Route selection program, route selection method, and route selection device

Abstract

To realize automation of path construction of state transition.SOLUTION: A route selection program causes a computer to execute processing of: extracting a plurality of representative points from an existence probability distribution of a target state; specifying a plurality of first state transition routes among the representative points; and selecting a plurality of second state transition routes from the first state transition routes based on probability density of each of the first state transition routes.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a route selection program, a route selection method, and a route selection device. [Background technology]

[0002] Determining the pathways involved in the state transitions of proteins and compounds is crucial for applications such as drug discovery, and discussing these pathways and free energy transitions using molecular dynamics (MD) and other methods is key to understanding reaction processes.

[0003] One technique for constructing such pathways is single-particle analysis software that uses deep neural networks to support the reconstruction of a continuous ensemble of three-dimensional protein structures from two-dimensional cryo-EM (Electron Microscopy) images. [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] Laurel F Kinman, Barrett M Powell, Ellen D Zhong, Bonnie Berger, and Joseph H Davis. Uncovering structural ensembles from single-particle cryo-em data using cryodrgn. Nature Protocols, pages 1-31, 2022. [Overview of the project] [Problems that the invention aims to solve]

[0005] However, the single-particle analysis software described above requires manual operation by experts to obtain reasonable continuity deformations from protein structures obtained from 2D cryo-EM images. Examples of such operations include preparing input for the single-particle analysis software, training deep neural networks, filtering particles, searching for models in the single-particle analysis software, investigating structural ensembles, and visualizing structural transitions.

[0006] In one aspect, the present invention aims to provide a route selection program, a route selection method, and a route selection device that can automate the construction of a path for state transitions. [Means for solving the problem]

[0007] A path selection program for one aspect causes a computer to perform the following steps: extract multiple representative points from the probability distribution of the target state, identify a first set of multiple state transition paths between the multiple representative points, and select a second set of multiple state transition paths from the first set of multiple state transition paths based on the probability density of each path in the first set of multiple state transition paths. [Effects of the Invention]

[0008] This enables the automation of constructing path paths for state transitions. [Brief explanation of the drawing]

[0009] [Figure 1] Figure 1 is a block diagram showing an example of the functional configuration of a server device. [Figure 2] Figure 2 shows an example of a sparse graph. [Figure 3] Figure 3 is a schematic diagram showing an example of pathway extraction criteria. [Figure 4] Figure 4 shows an example of a pathway graph. [Figure 5] Figure 5 shows an example of a pseudo-free energy transition in a pathway. [Figure 6]FIG. 6 is a flowchart showing a procedure of graph generation processing. [Figure 7] FIG. 7 is a flowchart showing a procedure of route selection processing. [Figure 8] FIG. 8 is a diagram showing an example of a hardware configuration. MODE FOR CARRYING OUT THE INVENTION

[0010] Hereinafter, embodiments of a route selection program, a route selection method, and a route selection apparatus according to the present application will be described with reference to the accompanying drawings. Each embodiment merely illustrates one example or aspect of the present invention, and the scope of numerical values, functions, usage scenes, and the like are not limited by such illustrations. Furthermore, the respective embodiments can be appropriately combined within a range that does not cause inconsistency in processing contents. [Embodiment]

[0011] FIG. 1 is a block diagram showing an example of a functional configuration of a server apparatus 10. The server apparatus 10 shown in FIG. 1 provides a route selection function that realizes automatic construction of a target state transition route, a so-called Pathway, from an EM image captured by an electron microscope such as a cryo-electron microscope.

[0012] Hereinafter, a compound such as a protein is taken as an example of the target, but the target is not limited to the compound. For example, examples of targets other than compounds include a network having the concept of energy (for example, a social network in which a node corresponding to an account can be expressed by a flaming degree indicating the degree of concentration of criticism, etc.).

[0013] The server device 10 is an example of a computer that provides the above route selection function. Merely by way of example, by implementing the server device 10 as a PaaS (Platform as a Service) type or SaaS (Software as a Service) type application, the above route selection function can be provided as a cloud service. In addition, the server device 10 can also be implemented as a server that provides the above route selection function on-premises.

