllers are learned in advance so as to be the optimal controller for the identified system. By doing so, the BMC can be switched instantaneously even for a sudden change in the controlled object.
More systematically, the present invention can be explained as follows.

  (1) An apparatus according to the present invention is an apparatus that constructs a self-organizing map realized by competitive learning between units composed of modules of a neural network, and the module of the neural network controls an object to be controlled. It includes a controller and a predictor that predicts the next time state of the controlled object.The controller outputs a control signal when the ideal state of the controlled object and the current state of the controlled object are input, and the predictor outputs the current state of the controlled object. By inputting the control signal of the time and the current state of the controlled object, the predicted state of the controlled object at the next time is output, and the unit equipped with the predictor that makes the closest prediction of the current state of the controlled object is the optimal unit The control target is actually controlled by the control signal output from the controller related to the optimal combination unit, and the unit that adopts the control signal as the optimal combination unit It is intended to update ourselves organizing map.

As described above, according to the present invention, the control signal of the controller related to the unit including the predictor that correctly predicts the predicted state of the control target at the next time among the units composed of a plurality of neural network modules existing in the apparatus. Since the control object is controlled by adopting it, it is possible to realize control with high immediacy and to form a self-organizing map.
The above-mentioned “apparatus for constructing a self-organizing map realized by competitive learning between units composed of modules of neural networks” is subordinate to “competitive learning between units composed of modules of neural network and neighborhood functions” An apparatus for constructing a self-organizing map realized by smoothing according to "."

  (2) The apparatus according to the present invention, if necessary, when a candidate unit that is a unit including a predictor that has performed the prediction that is closest to the current state is different from a unit that has become the previous optimal unit, If the current state of the candidate unit is not closer to the current state of the control target than the prediction of the current state of the unit that was the previous optimal combined unit, the unit that was the previous optimal combined unit is determined as the optimal combined unit To maintain.

  Thus, according to the present invention, when there is a possibility that the optimum combined unit may shift to another unit, the difference between the predicted state of the previous optimal combined unit and the current state of the control target is the predicted state of the candidate unit. If the difference between the control target and the current state of the control target is not greater than the predetermined threshold value, the previous optimal combination unit is continuously adopted, so that the optimal combination unit is not frequently changed and stable control is performed. Target control can be realized. In other words, even if the candidate unit accurately predicts the predicted state of the control target, switching of the unit is suppressed when the current optimum combined unit can be sufficiently controlled without much change. Consideration is given to avoid unstable control systems due to random switching of units.

(3) The device according to the present invention newly provides a linear feedback controller prepared for each controller that outputs a control signal and also outputs it to the controller by inputting the current state of the controlled object as necessary. Is included.
As described above, according to the present invention, since the linear feedback controller is arranged for each controller, the linear feedback interpolates the control signal even when the neural network as the controller is not sufficiently learned. Thus, appropriate control can be realized, and a signal output from the linear feedback controller can also be input to the controller to interpolate learning.

(4) The apparatus according to the present invention newly includes a delay unit prepared for each prediction that is held until at least the predicted time arrives at the predicted state of the predicted control target output by the predictor as needed. .
As described above, according to the present invention, even when the predictor outputs the predicted state at a time that is not the predicted time, the delay unit can adjust and appropriately specify the optimum combined unit.

(5) The apparatus according to the present invention is self-organized when necessary, when the target unit identified as the optimal combination unit is identified as the previous optimal combination unit, or with the unit previously identified as the optimal combination unit. When the object is close on the map, the condition of the control target targeted by the target unit is estimated based on the condition of the control target at that time.
As described above, according to the present invention, since the conditions of the same control target are arranged at the same position or the peripheral position of the self-organizing map, when the unit becomes the optimal combination unit, It is possible to grasp the approximate control target condition from the control target condition.

  (6) The apparatus according to the present invention specifies, when necessary, a position on the self-organizing map corresponding to the current control target condition when the current control target condition is input to the apparatus. And a current control target is controlled using a unit corresponding to the position on the self-organizing map.

