JP2008003819A - Interaction detector, medium with program for interaction detection recorded therein, and interaction detection method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a technique which accurately obtains interactions between explanatory variables which determine a target variable. <P>SOLUTION: An interaction detector includes: a first correlation operation means which operates correlations between respective limiting elements; and a first interaction term extraction means which extracts limiting elements having less correlation with an arbitrary limiting element, as limiting elements having interactions with the arbitrary limiting element in a system prescribed by a plurality of limiting elements. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to an apparatus for detecting an interaction in relation to a plurality of variables and a response of a system to the plurality of variables.

Conventionally, as a technique for confirming the existence of an interaction, a technique described in Patent Document 1 has been disclosed. This publication discloses a method for analyzing data obtained by the experimental design method both when there is an interaction and when there is no interaction.
JP-A-5-257923

  In product development, it is important from the viewpoint of development efficiency to grasp the interaction between explanatory variables (design parameters, etc.) that determine target variables (for example, characteristic values, etc.). In the experimental design used in the above prior art, the existence of an interaction can be confirmed. However, because there is a limit to the number of design variables that can be selected for the orthogonal table used in the design of experiments, there is an interaction between variables other than the design variables selected for the orthogonal table and variables that cannot be selected for the orthogonal table. In some cases, the interaction will be missed. In the first place, the determination of the explanatory variables to be selected in the orthogonal table is determined by human experience, and thus the accuracy of the obtained results tends to deteriorate. Moreover, although the interaction between the explanatory variables selected in the orthogonal table can be confirmed, the presence or absence of the interaction between all the explanatory variables cannot be completely grasped.

  The present invention has been made paying attention to the above-mentioned problems, and its object is to propose a technique for accurately grasping the interaction between explanatory variables for determining a target variable.

  In order to achieve the above object, in the interaction detection device of the present invention, when there is a system defined by a plurality of limiting elements, a first correlation calculating means for calculating a correlation between the limiting elements and an arbitrary limiting element On the other hand, there is provided first interaction term extracting means for extracting the limiting element having a weak correlation as a limiting element having an interaction with the arbitrary limiting element.

  In the medium on which the interaction detection program of the present invention is recorded, the first correlation for outputting a command for calculating the correlation between the limiting elements in the set of limiting elements in the system defined by the plurality of limiting elements. A calculation command unit, and a first interaction term extraction command unit that outputs a command to extract the limiting element having a weak correlation with respect to an arbitrary limiting element as a limiting element having an interaction with the arbitrary limiting element; , Provided.

  In the interaction detection method of the present invention, when there is a system defined by a plurality of limiting elements, a first correlation calculation step of calculating a correlation between the limiting elements and the correlation with respect to an arbitrary limiting element And a first interaction term extraction step for extracting a weak restriction element as a restriction element having an interaction with respect to the arbitrary restriction element.

  Therefore, the interaction term can be extracted efficiently.

  Hereinafter, the best mode for realizing the interaction detection technique of the present invention will be described based on an embodiment shown in the drawings.

[Technical concept of Example 1]
First, define the word “system”. A system is a processing system or order that exists between input results that produce a specific result when there is a specific input. A specific event (phenomenon) is realized by defining a specific system to a certain value (corresponding to a system defined by a plurality of limiting elements). And the unique system works in a limited number, range, and nature, not processing everything or giving order to everything. Therefore, even if the types of events are the same, if there are various types with different limitations, there is a system corresponding to each. Furthermore, there are host systems that handle these uniformly according to the type of event.

  Such a layered system structure related to a specific event can be applied to almost all events such as economy, culture, design, and biology. It is accepted as a classification method that is easy to catch.

  For example, in an automobile suspension, the abstract system is a suspension, the individual system is a multi-link or torsion beam, the concrete system is a specific multi-link or torsion beam determined by the specific geometry value or bush stiffness value taken by the individual system, etc. It is.

  However, this classification is not intended to specifically understand systems in the same hierarchy or upper and lower systems. As the analysis (understanding) of the events shown by the lowest-level system progresses (matures), in order to make new efforts and discoveries, it is necessary to accurately understand the relationships between systems and the commonality that defines the overall system. Must be used. Here, the top layer system is called an “abstract system”, the middle layer system is called a “formal system”, and the bottom layer system is called a “concrete system”.

  In this embodiment, in order to enable understanding of the entire system, a “trend system” is introduced as a system in which a trend or range is limited between an abstract system and a formal system, and between a concrete system and a formal system. By deciding (systems classified by Cluster), it became possible to consider the understanding of the whole system, the understanding of characteristics between systems, the further understanding of events, the possibility of creating a new system, and so on. FIG. 1 shows these relationships.

  It was stated that the three-layer system structure is classified based on some commonality. When a complex event (phenomenon) is considered to be realized as a result of a combination of several events (phenomena), the characteristic of a complex event (phenomenon) is the characteristic of a certain event (phenomenon) It is thought that the characteristics of the combination have an influence. Such a feature is related to the commonality described above, and can be defined as a “common concept” of the system for realizing the phenomenon.

  In a certain formal system, various phenomena that occur as a result of changing various parameters of a concrete system are governed by a common concept peculiar to that formal system, and this concept realizes the tendency of various phenomena. It is thought that there is. And the specific tendency of each phenomenon shown by the concrete system is realized by taking a specific form derived from it based on a common concept.

  Here, the common concept is the value of specific parameters that can best explain the tendency of various complex phenomena, the combination of specific parameters, the relationship between specific parameters, the tendency of specific parameters, the value of specific parameters. Any of the ranges, or some combination of these. On the other hand, based on the common concept, the value of a specific parameter other than the common concept, the combination of specific parameters, the relationship between specific parameters, the tendency of specific parameters, the range of specific parameter values, or Some combinations of these can be defined as specific forms (corresponding to factor terms described later).

  Note that the common concept may exist between different systems that exist to realize a certain phenomenon. That is, various systems that exist in the formal system hierarchy exist in order to realize a specific phenomenon, and therefore there is a common concept (that is, in an abstract system) at the upper level of the formal system. The trend of the phenomenon is realized. And the phenomenon peculiar phenomenon is realized by adding the peculiar form of the formal system or the concrete system to the common concept.

  The first embodiment is configured based on the concept as described above in order to understand complicated phenomena. FIG. 2 shows the concept of the embodiment. In FIG. 2, common concept 0 is a concept that prescribes all phenomena, common concept 1 is a concept that prescribes phenomena only in the hatched area, and common concept 2 prescribes phenomena only in the hatched area. It is a concept. Common concept 0 includes common concepts 1 and 2, and when each common concept is overlapped with another common concept, a region is further defined.

  The abstract system and the format system may be set as appropriate while paying attention only to the upper limit relationship between all layers. Therefore, the abstract system is not limited to the upper layer. Moreover, the order which connects between the abstract system, the formal system, and the concrete system which were set suitably is defined as a tendency system.