[0014] As shown in FIG. 1, the server device 10 may be communicably connected to a client terminal 30 via a network NW. For example, the network NW may be any type of communication network, regardless of whether it is wired or wireless, such as the Internet or a LAN (Local Area Network). Note that although FIG. 1 illustrates an example in which one client terminal 30 is connected to one server device 10, this does not preclude any number of client terminals 30 from being connected.

[0015] The client terminal 30 corresponds to an example of a computer that receives provision of the above route selection function. For example, the client terminal 30 may be implemented by a desktop or laptop personal computer, or the like. This is merely an example, and the client terminal 30 may be any computer such as a mobile terminal device or a wearable terminal.

[0016] Note that although FIG. 1 illustrates an example in which the above route selection function is provided in a client-server system, this is merely an example, and the above route selection function may be provided as a stand-alone system.

[0017] Next, an example of the functional configuration of the server device 10 according to this embodiment will be described. Figure 1 schematically shows the blocks related to the route selection function of the server device 10. As shown in Figure 1, the server device 10 has a communication control unit 11, a storage unit 13, and a control unit 15. Note that Figure 1 only shows an excerpt of the functional units related to the above-mentioned route selection function, and the server device 10 may also be equipped with functional units other than those shown.

[0018] The communication control unit 11 is a functional unit that controls communication with other devices such as the client terminal 30. As just one example, the communication control unit 11 can be implemented using a network interface card such as a LAN card. In one aspect, the communication control unit 11 receives EM images for pathway construction from the client terminal 30, receives requests for pathway construction, and outputs responses to such requests to the client terminal 30.

[0019] The memory unit 13 is a functional unit that stores various types of data. As an example, the memory unit 13 can be implemented using internal, external, or auxiliary storage within the server device 10. For example, the memory unit 13 stores graph information 13A. The graph information 13A will be explained in conjunction with the context in which it is registered or referenced.

[0020] The control unit 15 is a functional unit that performs overall control of the server device 10. For example, the control unit 15 can be implemented by a hardware processor. As shown in Figure 1, the control unit 15 has an acquisition unit 15A, an extraction unit 15B, a specific unit 15C, a selection unit 15D, and an output unit 15E. The control unit 15 may also be implemented by hardwired logic or the like.

[0021] The acquisition unit 15A is a processing unit that acquires the probability distribution of compound existence. As an example, the acquisition unit 15A accepts EM images captured by an electron microscope such as a cryo-electron microscope as input. The EM images accepted as input may contain particles of compounds such as proteins. The acquisition unit 15A then acquires the probability distribution of compound existence by inputting the received EM images to a machine learning model that outputs the probability distribution of compound existence using one or more EM images as input.

[0022] Such machine learning models can be implemented using neural networks, such as deep neural networks, as just one example. For instance, to train a machine learning model, EM images, to which probability distributions obtained through experiments are assigned as correct labels, are used as training data. The EM images are then used as explanatory variables in the machine learning model, and the probability distributions are used as the target variable, and the machine learning model can be trained according to any machine learning algorithm, such as deep learning. For example, the parameters of the machine learning model can be updated by backpropagating the loss between the output of the machine learning model (which takes an EM image as input) and the correct label back into the machine learning model.

[0023] The following is merely an example of how the probability distribution of a compound's existence can be modeled using a Gaussian Mixture Model (GMM), but the probability distribution of a compound's existence can also be modeled using other models besides GMM.

[0024] The extraction unit 15B is a processing unit that extracts multiple representative points from the probability distribution of compound existence. As just one example, the extraction unit 15B can extract the maximum points of the GMM obtained by the acquisition unit 15A as representative points. For example, the extraction unit 15B adjusts the number of samples of a set of points to which the GMM has a maximum value according to a mathematical definition, to match the scale of the GMM obtained by the acquisition unit 15A. Then, the extraction unit 15B samples the maximum value from the GMM obtained by the acquisition unit 15A. For such sampling, methods such as extracting centroids from K-means and using them as representative points, or estimating the GMM using Bayesian statistics criteria with a large number of components, estimating the GMM with a smaller number of components, and using the maximum points as representative points can be used.