  As described above, according to the present invention, the position on the self-organizing map corresponding to the input control target condition is specified, and control is performed using the controller according to the unit corresponding to the specified position. Even when the learning is not performed directly on the controlled condition, the control can be performed relatively stably. For example, when there is a control target condition A and a control target condition B, and learning is performed regarding these conditions, a control target condition C intermediate between the control target condition A and the control target condition B is input. When the control object is controlled by using the unit corresponding to the position between the control object condition A and the control object condition B on the self-organizing map, there is no learning about the condition. Can be controlled appropriately from the beginning.

  (7) A method according to the present invention is a method using an apparatus for constructing a self-organizing map realized by competitive learning between units composed of modules of a neural network, and is a control target included in the module of a neural network. A controller for controlling the output of the control signal by inputting the ideal state of the control target and the current state of the control target, and a predictor for predicting the next time state of the control target included in the module of the neural network A step of outputting a control signal at the current time of the controlled object and a current state of the controlled object to output a predicted state of the controlled object at the next time; and a predictor for performing a prediction that is closest to the current state of the controlled object The unit to be identified as the optimal unit and the control signal output from the controller associated with the optimal unit. A step that actually controls an object, is intended to include the step of updating the self-organizing map adopted unit a control signal as a best fit unit. The apparatus can also be grasped as a method.

(8) A program according to the present invention is a program for causing a computer to function so as to construct a self-organizing map realized by competitive learning between units composed of modules of a neural network. The controller that controls the control target included in the module of the neural network that outputs the control signal by inputting the state and the current state of the control target, and the control signal at the current time of the control target and the current state of the control target are input The predictor that predicts the next time state of the controlled object included in the module of the neural network that outputs the predicted state of the controlled object of the next time and the predictor that performed the closest prediction of the current state of the controlled object Means for identifying the unit provided as the optimum combination unit, and the control output from the controller associated with the optimum combination unit. This is for causing the computer to function as means for actually controlling the control object with the control signal and means for updating the self-organizing map with the unit adopting the control signal as the optimum unit. The device can also be grasped as a program.
These outlines of the invention do not enumerate the features essential to the present invention, and a sub-combination of these features can also be an invention.

(First embodiment of the present invention)
[1. Basic configuration]
The configuration of the SOAC is shown in FIG. The basic SOAC architecture is the same as that of mnSOM, and the functional module of mnSOM is composed of a predictor block and a controller block.
Is the controller block of the k-th module the current state x (t) to be controlled and the target state? x (t) is an input and a control signal u ^k (t) is an output. Ie

It is assumed that On the other hand, the predictor block of the k-th module receives the current state x (t) to be controlled and the control signal u (t) as inputs, and predicts the state to be controlled after Δt seconds to x ^k (t + Δt). Is output. Ie

It is assumed that
The SOAC has two modes, a learning mode and an execution mode. In the learning mode, the predictors and controllers of all modules are learned according to the mnSOM algorithm. In the execution mode, the control target is actually controlled using the module that has been learned.

[2. Execution mode]
Before describing the learning mode, first, an execution mode for actually operating the SOAC will be described. The error between the behavior of the controlled object and the behavior predicted by the predictor is defined by the following equation.

^p e ^k (t) is the exponential decay average of the prediction error. That is, in the execution mode, a time average of prediction errors from the very near past to the present is taken. The length of the time average interval is determined by ε. The smaller the ε, the longer the time average interval. Conversely, when ε = 1, ^p e ^k (t) is determined only by the prediction error at that moment. The module that minimizes ^p e ^k (t) is the BMC at time t. The value of ε is determined by the level of disturbance and noise applied to the controlled object, and it is generally better to set ε smaller as the disturbance and noise increase. If the BMC index is *,

となり、ＢＭＣの出力が実際の制御信号となり制御対象へ入力される。

Thus, the output of the BMC becomes an actual control signal and is input to the controlled object.

[3. Learning mode (predictor block)]
In this section, learning of the predictor block will be described, and learning of the controller block will be described in the next section. Now, there are I known control objects in advance, and these are used for learning. Therefore, I controllers for controlling these are also prepared. Therefore, I time-series data [(x _i (t), u _i (t))] (i = 1,..., I) are obtained.