[Information processing procedure flow]
In the first embodiment, after extracting a common concept that defines a complex phenomenon, a factor term that defines a specific phenomenon is extracted using the common concept. To extract the common concept, it is necessary to prepare several combinations (hereinafter referred to as sampling) of phenomena (hereinafter referred to as characteristics) and parameters (hereinafter referred to as limiting elements) taken by a system that realizes the phenomenon. Then, by classifying these characteristics into some and comparing the limiting elements, a common concept that best explains all phenomena is extracted. When this common concept is applied to a specific characteristic, a factor term that realizes a phenomenon peculiar to this characteristic is a state taken by a limiting element other than the common concept. Therefore, in Example 1, as shown in FIG.
Step [1] Site step to prepare for sampling [2] Site step to classify characteristics [3] Site step to compare limiting elements and extract common concepts [4] Specific characteristics or limiting elements of a specific group It is composed of four steps: a part that compares common concepts and extracts factor terms. These configurations are used repeatedly when traversing the system hierarchy.

(Preparation for sampling)
In the stage of sampling preparation in step [1], it is sufficient to prepare sampling of the target phenomenon that has been grasped so far. However, if there is a bias in the sampling to be compared, the common concept extracted as a result is biased to a certain characteristic, so it cannot often be said that all phenomena can be explained. Therefore, it is necessary to prepare sampling in which characteristics are not biased. When preparing for sampling, prepare all combinations of limiting elements, or combinations of limiting elements using an orthogonal table, and investigate the response of the characteristics to avoid sampling bias. That's fine.

  Here, an example of an orthogonal table is shown in FIG. An orthogonal table is a table created so that all the levels of other limiting elements are combined evenly when focusing on a specific level of an allocated limiting element. Therefore, the maximum value and minimum value of each limiting element that constitutes the limiting element are set, and the maximum and minimum values are divided into several according to the number of levels of the selected orthogonal table, and assigned to the orthogonal table. That's fine.

  If you have a simulator that simulates a system defined by multiple limiting elements and reproduces the characteristics that represent the relationship between input and output, link it with the simulator to work efficiently. It is desirable. The simulator may be in the same arithmetic device, or may be connected to another device with a cable or the like.

(Classification of characteristics)
Hierarchical clustering is used in the part for classifying the characteristics of step [2]. Clustering is an object of gathering groups that are similar to each other to create a community (hereinafter referred to as a cluster) in order to efficiently organize a meaningful system from a group of different natures. It is a general term for the method of classifying Of these, hierarchical clustering is a method of generating a hierarchy so that groups are nested. In the first embodiment, clustering is performed based on “similarity of characteristic tendency” as “similar”.

  Hierarchical clustering was adopted in the first embodiment because, as described in [Technical concept of the first embodiment], the system originally targeted by us is based on a hierarchical classification (i.e., most understood). This is because it is not possible to know in advance how many hierarchies and clusters exist in the trend system for understanding the relationship between the systems of each hierarchy. For example, when non-hierarchical clustering is performed, a threshold value or the like is set in advance, and operations within this threshold value are clustered. This threshold value may lead to the introduction of an existing concept. This is because when an existing concept is introduced, only a result confined to the existing concept is obtained, and the system cannot be classified correctly. The hierarchical clustering method is described below.

In hierarchical clustering, clusters are generated by joining individuals one by one based on similarity or dissimilarity, and gradually increasing from a small cluster to a larger cluster. Therefore, the cluster generation procedure is divided into two stages: definition of similarity (dissimilarity) and cluster generation. Here, the set of individuals x _i (1 ≦ i ≦ n), the set of all individuals X = {x ₁ , x ₂ , x ₃ ,..., X _n }, the similarity between individuals x _i and x _j Degrees d (x _i , x _j ) [1 ≦ x _i , x _j ≦ n, x _i ≠ x _j , x _i , x _j ∈X] are defined. Further, when an individual x _i is a cluster G _i , a cluster g including all the clusters is g = {G ₁ , G ₂ ,..., G _n }. At this time, the hierarchical clustering algorithm (Agglomerative Hierarchal Clustering: hereinafter referred to as AHC) is as follows.

(I) Define the following for the initial n clusters (individuals).
(3.2)

ここでG_qとG_rをgから取り除き、G'=G_q∪G_rをgに追加する。この際、クラスター数を一つ減らす。 (II) The cluster pair having the maximum similarity (or the minimum similarity) is combined.
(3.3)

Here, G _q and G _r are removed from g, and G ′ = G _q ∪G _r is added to g. At this time, the number of clusters is reduced by one.

(III) Recalculate the similarity d (G ′, G _i ) between clusters for all G _i ∈g and G _i ≠ G ′.

  (IV) Thereafter, (II) and (III) are repeated until the number of clusters becomes 1.

Various similarities (dissimilarities) taken up in (II) of the AHC have been proposed, but here, the Ward's Method is taken up. This method is based on the similarity based on the Euclid distance. That is, assuming that the value of the k-th element among the p elements constituting the individual x _i is x _i ^k , the Ward distance between the individuals x _{i and} x _j is expressed by Expression (3.4). Here, the element is a value included in the individual x _i .
(3.4)

(3.6)

At this time, if the center of gravity M (G) with respect to the cluster G is set as shown in formula (3.5), each component is expressed by formula (3.6).
(3.5)

(3.6)

(3.8)

(3.9)

Here, if the sum of squares E (G) of the difference between the center of gravity and the individual in the cluster G is defined as in the equation (3.7), the difference in distance between the two different clusters G _i and G _j is expressed by the equation ( It can be expressed as 3.8). Therefore, the coupling rule for the cluster of (II) of AHC selects G _q and G _r that minimize ΔE, as represented by the equation (3.9).
(3.7)

(3.8)

(3.9)

ここで、G'＝G_q∈G_rのとき
(3.11)

以上のように，AHCの（III）の再計算は、個体間の類似度を参照することなく、クラスター間の類似度のみを用いて再計算がなされる。図５に以上のアルゴリズムに基づくクラスターの生成方法を、図６に階層的クラスタリングの例を示す。 On the other hand, the recalculation of the similarity d (G ′, G _i ) of AHC (III) can be expressed using d (G _q , G _i ) and d (G _r , G _i ) before combining. If d (G _i , G _j ) = ΔE (G _i , G _j ) is defined, the initial cluster G _i = {x _i } can be expressed as shown in Expression (3.10).
(3.10)

Where G '= G _q ∈ G _r
(3.11)

As described above, the recalculation of (III) of AHC is performed by using only the similarity between clusters without referring to the similarity between individuals. FIG. 5 shows a cluster generation method based on the above algorithm, and FIG. 6 shows an example of hierarchical clustering.

Here, the cluster generation method is summarized as follows based on FIG.
(A) Sampling is clustered to generate clusters p, qr. In FIG. 5, it corresponds to a small circle.
(B) Calculate the center of gravity of each cluster.
(C) Combine clusters with small similarity (close distance). In FIG. 5, cluster p and cluster q are combined to generate a new cluster t.
(D) Calculate the center of gravity of the combined cluster t.
(E) Combine clusters with small similarity (close distance).
(F) Repeat (C) to (E) until there is one cluster.
In the step (A), not the cluster but the point information before clustering may be used, and there is no particular limitation.

[Extraction of common concepts]
In part [3], where the restriction elements are compared and the common concept is extracted (corresponding to the common concept extraction means), the relationship between the restriction elements existing for each classified hierarchy and the causal relationship between the characteristics are extracted. Later, we find causal relationships common to all layers. The common causality found here is called the common concept.