[0025] The identification unit 15C is a processing unit that identifies a first set of multiple state transition paths between multiple representative points. Here, the "first set of multiple state transition paths" refers to graph data used for constructing the pathway. As an example, the identification unit 15C uses n representative points extracted by the extraction unit 15B as nodes and selects combinations of 2 nodes from among the n nodes. n Edges are defined to connect nodes for each C2. This results in a fully connected graph where all nodes are connected by edges.

[0026] The fully connected graph obtained in this way corresponds to an example of a first set of state transition paths, and can be stored in the storage unit 13 as graph information 13A. For example, the nodes included in the fully connected graph may be associated with and stored with pseudo-free energies converted from the probability density corresponding to the nodes on the GMM. Furthermore, the edges included in the fully connected graph may be associated with and stored with data sets of pseudo-free energies corresponding to the path length of the edge on the GMM and the set of points forming the edge.

[0027] For example, the path length of an edge and the probability density corresponding to the set of points forming the edge can be obtained by calculating the most likely path, or so-called ridgeline, between two mean vectors corresponding to the maximum value on the GMM. For such ridge calculations, a technique can be used that outputs a path obtained by selecting transitions that result in a short path length and a large mean probability along the path for each transition between two points obtained by dividing the two mean vectors on the GMM into K partitions. Alternatively, the technique described in Reference 1, which constructs the most likely path between mean vectors of a GMM with 2 classes based on the mathematical definition of the set of points that give the GMM a maximum value, can be used. Reference 1: Hennig, C.: Ridgeline plot and clusterwise stability as tools for merging Gaussian mixture components. In Classification as a Tool for Research (pp.109-116) (2010).

[0028] Furthermore, pseudo-free energy can be obtained by transforming the probability density. As just one example, one transformation formula can be used in which an inverse correlation relationship is defined in which the pseudo-free energy E(z) decreases as the probability density P(z) increases, such as equations (1) and (2) below. P(z)∝exp(-βE(z))···(1) E∝-logP···(2)

[0029] While a fully connected graph can be used for pathway construction, to reduce the computational complexity during graph traversal, a graph with edges thinned out from a fully connected graph—that is, a graph in which only the edges of high importance for pathway construction are extracted—can also be used. Such a graph is sometimes referred to as a "sparse graph" to distinguish it from a fully connected graph.

[0030] By way of example only, the specifying unit 15C can generate a minimum spanning tree-based graph as a sparse graph by extracting a portion corresponding to the minimum spanning tree that minimizes the total sum of costs of edges constituting a spanning tree from a fully connected graph. Path length, probability density, or pseudo-free energy can be used as the edge cost formulated in such a minimum spanning tree problem. For example, when using probability density or pseudo-free energy, a value obtained by normalizing pseudo-free energy can be used by dividing the cumulative value of pseudo-free energy of a point set included in an edge by the path length.

[0031] An example of an algorithm for generating such a minimum spanning tree-based graph will be given below. More specifically, the specifying unit 15C can implement generation of a minimum spanning tree-based graph through the procedures from step S1 to step S3 described below. That is, in step S1, the GMM mean vector set {μ₁, ···, μ C}, μ₁∈R d for each pair (μ i , μ j ), the ridge distance, that is, the path length of the edge, is approximately calculated, and a C×C ridge distance matrix M is defined (step S1). Next, in step S2, for {μ₁, ···, μ C} as the vertex set, a distance is defined using M for each edge on the complete undirected graph. Then, the shortest graph path distance (geodesic distance) between all vertices on the undirected graph is calculated. At this time, let G be the C×C shortest graph path distance matrix. Next, in step S3, based on i * =argmax c π c , the vertex j * at which the shortest graph path distance is maximized is searched from the matrix G, and the path i * →···→j * is output. Thereafter, remaining vertices are added using the matrix G. When such a tree (minimum spanning tree) is defined, a trained decoder is used on each directed edge to construct a 3D density.

[0032] The minimal spanning tree-based graph generated in this way is also a sparse graph obtained by processing a fully connected graph, and corresponds to an example of the first multiple state transition pathway. Figure 2 shows an example of a sparse graph. As an example, Figure 2 shows a sparse graph generated from a GMM obtained from EM images of ribosomes. As shown in Figure 2, it is clear that unnecessary edges are excluded in the sparse graph compared to the fully connected graph. Therefore, when using the sparse graph shown in Figure 2 for pathway construction, the computational cost of pathway construction can be reduced by the amount of unnecessary edges that have been excluded. Such a minimal spanning tree-based graph can also be stored in the storage unit 13 as graph information 13A.