The learning algorithm for the predictor block is equivalent to the mnSOM algorithm. Therefore, the algorithm of the predictor block is composed of four processes: (1) an evaluation process, (2) a competition process, (3) a coordination process, and (4) an adaptation process, similar to mnSOM. Here, it is assumed that the predictor is an MLP module, and the weight vector is ^p w ^k .

[3.1 Evaluation process]
First, a prediction error from the teacher pattern is obtained for all I pieces.

here,? x ^k _i (t) and ^p E ^k _i are respectively the output of the k-th predictor and the average prediction error for the i-th teacher. T represents the length of the time series.

[3.2 Competition process]
After obtaining the prediction error, BMC is determined for all the teacher patterns. The BMC is determined by the module that minimizes the average prediction error as shown in the following equation.

[3.3 Cooperation process]
The learning distribution rate is determined using a neighborhood function.

ここで、ξ^k、ξ^* _iはｋ−ｔｈモジュールとＢＭＣのマップ空間における座標を表す。

Here, ξ ^k and ξ ^* _i represent coordinates in the map space of the k-th module and BMC.

[3.4 Adaptation process]
The weight vector of the predictor is expressed by the following equation using the learning distribution rate {ψ ^k _i }.

These four processes are repeated until the network reaches a steady state. As a result, modules having close properties are arranged at close positions in the map space.
The map is updated according to the learning distribution rate.

[3.5 Learning mode (controller block)]
Feedback error learning is used as a controller for the SOAC. The advantage of using feedback error learning is that it can be trained using a conventional linear feedback controller as a controller, eliminating the need to determine the optimal controller in advance, thus allowing additional learning That is.

A block diagram of one SOAC module is shown in FIG. This model introduces feedback error learning in a closed-loop adaptive control system. In this model, the controller is composed of a conventional linear feedback controller (Conventional Feedback Controller: CFC) and a neural network controller (Neural Network Controller: NNC). By making CFC and NNC parallel, not only can NNC be learned by CFC, but also the control system can be stabilized by CFC, and NNC can realize nonlinear compensation. Now, ^{let cfc} W be the feedback coefficient matrix of the multi-input / output system, and ^cfc W ^k be subscripted with the feedback coefficient matrix of the k-th module. At this time, the control law of SOAC is expressed as follows.

The NNC error signal ^nnc E is defined by the following equation using the output of the CFC.

Finally, the feedback ^cfc W ^k and the weight vector ^nnc W ^k are updated according to the following equations. Here, the learning distribution rate ψ ^k _i uses a value obtained by learning of the predictor. That is, the controller learns to correctly control the system identified by the pair of predictors.

以上がSOACのアーキテクチャと学習アルゴリズムである。

This is the SOAC architecture and learning algorithm.

[4. Hardware configuration diagram]
FIG. 4 is a hardware configuration diagram of components of the apparatus according to the present embodiment. This apparatus can use a general-purpose computer. The hardware configuration includes a CPU (Central Processing Unit) 11, a main memory such as a DRAM (Dynamic Random Access Memory) 12, an HD (hard disk) 13 as an external storage device, a display 14 as a display device, and an input device. It includes a keyboard 15 and a mouse 16, a LAN card 17, which is an expansion card for connecting to a network, a CD-ROM drive 18, and the like.
For example, a program stored in a CD-ROM is duplicated (installed) on the HD 13, the program is read into the main memory 12 as necessary, and the CPU 11 executes the program to configure the apparatus.

[5. Operation]
FIG. 5 is an example of a flowchart of the operation in the execution mode of the apparatus according to the present embodiment.
The CPU 11 (predictor 2) predicts the state of the control target at the next time using the control signal at the current time of the control target and the current state of the control target (step 100). The prediction here is performed by the predictors 2 of all units.
The CPU 11 (delay unit 4) waits until the actual state of the control target at the predicted next time is input (step 200). The waiting here is performed by the delay units 4 of all units.
The CPU 11 compares the predicted actual state of the control target at the next time with the predicted state, and identifies the predictor 2 that has performed the closest prediction (step 300). The unit including the predictor 2 specified here is the optimum combined unit.