(Extraction of the causal relationship between the characteristics and the relationship between the restriction elements that exist for each classified hierarchy)
Extract the physical causal relationship between the limiting elements and phenomena that exist for each classified phenomenon hierarchy. The feature that the phenomenon shows can only be said in a complete way that various limiting elements are involved. However, in other words, the phenomenon is realized through various forms of relationships while changing the relationship between the limiting elements. If this is a network of limiting elements leading to the realization of the phenomenon, this network can be considered as a causal relationship. Here, this network is called a “causal network”.

  When one path is considered, the formation of this path may be influenced by other limiting factors, and this influence may also be influenced by other limiting factors. When finding a route with such characteristics, rather than judging the route from pure connections after eliminating the influence of other restrictive elements, the route is based on the relationship of the restrictive elements that have the influence of other restrictive elements. It is better to judge.

  In other words, when a route is determined from a pure connection that eliminates the influence of other limiting elements, a determination is made based on the magnitude of the numerical value of the degree of influence between certain limiting elements or between a certain limiting element and a phenomenon. It will be. Therefore, it is difficult to say that the physical relationship between the cut-off restriction element and the path is cut off, and the whole represents a causal network without knowing whether the cut-off is correct. On the other hand, when judging a route that has the influence of other limiting factors, truncation based on the existing concept is not performed, so a causal network that can explain all the physical connections describing the phenomenon itself This is because it is considered to form.

  However, since it tends to be complicated, it is necessary to provide a numerical index in the path between the limiting elements. Here, Pearson's product-moment correlation coefficient is taken up as a measure for measuring the strength of the connection between two limiting elements that have the influence of other limiting elements. In order to extract the causal network from the limiting element to the phenomenon, each limiting element and the phenomenon are considered in the same dimension. Each limiting element and phenomenon placed in the same dimension will be called the fulcrum of the path that makes up the causal network.

The number of data one fulcrum with n, 1 single fulcrum x, average x fulcrum x ^-, the other fulcrum y, the mean of the fulcrum y y ^- if that, the are two fulcrums x, between y A correlation coefficient r (xy) representing the strength of connection is expressed by equation (5.2).
(5.2)

  By applying the formula (5.2) between all the fulcrums, all the causal networks up to the phenomenon can be extracted together with the strength of connection including the influence of other limiting factors (see Fig. 7). . By applying this to a phenomenon cluster of all layers, it becomes possible to grasp a phenomenon process that is gradually hierarchized from a complicated phenomenon to a simple phenomenon together with a change in the causal network.

(Extraction of common concepts)
Complex phenomena have a hierarchical structure in which they are gradually divided into simple phenomena based on physical characteristics. Therefore, it is considered that the causal network changes along the hierarchy accordingly. The factors that determine a single phenomenon in a hierarchy and the factors that determine its complexity are: a causal network that is common to single phenomena in all hierarchies, the target phenomenon, and its upper and lower hierarchies. It can be defined as a heterogeneous causal network that exists between these phenomena.

  In the case of hierarchization accompanied by feature differentiation of complex phenomena using hierarchical clustering, the lowest layer is a cluster composed of one sample. Since it becomes a hierarchy which emphasizes the complexity of a phenomenon as it goes to the lowest layer, there is a feature that commonality fades. On the other hand, the cluster is composed of more samples as it goes to the top layer, but since the number of clusters included in the hierarchy is reduced, there is a feature that there is a lot of commonness including noise.

  Therefore, it can be considered that there is a most suitable hierarchy for extracting a common concept from this relationship. Here, the hierarchy which can extract a common concept is specified, and the method of extracting a common concept from here is described.

First, the hierarchy suitable for the extraction of the common concept is specified. Here, the sensitivity S and SN ratio η of the correlation coefficient of a certain path p are used. The hierarchy of interest i, when the number of clusters included in the layer n, the correlation coefficient in the path p in the m-th cluster included in the layer and r _ipm, the correlation coefficient superposed r _ip ^- in the formula ( It is expressed as 5.3).
(5.3)

If one of the common causal networks in this hierarchy is the path p, the sensitivity S of the correlation coefficient can be expressed as in equations (5.3) to (5.4).
(5.4)

Further, the total variation S _t of the correlation coefficient in the path p for each cluster included in the layer i is expressed by equation (5.5).
(5.5)

Further, the correlation coefficient variation S _β of the path p is expressed by Expression (5.6), where Euclidean distance d _im for dividing each cluster and average Euclidean distance are di ⁻ .
(5.6)

Therefore, the error variance V _e in the path p can be expressed by Equation (5.7).
(5.7)

Therefore, the SN ratio η of the correlation coefficient in the path p of each cluster included in the hierarchy i can be expressed by Expression (5.8).
(5.8)

  Since the common concept is a common causal network that can explain all phenomena, the sensitivity S expressed by equation (5.4) is large and the SN ratio η expressed by equation (5.8) is large in all common paths. The hierarchy is suitable for extracting common concepts. However, the hierarchy of common concept extraction must be examined in a hierarchy that is less than or equal to the maximum Euclidean distance that causes a branch when searching from the top layer to the bottom layer of the tree diagram.

  In the hierarchy suitable for common concept extraction obtained as described above, the common causal network that becomes the common concept corresponds to the path p having a high correlation coefficient sensitivity expressed by the equation (5.4). FIG. 7 shows an image of common concept extraction. FIG. 8 shows an example of a network display method, and FIG. 9 shows an example of a common concept display method common to these networks.

  In addition, although the notation method of a restriction element was described by arranging each restriction element on the circumference and connecting the restriction elements with a straight line as shown here, it may be arranged other than on the circumference. In addition to the method of changing the line type, a method of coloring a line, a method of expressing the line by the thickness of the line, and the like can be considered. The common concept of FIG. 9, that is, the common network is naturally included in the network of individual clusters of FIG.

(Extraction of factor terms)
In step [4], the limiting element is compared with the limiting element of the specific characteristic or the specific group classified, and the factor term is extracted. A factor term is a form of a specific limiting element based on a common concept that determines a specific phenomenon. Therefore, the causal relationship between the common concept extracted in the above (extraction of the common concept) and the specific form is compared, and the portion not corresponding to the common concept becomes the factor term. FIG. 10 shows a display example of extraction of factor terms.

(Extraction of interaction terms)
Next, extraction of interaction terms will be described. As described above, when there is a complicated phenomenon that realizes a certain characteristic, these are clustered hierarchically based on the tendency of the characteristic to extract a common concept. As a result, we grasped the limiting factors that are important for realizing certain characteristics (restricting factors with strong correlation) and the relationships between important limiting factors (causal network, etc.).

  Here, it is clear that grasping the degree of influence of the limiting element on the characteristic value is very useful for understanding the entire system. However, the more complicated the phenomenon, the more effective the interaction effect is that one limiting element affects another limiting element, but these simultaneously affect the characteristic value. In the basic design stage, a wide design space is analyzed in consideration of various characteristics, so that the interaction effect becomes remarkable. Therefore, the method for extracting the interaction term will be described below.