[0033] The selection unit 15D is a processing unit that selects a second set of state transition paths from a first set of state transition paths based on the probability density of each path in the first set of state transition paths. An example of the "second set of state transition paths" here is a Pathway. In one embodiment, the selection unit 15D selects one or more Pathways from the fully connected graph or sparse graph included in the graph information 13A based on the probability density of each path in the fully connected graph or sparse graph.

[0034] The following is merely an example of how pathways are extracted from a sparse graph. More specifically, the selection unit 15D specifies the conditions for generating pathways. As merely an example, the selection unit 15D can manually accept user-defined pathway generation conditions from the client terminal 30. Such pathway generation conditions may include the number of pathway candidates to generate from the sparse graph, the specification of the start or end node of the pathway, the number of nodes forming the pathway, the number of edges, the total path length, the lower limit of the total path length, or the upper limit of the total path length. These conditions can be freely set by the user of the above-mentioned route selection function according to their task. Note that while an example of manually setting pathway generation conditions has been given here, they do not necessarily have to be set manually, and naturally, this does not preclude examples where the pathway generation conditions are system-defined.

[0035] Next, the selection unit 15D generates multiple candidate pathways according to the pathway generation conditions. For example, the selection unit 15D can generate multiple candidate pathways by performing a random walk on a sparse graph according to the pathway generation conditions.

[0036] The selection unit 15D then performs filtering to select multiple candidate pathways based on one or more combinations of the path length of each edge of the multiple candidate pathways, a data sequence of pseudonatural energy corresponding to the set of points forming the edge, and so on.

[0037] For this type of filtering, the following pathway extraction conditions can be used as just one example. For instance, since state transitions become more natural as the edge path length decreases, a condition can be set for pathway extraction such that the path length of candidate pathway edges is below a threshold.

[0038] In addition, the pathway extraction conditions may include various conditions related to pseudofree energy. Figure 3 is a schematic diagram showing an example of pathway extraction conditions. For the sake of explanation, Figure 3 shows a graph plotting the transition of pseudofree energy for a path that starts at node B and transitions through nodes C2, E1, E2, and E4 to node E5. In the graph shown in Figure 3, the horizontal axis represents the path, and the vertical axis represents the pseudofree energy.

[0039] For example, condition A can be set as a pathway extraction criterion, such as the maximum pseudo-free energy Emax of all structures on the pathway shown in Figure 3 being less than or equal to an arbitrary upper limit. Condition B can also be set as a pathway extraction criterion, such as the difference ΔE = Emax - Emin between the maximum and minimum pseudo-free energy of all structures on the pathway shown in Figure 3 being less than or equal to a threshold. Furthermore, condition C can be set as a pathway extraction criterion, such as the pseudo-free energy E0 of the initial structure shown in Figure 3 being less than or equal to a threshold. Additionally, condition D can be set as a pathway extraction criterion, such as the energy difference ΔE = E1 - E0 between the pseudo-free energy E0 of the initial structure shown in Figure 3 and the highest energy E1 during the transition to the pseudo-free energy of the next structure being less than or equal to a threshold. These conditions A to D may be system-defined or user-defined.

[0040] Under these pathway extraction conditions, the selection unit 15D extracts one or more pathway candidates from among multiple pathway candidates that satisfy the above pathway extraction conditions. At this time, the selection unit 15D can also calculate a score for each pathway candidate. For example, it can calculate a score that increases as the difference ΔE between the maximum and minimum values ​​of the pseudo-free energy of all structures on the pathway increases, or as the pseudo-free energy E0 of the initial structure increases, or as the energy difference ΔE between the pseudo-free energy E0 of the initial structure and the highest energy E1 during the transition to the pseudo-free energy of the next structure increases. The condition for pathway extraction may also be that such a score is above a threshold.

[0041] The output unit 15E is a processing unit that outputs information about pathways. As an example, the output unit 15E outputs information about pathways extracted by the selection unit 15D to the client terminal 30. In this case, the output unit 15E can prioritize outputting information about pathways with high scores among the pathways extracted by the selection unit 15D. For example, it can display information about the pathway with the highest score, or information about pathways that fall within a specific top score range.