The CPU 11 (controller 1) obtains a control signal using the ideal state of the controlled object and the current state of the controlled object, and outputs the control signal to a drive source such as a motor (step 400).
The CPU 11 updates the self-organizing map based on the optimal unit (step 500).
Here, the controller 1 related to the optimum combination unit obtains the control signal after the optimum combination unit is determined, but the controller 1 of all the units obtains the control signal before it is determined to be the optimum combination unit. You can also.

(Other embodiments)
[Control condition estimation using self-organizing map]
For example, when the optimal unit is located in the middle on the map shown in FIG. 6B when a certain control target condition is controlled, the distance to the center of gravity of the pendulum is “Long”. It is presumed that the mass of the pendulum is “Heavy”.
That is, by controlling the control object, the position on the self-organizing map can be specified, and the condition of the current control object can be estimated from the condition of the previous control object associated with the position.

[Identification of units using self-organizing maps]
When a condition for a certain control target is input, even if the same condition as the condition for the control target is not learned, the self-organization map with which the similar control target condition is associated is used. By using a unit that is associated with a close position, it is possible to suppress control disturbance during the initial movement.

  It is also possible to demarcate on the self-organizing map according to the condition of the controlled object, and the same is achieved by using the unit in the demarcated area that most closely matches the newly input condition of the controlled object in each demarcated area. In addition, it is possible to suppress control disturbance at the time of initial movement. Further, by limiting the units that can be selected, it is possible to reduce the labor required for selecting the units used for control.

[Others]
If the dynamics to be controlled change continuously according to the hidden parameters, it is considered that a map corresponding to the dynamics can be formed, and the feature map thus generated can be used effectively.
Further, in the execution mode, an additional learning function for correcting the characteristics of each module while controlling an unlearned target can be added.
Although the present invention has been described with the above embodiments, the technical scope of the present invention is not limited to the scope described in the embodiments, and various modifications or improvements can be added to these embodiments. . And embodiment which added such a change or improvement is also contained in the technical scope of the present invention. This is apparent from the claims and the means for solving the problems.

[Example of applying SOAC to control of inverted pendulum]
In order to investigate the performance of SOAC, a simulation experiment was performed using an inverted pendulum system. The parameters of the pendulum used in the experiment are shown in Table 1 (see FIG. 6A).

  A SOAC module similar to that shown in FIG. 3 was used. In the simulation, the length and weight of the pendulum are variable, and nine parameter sets with different parameters are prepared as learning patterns. As shown in Table 1, there are three types of learning patterns with pendulum lengths of “Long”, “Half”, and “Short” and three types of pendulum weights of “Heavy”, “Middle”, and “Light”. Generated by a combination of The CFC feedback coefficient matrix (vector) was obtained by the state feedback control method. NNC used three-layer MLP, and the predictor used a linear neural network. In addition, Gaussian white noise was given to the carriage as a disturbance.

  After learning, the network was fixed and a control experiment was conducted. FIG. 6B shows a map obtained by SOAC learning. The map formed three clusters of “Short”, “Middle”, and “Long”. FIG. 6B shows a map of the inverted pendulum control module, and the gray scale in the map shows the distance between the predictor and the vicinity thereof.

  In order to examine the adaptability of the SOAC, the length and weight of the pendulum were changed at 30 second intervals. However, for the first 30 seconds, a parameter (Half-Middle) given at the time of learning was used, and thereafter, an unlearned parameter was used. In addition, the experiment was performed for each of the four cases of the case where the controller is switched and the case where the controller is not switched, the case where only CFC is used as the controller to be used, and the case where only NNC is used. The experimental results are shown in FIG. As can be seen from the figure, the learned parameters could be controlled without tilting the pendulum in all cases. However, if an unlearned parameter is given and the controller is not switched (non-adaptive) without notice, the pendulum collapses around 75 seconds from the start in both CFC and NNC cases. It was. On the other hand, when the controller was switched (adaptive), control was possible without tilting the pendulum in both cases of CFC and NNC. In particular, when NNC was used, control with less vibration was possible than with CFC.