  In the past, the interaction between the limiting elements has been uniquely determined based on the designer's subjectivity because of a simple theoretical relationship or when the phenomenon becomes complicated. In the basic design stage, the phenomenon is complicated because the design area to be handled is wide and various characteristics must be considered simultaneously. In such a case, the determination of the interaction has to rely on the subjectivity that comes from the experience of the skilled engineer and is difficult for an inexperienced engineer. Moreover, it can be said that it is unclear whether all the interactions can be considered. In the case of complex multimodal phenomena, this effect is thought to affect the characteristics of the characteristics.

  Therefore, the region is divided into regions corresponding to certain characteristics and considered as the interaction effect at the unit region level. As described above, each design area has a common concept, a factor term corresponding to a certain design area based on this common concept, and another limiting element that is a characteristic that exists for each unit area. It is thought that it is composed of interaction terms that have a strong influence on the behavior of. Therefore, the interaction term is extracted based on this concept.

  An interaction effect is an effect in which a certain limiting factor affects other limiting factors. Therefore, a measure for the strength of connection between variables is required. Here, after removing the influence from other variables, the partial correlation coefficient is used to achieve the strength of the connection between pure variables, that is, the interaction.

  When examining the correlation of two variables, the observed correlation may not represent a true correlation because each variable has a correlation with the third variable. Therefore, a correlation coefficient obtained by removing the influence of variables other than the two variables of interest, that is, a partial correlation coefficient is obtained.

If the number of data in one variable is n, one variable is x, the average of the variable x is x ⁻ , the other variable is y and the average of the variable y is y ⁻ , the relationship between two variables x and y The number r (xy) is expressed by the following equation.
(4.15)

  When there are p variables, the partial correlation coefficient between the p-q variables in which q variables are fixed (the influence is removed) is called a “qth order partial correlation coefficient”.

(4.17)

式(4.17)では、r(xy)_q-1＝r(xy・k₁k₂・・・k_q-1)などと略記した。 When the fixed variables are k ₁ , k ₂ ,..., K _q , the q-order order partial correlation coefficient between the two variables x and y is expressed by the following equations (4.16) and (4.17). It can be calculated with a recurrence formula.
(4.16)

(4.17)

In the equation (4.17), it is abbreviated as r (xy) _q-1 = r (xy · k ₁ k ₂ ... K _q-1 ).

The partial correlation coefficient when all variables other than two variables x and y are fixed can be obtained by the following equation (4.18), where rxy is an element of the inverse matrix of the correlation coefficient matrix r (xy). .
(4.18)

  From these equations, it is possible to measure the strength of a pure connection between two variables. Therefore, it is sufficient to select a combination of variables having a strong interaction that increases the partial correlation coefficient. As described above, it is possible to specify a combination of variables having an interaction relationship.

  Next, paying attention to a cluster having a certain characteristic, all the limiting elements and all the characteristics are arranged in the same dimension, and all these partial correlation coefficients are calculated. Thereby, the strength of the connection between each limiting element and one evaluation characteristic value becomes clear. The interaction term is different for each evaluation characteristic value. Therefore, attention is paid to a certain evaluation characteristic value.

  FIG. 11 is a graphical model representing the strength of connection between the characteristic value 1 and the limiting elements 1 to 4. In FIG. 11, characteristic value 1 and each limiting element are arranged on the circumference, and those having a large partial correlation coefficient between characteristic value 1 and each limiting element are connected by a solid line. Note that the graphical model of FIG. 11 is expressed in order to visually understand the strength of the correlation between the characteristic value 1 and each limiting element, and the arrangement or the like does not have physical significance.

  As shown in FIG. 11, the characteristic value 1 has a strong correlation between the limiting element 1 and the limiting element 3. From this, it can be considered that the limiting elements 1 and 3 are all similar data movements.

  A limiting element having a strong correlation with the characteristic value 1 can be considered not to be an interaction term for the characteristic value. FIG. 12 is a diagram showing a comparison between the pseudo limiting element virtual and the characteristic value 1 when the limiting elements 1 and 3 interact. That is, when the interaction term is expressed as a product of the limiting elements, when the data having similar movements are multiplied with each other, as shown in the virtual of FIG. Therefore, the correlation is weakened and it is not considered that there is an interaction effect.

  Note that the interaction is not limited to the product, and various interactions such as sum and division may be prepared to examine various interactions.

  Conversely, the limiting element 2 and the limiting element 4 that are weakly correlated with the characteristic value 1 are candidates for interaction terms. FIG. 13 is a diagram showing a comparison between the pseudo limiting element virtual and the characteristic value 1 when the limiting elements 2 and 4 interact. That is, as shown in FIG. 13, in each of the limiting elements 2 and 4, the correlation with the characteristic value 1 is not strong, that is, the data movement is not similar, but the virtual value obtained by multiplying them is the characteristic value 1 This is because there is a possibility that the correlation will be strong.

  Therefore, we found some variables that have strong connections between the limiting elements that remain after removing the limiting elements that have a strong influence on the characteristics alone, and calculated the partial correlation coefficient between the candidate interaction term and the characteristics by multiplying them. Measured, the larger is the interaction term that has a strong influence on the desired characteristics. In summary, the interaction term extraction algorithm is as follows.

Step 1 Measure all partial correlations and remove characteristics and particularly strong limiting elements Step 2 Multiply the connected limiting elements among the remaining limiting elements to create an interaction term Step 3 Newly created interaction It is possible to extract the interaction term by the above steps by measuring the partial correlation between the term and the characteristic and extracting the interaction term having a large partial correlation as the interaction term.

(Concrete example)
Hereinafter, an example applied to a specific mode based on the first embodiment will be described. Here, a multi-link suspension, which is a type of automobile suspension, is taken up. FIG. 14 shows the structure of the multilink suspension. Here, the characteristic to be handled is a change in the camber angle when the tire is stroked, and the limiting element is an attachment point (hereinafter referred to as geometry) of each link of the multilink suspension (see M1 to M5 in FIG. 5). ).

  The multi-link suspension has a large difference in the characteristics shown in FIG. In actual suspension design, a design target value of characteristics is set in advance, and an operation of searching for a limiting element that matches or exceeds the target value is performed. Therefore, parametric work is often performed ignoring mechanistic relationships, and it is impossible to understand why the optimum structure has been determined.

  In addition, because there is no understanding of the suspension mechanism, when designing another multi-link suspension, the same parametric optimization work will be performed, which is inefficient and creates a new suspension structure. It does not lead to. It also failed to understand whether there was an interaction term between limiting elements. Here, we extracted the common concepts that lead to the understanding of the relationship between the characteristics of the multilink suspension and the limiting factors, the creation of a new suspension structure, and the factor terms to understand the structure-specific phenomena.

(Preparation for sampling)
The geometry of the multi-link suspension shown in FIG. 14 is shaken in accordance with the orthogonal table L81 within the geometry range of FIG. 16, mechanism calculation is performed according to each shaked geometry value, the camber angle is calculated, and sampling is prepared.

(Classification of characteristics)
The sampling prepared in (Preparation for sampling) is classified according to characteristics, that is, the camber angle. FIG. 17 shows a tree diagram of characteristics obtained as a result of classification. FIG. 18 shows the characteristics of groups (hereinafter referred to as clusters) in a certain classified hierarchy.