[0042] Here, the output unit 15E can display, as an example of information about the Pathway, a graph of the Pathway, transitions of pseudo-free energy corresponding to the state transitions of the Pathway, or deformation videos of compounds corresponding to the state transitions on the paths included in the Pathway. In this example, the client terminal 30 is used as the output destination for information about the Pathway, but it is not limited to this, and the transitions of pseudo-free energy of the Pathway can also be input to a simulator that performs molecular dynamics simulations.

[0043] Figure 4 shows an example of a pathway graph. In Figure 4, some of the pathways extracted by the selection unit 15D are plotted on a sparse graph generated from a GMM obtained from EM images of ribosomes. Furthermore, in Figure 4, node symbols are rendered in increasing size as the pseudo-free energy decreases among the nodes included in the sparse graph. This type of pathway graph allows us to understand that pathways transitioning in the order of node B to node C2, node C3, node C1, node E2, node E4, and node E5 are likely to occur, thus providing information that contributes to understanding the reaction processes of compounds such as proteins.

[0044] Figure 5 shows an example of pseudo-free energy transitions in a pathway. In the graph shown in Figure 5, the vertical axis represents the path, and the vertical axis represents the pseudo-free energy. In Figure 5, a data sequence of pseudo-free energy corresponding to the set of points forming each edge included in the pathway shown in Figure 4 is plotted, rendering a waveform corresponding to the pseudo-free energy transition. Such a display of pseudo-free energy transitions in a pathway can provide information that contributes to understanding the reaction processes of compounds such as proteins.

[0045] In the explanation so far, we have used an example in which pathways are extracted and output using pseudo-free energy. However, probability density, or the abundance ratio obtained from probability density, may also be used for such pathway extraction and output. In this case, after extracting pathways using probability density, the probability densities of the nodes included in the pathway may be converted to pseudo-free energy and the transition of the pseudo-free energy of the pathway may be displayed. Alternatively, pathways may be extracted using probability density and the transition of the probability density of the extracted pathway may be displayed.

[0046] Figure 6 is a flowchart showing the procedure for graph generation. As shown in Figure 6, the acquisition unit 15A receives input of an EM image captured by an electron microscope such as a cryo-electron microscope (step S101). Here, the EM image received in step S101 may contain particles of compounds such as proteins.

[0047] Next, the acquisition unit 15A acquires the probability distribution P(z) of the compound by inputting the EM image received in step S101 to a machine learning model that outputs the probability distribution of the compound's existence using the EM image as input (step S102).

[0048] Then, the extraction unit 15B extracts several representative points, such as the maximum points of the GMM, from the probability distribution P(z) of the compound obtained in step S102 (step S103).

[0049] Then, the specific unit 15C uses the n representative points extracted in step S103 as nodes and selects two nodes from among the n nodes to determine combinations. n By setting edges to connect nodes for each C2, a fully connected graph is generated (step S104), and the process ends.

[0050] The fully connected graph obtained in this way is stored in the storage unit 13 as graph information 13A. Although not explained in the flowchart shown in Figure 6, as described above, a minimum spanning tree-based graph can be generated as a sparse graph from the fully connected graph.

[0051] Figure 7 is a flowchart showing the procedure for route selection processing. As shown in Figure 7, the selection unit 15D specifies the conditions for generating the Pathway (step S301). As just one example, the selection unit 15D can manually accept user-defined conditions for generating the Pathway from the client terminal 30.

[0052] Next, the selection unit 15D generates multiple candidate pathways by performing a random walk on the sparse graph contained in the graph information 13A, according to the pathway generation conditions specified in step S301 (step S302).

[0053] Then, the selection unit 15D extracts one or more candidate pathways from among the multiple pathway candidates generated in step S302 that satisfy the extraction conditions based on the probability density of edges (step S303).

[0054] Subsequently, the output unit 15E outputs information about the Pathway extracted by the selection unit 15D to the client terminal 30 (step S304). At this time, the output unit 15E can prioritize outputting information about the Pathway with the highest score among the Pathways extracted in step S303. The information about the Pathway output here may include a graph of the Pathway, the transition of pseudo-free energy corresponding to the state transition of the Pathway, or a video of the deformation of the compound corresponding to the state transition on the path included in the Pathway.