  As a result of the simulation, the SOAC adaptively switches the BMC in response to the parameter change of the inverted pendulum, and can perform stable control. This shows that SOAC has a high adaptability. Furthermore, the SOAC can acquire not only the function as an adaptive controller but also the feature map of the controlled object in a self-organizing manner.

It is a figure which shows the basic composition of SOAC of this invention. It is explanatory drawing of module switching of this invention. It is a block diagram of one module of SOAC concerning the embodiment of the present invention. It is a hardware block diagram used with the apparatus which concerns on embodiment of this invention. It is an example of the flowchart of the operation | movement of the execution mode of the apparatus which concerns on embodiment of this invention. It is an example of the map obtained by learning of SOAC which concerns on an Example. It is an experimental result which concerns on an Example.

Explanation of symbols

1 Controller 2 Predictor 3 CFC
4 Delay device 10 Computer 11 CPU
12 DRAM
13 HD
14 Display 15 Keyboard 16 Mouse 17 LAN card 18 CD-ROM drive

Claims (8)

An apparatus for constructing a self-organizing map realized by competitive learning between units composed of modules of a neural network,
The neural network module includes a controller that controls the control object and a predictor that predicts the next time state of the control object,
The controller outputs a control signal when the ideal state of the controlled object and the current state of the controlled object are input,
The predictor outputs the predicted state of the controlled object at the next time by inputting the control signal at the current time of the controlled object and the current state of the controlled object,
Specify the unit that has the predictor that made the closest prediction of the current state of the control target as the optimal unit,
The control object is actually controlled by the control signal output from the controller related to the optimal unit,
A device that updates a self-organizing map with a unit that adopts a control signal as an optimal unit. If the candidate unit that is the unit that has the predictor that made the closest prediction in the current state is different from the unit that was the previous optimal combined unit,
If the current state of the candidate unit is not closer to the current state of the control target than the prediction of the current state of the unit that was the previous optimal combined unit, the unit that was the previous optimal combined unit is determined as the optimal combined unit The apparatus of claim 1. The apparatus according to claim 1, further comprising a linear feedback controller prepared for each controller that outputs a control signal and also outputs a control signal when a current state of a control target is input. The apparatus according to claim 1, further comprising a delay unit newly prepared for each prediction that holds at least the predicted state of the predicted control target output by the predictor until the predicted time arrives. When the target unit identified as the optimal combination unit was previously identified as the optimal combination unit, or when it was close to the unit previously identified as the optimal combination unit on the self-organizing map, the control target at that time The apparatus according to claim 1, wherein a condition of a control target that is a target of the target unit is estimated based on the condition. When a current control target condition is input to the apparatus, a means for specifying a position on the self-organizing map corresponding to the current control target condition is newly included.
The apparatus according to claim 1, wherein a current control target is controlled using a unit corresponding to a position on a self-organizing map. A method of using a device for constructing a self-organizing map realized by competitive learning between units consisting of modules of a neural network,
A controller that controls a control target included in the module of the neural network outputs a control signal by inputting an ideal state of the control target and a current state of the control target; and
The predictor for predicting the next time state of the controlled object included in the module of the neural network outputs the predicted state of the controlled object at the next time by inputting the control signal of the current time of the controlled object and the current state of the controlled object. Steps,
Identifying a unit comprising a predictor that has performed the closest prediction of the current state of the controlled object as an optimal combined unit;
A step of actually controlling a control target with a control signal output from a controller related to the optimal combination unit;
Updating the self-organizing map with the unit adopting the control signal as the optimal unit. A program for causing a computer to function to build a self-organizing map realized by competitive learning between units consisting of modules of a neural network,
A controller that controls the control object included in the module of the neural network that outputs a control signal by inputting the ideal state of the control object and the current state of the control object;
A predictor for predicting a next time state of a control object included in a module of a neural network that outputs a predicted state of a control object of a next time by inputting a control signal of the current time of the control object and a current state of the control object; ,
Means for identifying a unit having a predictor that has performed the closest prediction of the current state of the control target as an optimal combined unit;
Means for actually controlling the controlled object with a control signal output from the controller associated with the optimal unit;
A program for causing a computer to function as a means for updating a self-organizing map with a unit employing a control signal as an optimal unit.

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