(Extraction of common concepts)
From the classification result obtained in the above (classification of characteristics), the hierarchy from which the common concept is extracted is specified according to the method for extracting the common concept. A causal network between the restriction elements of each cluster existing in the identified hierarchy is extracted according to the above-described common concept extraction method. The causal network between the limiting elements obtained as a result is expressed using limiting element notation means.

  FIG. 19 shows some examples of the causal network between the limiting elements. In this notation, the connections between the limiting elements that are very influential in realizing the characteristics of the characteristics indicated by the cluster are indicated by solid lines, and the dotted lines indicate the connections between the limiting elements that are the next most influential. Show. Here, the common concept is a causal network of common limiting elements existing in all clusters. Therefore, the extraction of the common concept is equivalent to finding the common causal network by comparing the notation of the restriction elements of the clusters obtained here. FIG. 20 shows the notation of the common concept obtained.

  The common concept obtained here is the relationship of the geometry necessary to control the camber angle in the multilink suspension. That is, in order to realize a desired camber angle, it is possible to guarantee at least by designing with an emphasis on the relationship (tendency) between geometries as a common concept. For example, when it is desired to realize the characteristic tendency as shown in FIG. 21, the relationship of the limiting elements as a common concept may be designed with the tendency as shown in FIG. 22, and the characteristic tendency as shown in FIG. 23 is realized. If desired, the relationship between the limiting elements that are common concepts may be designed with a tendency as shown in FIG.

(Extraction of factor terms)
Remove common concepts from the notation of restriction elements for specific clusters. Accordingly, it can be seen that a change in a certain camber angle can be realized by adding a tendency of a limiting element of a common concept to be realized to a tendency of another limiting element. FIG. 25 shows a causal network of limiting elements of the factor term of cluster 2.

(Extraction of interaction)
As described above, by extracting common concepts common to each cluster and extracting factor terms existing in individual clusters, it was possible to extract limiting elements having strong characteristics and correlation within a certain cluster. Here, the extraction of interaction terms in cluster 2 will be examined. FIG. 26 shows whether or not there is an interaction term in the remaining restriction elements (Lower_Outer_x, Lower_Outer_y, Upper_Outer_x, Upper_Outer_y, Tierod_Outer_x, Tierod_Outer_y) excluding the restriction elements constituting the common concept and the factor term in cluster 1. It is a figure showing the graphical model which considers.

As shown in FIG. 26, a pseudo restriction element is created from the remaining restriction elements (Lower_Outer_x, Lower_Outer_y, Upper_Outer_x, Upper_Outer_y, Tierod_Outer_x, Tierod_Outer_y). The following 15 combinations are conceivable as combinations of these pseudo limiting elements.
virtual1 ＝ Lower_Outer_x ・ Lower_Outer_y
virtual2 = Lower_Outer_x / Upper_Outer_x
virtual3 = Lower_Outer_x / Upper_Outer_y
virtual4 = Lower_Outer_x / Tierod_Outer_x
virtual5 = Lower_Outer_x / Tierod_Outer_y
virtual6 = Lower_Outer_y / Upper_Outer_x
virtual7 = Lower_Outer_y / Upper_Outer_y
virtual8 = Lower_Outer_y / Tierod_Outer_x
virtual9 = Lower_Outer_y / Tierod_Outer_y
virtual10 = Upper_Outer_x / Upper_Outer_y
virtual11 = Upper_Outer_x / Tierod_Outer_x
virtual12 = Upper_Outer_x / Tierod_Outer_y
virtual13 = Upper_Outer_y / Tierod_Outer_x
virtual14 = Upper_Outer_y / Tierod_Outer_y
virtual15 = Tierod_Outer_x / Tierod_Outer_y
It is. Here, the noticed characteristic Char is a camber angle change characteristic Char (= camber-stroke) with respect to the stroke.

  These pseudo limiting elements, the remaining limiting elements, and the characteristic Char are arranged in the same dimension as shown in FIG. 26, and all the partial correlation coefficients are calculated. As a result, virtual4 (= Lower_Outer_x / Tierod_Outer_x), virtual9 (= Lower_Outer_y / Tierod_Outer_y), virtual11 (= Upper_Outer_x / Tierod_Outer_x), virtual14 (_Up_Out_d I was able to find.

  From this, as an example of expressing the relationship between the limiting elements constituting each pseudo limiting element in FIG. 27, a diagram is shown in which limiting elements are arranged on the horizontal axis and the values of limiting elements are plotted on the vertical axis. Show. Looking at the relationship between the limiting elements in each virtual (4, 9, 11, 14), it is between Lower_Outer_x and Tierod_Outer_x, between Lower_Outer_y and Tierod_Outer_y, between Upper_Outer_x and Tierod_Outer_x, and between Upper_Outer_y and Tierod_Outer_y It can be understood that all maintain the upward relationship.

  In other words, the restriction element alone has no correlation with the characteristics, and even if it is a restriction element that is not considered to be a restriction element that defines a particular design area, when looking at the interaction terms, It can be seen that the upward trend is maintained. Therefore, it was understood that in order to determine the limiting element that realizes this characteristic, it is necessary to select within a range that maintains the upward trend of each limiting element.

  Needless to say, when a combination of other limiting elements is described, a particular tendency cannot be found, and the values vary throughout.

  As described above, in the first embodiment, the following effects can be obtained.

  (1) When there is a system defined by a plurality of limiting elements, the correlation between the limiting elements is calculated (corresponding to the first correlation calculating means), and the limiting element having the weak correlation with respect to an arbitrary limiting element is Extraction is made as a limiting element having an interaction with respect to the arbitrary limiting element (corresponding to the first interaction term extracting means).

  In other words, those that have a strong correlation with an arbitrary limiting factor are those that affect an arbitrary limiting factor alone without any interaction, and those that are not likely to be affected by the interaction. Can think. Therefore, a candidate having an interaction can be extracted efficiently.

  (2) A pseudo limiting element is created by acting the weakly limiting elements (corresponding to the pseudo limiting element creating means), and a correlation between the pseudo limiting element and the arbitrary limiting element is calculated (first 2), the limiting element constituting the pseudo-limiting element having a strong calculated correlation is extracted as a limiting element having an interaction (corresponding to the second interaction term extracting means).

  Therefore, it is possible to specifically determine whether or not there is actually an interaction, and more accurate interaction extraction can be achieved.

  (3) The optional limiting factor is the response characteristic of the system defined by other limiting factors. Therefore, it is possible to understand the relationship between the characteristic and the limiting element, and for example, it is possible to extract the relationship between the limiting element that realizes the targeted characteristic.

  (4) When there is a set of combinations of characteristics and the above restriction elements that represent the relationship between input and output for the system, this set is classified based on the tendency of the characteristics (corresponding to the classification means), and the restriction elements in a certain classification Are compared with restriction elements in other classifications, and a common concept is extracted based on the restriction elements common between the classifications (corresponding to common concept extraction means). And it decided to extract limiting elements other than the limiting element which comprises a common concept as a limiting element which has an interaction. In other words, by comparing the characteristics classified based on the tendency between the limiting elements that define this characteristic, it becomes possible to grasp the limiting elements that define the tendency, and to understand the technical meaning of the classification. it can. From this, it is possible to efficiently eliminate the limiting element that does not have an interaction.