[0055] As described above, the path selection function in this embodiment extracts candidate pathways from among multiple pathway candidates generated using a graph that includes representative points of the compound's probability distribution, selecting pathways whose edge probability density satisfies specific conditions. Therefore, the path selection function in this embodiment enables the automation of pathway construction. This also reduces the need for manual operations by experts. [Examples]

[0056] Now, while embodiments of the disclosed apparatus have been described, the present invention may be implemented in various other forms besides those described above. Therefore, other embodiments included in the present invention will be described below.

[0057] The processing procedures, control procedures, specific names, and various data and parameters shown in the documents and drawings of the above-described embodiment 1 may be changed at will unless otherwise specified.

[0058] Furthermore, the specific forms of distribution and integration of the components of each device are not limited to those shown in the diagram. In other words, all or part of the components may be functionally or physically distributed and integrated in any unit depending on various loads and usage conditions. Moreover, all or any part of the processing functions of each device may be implemented by a CPU and the program that is analyzed and executed by the CPU, or by hardware using wired logic.

[0059] The various processes described in Example 1 above can be implemented by executing a pre-prepared program on a computer such as a personal computer or workstation. Therefore, below, an example of a computer that executes a route selection program having the same functions as in Example 1 and Example 2 will be described using Figure 8.

[0060] Figure 8 shows an example of a hardware configuration. As shown in Figure 8, the computer 100 has an operating unit 110a, a speaker 110b, a camera 110c, a display 120, and a communication unit 130. Furthermore, the computer 100 has a CPU 150, a ROM 160, an HDD 170, and RAM 180. These parts 110 to 180 are connected via a bus 140.

[0061] As shown in Figure 8, HDD170 stores a route selection program 170a that performs the same functions as the acquisition unit 15A, extraction unit 15B, identification unit 15C, selection unit 15D, and output unit 15E shown in Embodiment 1 above. This route selection program 170a may be integrated or separated, similar to the components of the acquisition unit 15A, extraction unit 15B, identification unit 15C, selection unit 15D, and output unit 15E shown in Figure 1. In other words, HDD170 does not necessarily have to store all the data shown in Embodiment 1 above; it is sufficient that the data used for processing is stored in HDD170.

[0062] Under these conditions, the CPU 150 reads the route selection program 170a from the HDD 170 and then loads it into the RAM 180. As a result, the route selection program 170a functions as a route selection process 180a, as shown in Figure 8. This route selection process 180a loads various data read from the HDD 170 into the memory area of ​​the RAM 180 allocated to the route selection process 180a, and then executes various processes using the loaded data. For example, the processes that the route selection process 180a executes may include those shown in Figures 6 and 7. It should be noted that the CPU 150 does not necessarily need to operate all of the processing units shown in the above embodiment 1; it is sufficient if the processing units corresponding to the processes to be executed are virtually implemented.

[0063] The route selection program 170a described above does not necessarily have to be stored in the HDD 170 or ROM 160 from the beginning. For example, the route selection program 170a could be stored on a "portable physical medium" such as a flexible disk, CD-ROM, DVD disk, magneto-optical disk, or IC card inserted into the computer 100. The computer 100 could then retrieve and execute the route selection program 170a from these portable physical media. Alternatively, the route selection program 170a could be stored on another computer or server device connected to the computer 100 via a public network, the internet, LAN, WAN, etc. The computer 100 could then download and execute the route selection program 170a stored in this manner.

[0064] With respect to embodiments including the above examples, the following additional information is disclosed.

[0065] (Note 1) Multiple representative points are extracted from the probability distribution of the state in question. Identify a first set of state transition paths between the aforementioned set of representative points, From the first set of state transition paths, a second set of state transition paths is selected based on the probability density of each of the first set of state transition paths. A route selection program characterized by having a computer perform the processing.

[0066] (Note 2) The extraction process includes extracting the maximum points of the Gaussian mixture distribution corresponding to the probability distribution of existence of the target state as representative points. The route selection program described in Appendix 1, characterized by the features described herein.