  (5) As a means of classification, a hierarchical clustering method of hierarchical clustering based on trends was used. In other words, considering the fact that our target system is based on hierarchical classification, the most understandable system can be obtained by hierarchical clustering. Further, considering that the number of layers existing in the system is not known in advance, it is not necessary to set a threshold or the like in advance, and a result that is not bound by an existing concept can be obtained.

  (6) The common concept was extracted based on the limiting elements common to each layer. Therefore, it is possible to extract a common concept that defines between hierarchies.

  (7) The common concept was extracted based on the restriction elements common to only a certain hierarchy. Therefore, a common concept that defines a certain hierarchy can be extracted.

  (8) Comparing a specific characteristic or a restriction element of a specific classification with a common concept, extracting a factor term, and constituting a factor term that is a restriction element other than the restriction factor constituting the common concept A limiting element other than the limiting element is extracted as a limiting element having an interaction. Therefore, it becomes possible to exclude a limiting element that causes a specific characteristic or a specific classification from a limiting element having an interaction, thereby improving the accuracy of the interaction term.

  (9) The characteristics are classified based on the similarity according to the distance in the Euclidean space. Therefore, it becomes possible to express a multidimensional restriction element in an orthogonal coordinate system based on the similarity, and it is possible to easily compare in a form that can be understood by humans.

  (10) The classification is based on the similarity based on the distance between the center of gravity of a certain classification and each characteristic. Therefore, it becomes possible to observe complex phenomena on a scale of distance, and to compare in a form that can be understood by humans.

  (11) An error variance representing the size of the variance area of the limiting element is calculated, and a common concept is extracted in a hierarchy having a large correlation coefficient and a small error variance. Therefore, a numerical index can be provided in the path between the limiting elements, and even if all the limiting elements are compared, a causal network can be easily formed without complication.

  (12) The partial correlation coefficient is calculated as the correlation between the remaining limiting elements excluding the limiting elements related to the common concept and the factor term and the pseudo limiting element. Therefore, it is possible to calculate the strength of connection between pure variables after removing the influence from other variables.

(Other examples)
Next, another embodiment will be described. In the above embodiment, when the causal network is described, the limiting elements are arranged on the polygon. However, for example, they may be arranged on attribute axes arranged in parallel.

  FIG. 28 is a schematic view showing another embodiment. Assume that there are limiting elements A, B, C, and D for a system. At this time, the characteristics representing the relationship between input and output to the system are classified into cluster A and cluster B. Next, attribute axes arranged in parallel on the two-dimensional plane are set, and the restriction element existence regions (dispersions) of the clusters A and B are superimposed on the attribute axes. In FIG. 28, the range surrounded by the solid line is the existence range of the restriction element of cluster A, and the range surrounded by the dotted line is the existence range of the restriction element of cluster B. At this time, the hatched area where cluster A and cluster B overlap may represent a causal network having a strong correlation.

  In the first embodiment, common concepts and factor terms are extracted by hierarchical clustering, and then interaction terms are extracted. For example, no correlation is performed and no correlation is performed between the limiting elements. Then, a pseudo limiting element may be created from these weakly correlated limiting elements to extract the interaction term.

  In the first embodiment, the relationship between the characteristic and the limiting element has been described. However, it may be determined whether or not the configuration of the limiting elements has an interaction.

  In the first embodiment, the classification is performed by hierarchical clustering. However, the distance between the centers of gravity calculated from the Euclidean distance of the limiting element that realizes a certain characteristic may be classified as the similarity.

  Although not specifically shown in the first embodiment, it is industrially effective to use the interaction detection technique based on the logical configuration as a program medium so that it can be processed by a computer or the like. The program medium may be a medium such as a CD or a DVD, or may be configured to store the program in a server or the like and download the program as appropriate. Also, a device written in advance in a Flash memory or ROM may be provided.

  Specifically, it is desirable that each of the following command units is provided. Each command unit outputs a command to execute each process described in the first embodiment, and it is needless to say that the same operational effects as those in the first embodiment can be obtained.

  (P1) A first correlation calculation command unit that outputs a command for calculating a correlation between each limiting element for a set of limiting elements in a system defined by a plurality of limiting elements, and the correlation for an arbitrary limiting element And a first interaction term extraction command unit for outputting a command for extracting a weak restriction element as a restriction element having an interaction with respect to the arbitrary restriction element. The medium on which is recorded.

  (P2) Creates a pseudo limiting element by causing the limiting elements extracted by the first interaction term extraction command unit to act on the medium in which the interaction detection program according to (P1) is recorded Calculated by a pseudo-restriction element creation command unit that outputs a command, a second correlation calculation command unit that outputs a command for calculating a correlation between the pseudo-restriction element and the arbitrary limit element, and the second correlation calculation unit And a second interaction term extraction command unit for outputting a command for extracting a limiting element constituting a pseudo-limiting element having a strong correlation as a limiting element having an interaction. The medium on which is recorded.

  (P3) In the medium on which the interaction detection program according to (P1) or (P2) is recorded, the arbitrary limiting element is a response characteristic of a system defined by the other limiting element. A medium on which a characteristic interaction detection program is recorded.

  (P4) In the medium on which the interaction detection program according to the above-mentioned claim (P3) is recorded, when there is a set of combinations of characteristics representing the relationship between input and output and the limiting element for the system, The first correlation calculation command unit compares a classification command unit that outputs a command to classify the set based on the tendency of the characteristics, and a common element among the classifications by comparing a limiting element in one classification with a limiting element in another classification A common concept extraction command unit that outputs a command for extracting a common concept based on the limiting element, and the first interaction term extraction command unit includes a limiting element other than the limiting elements constituting the common concept. A medium on which a program for detecting an interaction is recorded, wherein a command to be extracted as a limiting element having an interaction is output.

  (P5) In the medium on which the interaction detection program according to (P4) is recorded, the classification command unit outputs a command to execute a hierarchical clustering method for hierarchical clustering based on a tendency. A medium on which a characteristic interaction detection program is recorded.

  (P6) In the medium on which the interaction detection program according to (P5) is recorded, the common concept extraction command unit outputs a command for extracting a common concept based on a limiting element common among the layers. A medium on which an interaction detection program is recorded.

  (P7) In the medium on which the interaction detection program according to (P5) or (P6) is recorded, the common concept extraction command unit extracts a common concept based on a limiting element common only to a certain hierarchy. A medium on which is recorded an interaction detection program characterized by outputting a command.

  (P8) On the medium on which the interaction detection program described in any one of (P4) to (P7) above is recorded, the limiting factors that are common only in specific characteristics or specific classification are extracted as factor terms A factor term extraction command unit for outputting a command to perform, wherein the first interaction term extraction command unit is a limiting element other than the limiting elements constituting the common concept, and the limiting factor constituting the factor term A medium on which a program for detecting an interaction is recorded that outputs a command for extracting a limiting element other than the above as a limiting element having an interaction.

  (P9) In the medium on which the interaction detection program according to any one of (P4) to (P8) is recorded, the classification command unit classifies the characteristics based on a similarity based on a distance in Euclidean space. A medium on which a program for detecting an interaction is recorded, characterized in that a command to output is output.

  (P10) In the medium on which the interaction detection program according to any one of (P4) to (P8) is recorded, the classification command unit determines the similarity according to the distance between the center of gravity of a certain classification and each characteristic. A medium on which a program for detecting an interaction is recorded, characterized in that a command for classification is output.

  (P12) An error variance calculation command for outputting a command for calculating the size of the dispersion region of the limiting element in the medium on which the interaction detection program according to any one of (P4) to (P11) is recorded A program for detecting an interaction is recorded, wherein the common concept extraction command unit outputs a command for extracting a common concept in a hierarchy having a large correlation coefficient and a small error variance. Medium.

  (P13) In the medium on which the interaction detection program according to any one of (P1) to (P3) is recorded, the first correlation is a partial correlation coefficient. Medium on which the program is recorded.

  (P14) In the medium on which the interaction detection program according to any one of (P1) to (P13) is recorded, the second correlation is a partial correlation coefficient. Medium on which the program is recorded.

It is a figure showing the concept which introduce | transduces the tendency system which added the limitation of a tendency or a range between the abstract system of Example 1, and a format system, and between a concrete system and a format system. It is a conceptual diagram showing the relationship between the cluster of Example 1, and a common concept. It is a figure showing the information processing procedure flow of Example 1. FIG. It is a figure showing the example of the direct table which prepares the sampling of Example 1. FIG. FIG. 6 is a diagram illustrating a specific example of clustering according to the first exemplary embodiment. 3 is a diagram illustrating a specific example of hierarchical clustering according to Embodiment 1. FIG. It is a figure showing the causal network of Example 1. FIG. It is a figure showing an example of the display method of the causal network of Example 1. FIG. An example is shown in the common concept display method common to the causal network of the first embodiment. The example of a display of extraction of the factor term using the causal network of Example 1 is shown. 3 is a graphical model representing the strength of connection between the characteristic value 1 of Example 1 and the limiting elements 1 to 4. It is a figure showing contrast with the pseudo limiting element virtual and the characteristic value 1 when the limiting elements 1 and 3 of Example 1 interact. It is a figure showing contrast with the pseudo limiting element virtual and the characteristic value 1 when the limiting elements 2 and 4 of Example 1 interact. It is a figure which shows the structure of the multilink suspension in a specific example. It is a figure showing the difference in the characteristic by the difference in the limiting element of the multilink suspension in a specific example. It is a figure showing the sampling which created the geometry of the multilink suspension in a specific example according to the orthogonal table. It is a figure showing the dendrogram of the characteristic obtained as a result of the clustering in a specific example. It is a figure showing the characteristic of the cluster in a classified hierarchy. It is a figure showing some examples of the causal network of the restriction elements in a specific example. It is a figure showing the common concept in the common causal network in a specific example, and the multilink suspension part corresponding to this common concept. It is a figure showing the stroke amount-camber angle characteristic with a specific example. It is a figure showing the multilink suspension shape corresponding to a certain characteristic of a specific example. It is a figure showing the stroke amount-camber angle characteristic with a specific example. It is a figure showing the multilink suspension shape corresponding to a certain characteristic of a specific example. It is a figure showing the causal network of the restriction | limiting element of the factor term of a cluster with a specific example. Whether or not there is an interaction term in the remaining restriction elements (Lower_Outer_x, Lower_Outer_y, Upper_Outer_x, Upper_Outer_y, Tierod_Outer_x, Tierod_Outer_y) excluding the restriction elements constituting the common concept and the factor term in the cluster 2 of the specific example It is a figure showing the graphical model which examines about. FIG. 6 is a diagram in which limiting elements are arranged on the horizontal axis and limiting element values are plotted on the vertical axis, as an example of expressing the relationship between the limiting elements constituting each pseudo limiting element of a specific example. It is a figure showing the causal network of the restriction | limiting element in another Example.

Explanation of symbols

p, q, r cluster
t cluster (cluster p + cluster q)
M1, M2, M3, M4, M5 Ditometry

Claims (39)

When there is a system defined by multiple restrictive elements,
First correlation calculating means for calculating a correlation between each limiting element;
First interaction term extracting means for extracting a limiting element having a weak correlation with respect to an arbitrary limiting element as a limiting element having an interaction with the arbitrary limiting element;
An interaction detection device comprising: The interaction detection device according to claim 1,
Pseudo limiting element creating means for creating a pseudo limiting element by acting the limiting elements extracted by the first interaction term extracting means;
Second correlation calculating means for calculating a correlation between the pseudo limiting element and the arbitrary limiting element;
Second interaction term extraction means for extracting a limiting element constituting a pseudo limiting element having a strong correlation calculated by the second correlation calculating means as a limiting element having an interaction;
An interaction detection device comprising: In the interaction detection device according to claim 1 or 2,
The interaction detecting apparatus according to claim 1, wherein the arbitrary limiting element is a response characteristic of a system defined by the other limiting element. In the interaction detection device according to claim 3,
When the system has a set of combinations of characteristics and the limiting elements representing the relationship between input and output,
The first correlation calculating means compares the classifying means for classifying the set based on the tendency of the characteristic, and compares the limiting elements in one classification with the limiting elements in another classification, and based on the limiting elements common to the respective classes. And a common concept extraction means for extracting a common concept
The first interaction term extracting means extracts a limiting element other than the limiting elements constituting the common concept as a limiting element having an interactive action. In the interaction detection device according to claim 4,
An interaction detection apparatus, wherein the classification means is a hierarchical clustering technique for hierarchical clustering based on a tendency. In the interaction detection device according to claim 5,
The interaction detecting device, wherein the common concept extracting means extracts a common concept based on a limiting element common between the layers. In the interaction detection device according to claim 5 or 6,
The interaction detecting device, wherein the common concept extracting means extracts a common concept based on a limiting element common only to a certain hierarchy. In the interaction detection device according to any one of claims 4 to 7,
There is provided a factor term extraction means for extracting a limiting factor that is common only in a specific characteristic or a specific classification as a factor term,
The first interaction term extracting means extracts a limiting element other than the limiting element constituting the common concept and a limiting element other than the limiting element constituting the factor term as a limiting element having an interaction. An interaction detecting device characterized by that. In the interaction detection device according to any one of claims 4 to 8,
The interaction detecting device, wherein the classifying unit classifies the characteristics based on a similarity based on a distance in an Euclidean space. In the interaction detection device according to any one of claims 4 to 9,
The interaction detecting apparatus according to claim 1, wherein the classification means performs classification based on a similarity based on a distance between a center of gravity of a certain classification and each characteristic. In the interaction detection device according to any one of claims 4 to 10,
An error variance calculating means for calculating the size of the variance area of the limiting element is provided,
The interaction detecting device, wherein the common concept extracting means extracts a common concept in a hierarchy having a large correlation coefficient and a small error variance. In the interaction detection device according to any one of claims 1 to 3,
The interaction detecting apparatus according to claim 1, wherein the first correlation is a partial correlation coefficient. In the interaction detection device according to any one of claims 1 to 12,
The interaction detecting apparatus according to claim 2, wherein the second correlation is a partial correlation coefficient. For a set of limiting elements in a system defined by multiple limiting elements,
A first correlation calculation command unit that outputs a command for calculating a correlation between the limiting elements;
A first interaction term extraction command unit for outputting a command for extracting the limiting element having a weak correlation with respect to an arbitrary limiting element as a limiting element having an interaction with the arbitrary limiting element;
A medium on which is recorded an interaction detection program. In a medium on which the interaction detection program according to claim 14 is recorded,
A pseudo limiting element creation command unit that outputs a command to create a pseudo limiting element by acting the limiting elements extracted by the first interaction term extraction command unit;
A second correlation calculation command unit that outputs a command for calculating a correlation between the pseudo limiting element and the arbitrary limiting element;
A second interaction term extraction command unit that outputs a command for extracting a limiting element constituting a pseudo-limiting element having a strong correlation calculated by the second correlation calculating means as a limiting element having an interaction;
A medium on which is recorded an interaction detection program. A medium in which the interaction detection program according to claim 14 or 15 is recorded,
The medium on which the program for detecting an interaction is recorded, wherein the arbitrary limiting element is a response characteristic of a system defined by the other limiting element. A medium on which the interaction detection program according to claim 16 is recorded,
When the system has a set of combinations of characteristics and the limiting elements representing the relationship between input and output,
The first correlation calculation command unit compares a classification command unit that outputs a command to classify the set based on the tendency of the characteristics, a restriction element in one classification and a restriction element in another classification, A common concept extraction command unit that outputs a command to extract a common concept based on a common restriction element,
The first interaction term extraction instruction unit outputs a command for extracting a restriction element other than the restriction elements constituting the common concept as a restriction element having an interaction. Medium. A medium on which the interaction detection program according to claim 17 is recorded,
A medium on which a program for detecting an interaction is recorded, which outputs a command for executing a hierarchical clustering method for hierarchically clustering the classification command unit based on a tendency. In the medium on which the interaction detection program according to claim 18 is recorded,
The medium on which the program for detecting an interaction is recorded, wherein the common concept extraction command unit outputs a command for extracting a common concept based on a limiting element common among the layers. A medium on which the interaction detection program according to claim 18 is recorded,
The medium on which the program for detecting interaction is recorded, wherein the common concept extraction command unit outputs a command for extracting a common concept based on a limiting element common only to a certain hierarchy. A medium on which the interaction detection program according to any one of claims 17 to 20 is recorded,
A factor term extraction command unit that outputs a command to extract a limiting factor that is common only in a specific characteristic or a specific classification as a factor term,
The first interaction term extraction command unit extracts restriction elements other than the restriction elements constituting the common concept and restriction elements other than the restriction elements constituting the factor term as restriction elements having an interaction. A medium on which a program for detecting an interaction is recorded, characterized in that a command to output is output. In the medium in which the interaction detection program according to any one of claims 17 to 21 is recorded,
The medium on which the program for detecting interaction is recorded, wherein the classification command unit outputs a command to classify the characteristics based on a similarity based on a distance in the Euclidean space. In the medium in which the interaction detection program according to any one of claims 17 to 21 is recorded,
The medium on which an interaction detection program is recorded, wherein the classification command unit outputs a command to classify based on a similarity based on a distance between a center of gravity of a certain class and each characteristic. A medium on which the interaction detection program according to any one of claims 17 to 23 is recorded,
An error variance calculation command unit that outputs a command for calculating the size of the variance region of the limiting element is provided,
The medium on which an interaction detection program is recorded, wherein the common concept extraction command unit outputs a command for extracting a common concept in a hierarchy having a large correlation coefficient and a small error variance. A medium on which the interaction detection program according to any one of claims 14 to 16 is recorded,
The medium in which the interaction detection program is recorded, wherein the first correlation is a partial correlation coefficient. In the medium on which the interaction detection program according to any one of claims 14 to 25 is recorded,
The medium on which the program for detecting interaction is recorded, wherein the second correlation is a partial correlation coefficient. When there is a system defined by multiple restrictive elements,
Calculating a first correlation for calculating a correlation between the limiting elements;
A first interaction term extraction step for extracting the weakly correlated limiting element with respect to an arbitrary limiting element as a limiting element having an interaction with the arbitrary limiting element;
An interaction detection method comprising: The interaction detection method according to claim 27,
A pseudo limiting element creation step of creating a pseudo limiting element by causing the limiting elements extracted in the first interaction term extraction step to act;
A second correlation calculating step of calculating a correlation between the pseudo limiting element and the arbitrary limiting element;
A second interaction term extracting step for extracting a limiting element constituting a pseudo-limiting element having a strong correlation calculated in the second correlation calculating step as a limiting element having an interaction;
An interaction detection method comprising: The interaction detection method according to claim 27 or 28, wherein:
The interaction detection method according to claim 1, wherein the arbitrary limiting element is a response characteristic of a system defined by the other limiting element. The interaction detection method according to claim 29,
When the system has a set of combinations of characteristics and the limiting elements representing the relationship between input and output,
In the first correlation calculation step, a classification step for classifying the set based on the tendency of the characteristics, a restriction element in a certain classification and a restriction element in another classification are compared, and based on a restriction element that is common among the classifications. And a common concept extraction step for extracting the common concept.
In the first interaction term extracting step, a limiting element other than the limiting elements constituting the common concept is extracted as a limiting element having an interaction. The interaction detection method according to claim 30,
An interaction detection method, wherein the classification step is a hierarchical clustering method for hierarchical clustering based on a tendency. The interaction detection method according to claim 31,
The interaction detection method, wherein the common concept extraction step extracts a common concept based on a limiting element common between the layers. In the interaction detection method according to claim 31 or 32,
The interaction detection method, wherein the common concept extraction step extracts a common concept based on a limiting element common only to a certain hierarchy. 34. The interaction detection method according to any one of claims 30 to 33,
A factor term extraction step for extracting a limiting factor that is common only in a specific characteristic or a specific classification as a factor term is provided,
The first interaction term extraction step extracts a limiting element other than the limiting element constituting the common concept and a limiting element other than the limiting element constituting the factor term as a limiting element having an interaction. The interaction detection method characterized by the above-mentioned. In the interaction detection method according to any one of claims 30 to 34,
In the classification step, the characteristic is classified based on a similarity based on a distance in the Euclidean space. In the interaction detection method according to any one of claims 30 to 34,
The interaction detection method according to claim 1, wherein the classification step classifies the classification based on a similarity based on a distance between a center of gravity of a certain classification and each characteristic. The interaction detection method according to any one of claims 30 to 36,
An error variance calculating step for calculating the size of the variance area of the limiting element is provided,
The interaction detection method, wherein the common concept extraction step extracts a common concept in a hierarchy having a large correlation coefficient and a small error variance. The interaction detection method according to any one of claims 27 to 29,
The interaction detection method according to claim 1, wherein the first correlation is a partial correlation coefficient. In the interaction detection method according to any one of claims 27 to 38,
The interaction detection method, wherein the second correlation is a partial correlation coefficient.

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