[0067] (Note 3) The process of identifying the above includes a process of identifying a fully connected graph that includes nodes corresponding to each of the above-mentioned representative points and includes edges connecting all nodes as the first set of state transition paths. The route selection program described in Appendix 1, characterized by the features described herein.

[0068] (Note 4) The process of identifying the above includes a process of identifying the portion of the fully connected graph that corresponds to the minimum spanning tree, which includes nodes corresponding to each of the multiple representative points and edges connecting all nodes, as the first multiple state transition paths. The route selection program described in Appendix 1, characterized by the features described herein.

[0069] (Note 5) The selection process includes a process of selecting the second set of state transition paths based on the difference between the maximum and minimum probability densities along each of the first set of state transition paths. The route selection program described in Appendix 1, characterized by the features described herein.

[0070] (Note 6) The selection process includes a process of selecting the second set of state transition paths based on the probability density of the first state among the states included in each of the first set of state transition paths. The route selection program described in Appendix 1, characterized by the features described herein.

[0071] (Note 7) The selection process includes a process of selecting the second set of state transition paths based on the difference between the probability density of the first state and the probability density of the second state among the states included in each of the first set of state transition paths. The route selection program described in Appendix 1, characterized by the features described herein.

[0072] (Note 8) Extract multiple representative points from the probability distribution of the state in question, Identify a first set of state transition paths between the aforementioned set of representative points, From the first set of state transition paths, a second set of state transition paths is selected based on the probability density of each of the first set of state transition paths. A route selection method characterized by having a computer perform the processing.

[0073] (Note 9) The extraction process includes extracting the maximum points of the Gaussian mixture distribution corresponding to the probability distribution of existence of the target state as representative points. The route selection method described in Appendix 8, characterized by the features described herein.

[0074] (Note 10) The process of identifying the above includes a process of identifying a fully connected graph that includes nodes corresponding to each of the above-mentioned multiple representative points and includes edges connecting all nodes as the first multiple state transition paths. The route selection method described in Appendix 8, characterized by the features described herein.

[0075] (Note 11) The process of identifying the above includes a process of identifying the portion of the fully connected graph that corresponds to the minimum spanning tree, which includes nodes corresponding to each of the multiple representative points and edges connecting all nodes, as the first multiple state transition paths. The route selection method described in Appendix 8, characterized by the features described herein.

[0076] (Note 12) The selection process includes a process of selecting the second set of state transition paths based on the difference between the maximum and minimum probability densities along each of the first set of state transition paths. The route selection method described in Appendix 8, characterized by the features described herein.

[0077] (Note 13) The selection process includes a process of selecting the second set of state transition paths based on the probability density of the first state among the states included in each of the first set of state transition paths. The route selection method described in Appendix 8, characterized by the features described herein.

[0078] (Note 14) The selection process includes a process of selecting the second set of state transition paths based on the difference between the probability density of the first state and the probability density of the second state among the states included in each of the first set of state transition paths. The route selection method described in Appendix 8, characterized by the features described herein.

[0079] (Note 15) Extract multiple representative points from the probability distribution of the state of the target, Identify a first set of state transition paths between the aforementioned set of representative points, From the first set of state transition paths, a second set of state transition paths is selected based on the probability density of each of the first set of state transition paths. A route selection device including a control unit that performs processing.

[0080] (Note 16) The extraction process includes extracting the maximum points of the Gaussian mixture distribution corresponding to the probability distribution of existence of the target state as representative points. The route selection device described in Appendix 15, characterized in that it is a route selection device.

[0081] (Note 17) The process of identifying the above includes a process of identifying a fully connected graph that includes nodes corresponding to each of the above-mentioned multiple representative points and includes edges connecting all nodes as the first multiple state transition paths. The route selection device described in Appendix 15, characterized in that it is a route selection device.

[0082] (Note 18) The process of identifying the above includes a process of identifying the portion of the fully connected graph that corresponds to the minimum spanning tree, which includes nodes corresponding to each of the multiple representative points and edges connecting all nodes, as the first multiple state transition paths. The route selection device described in Appendix 15, characterized in that it is a route selection device.

[0083] (Note 19) The selection process includes a process of selecting the second set of state transition paths based on the difference between the maximum and minimum probability densities along each of the first set of state transition paths. The route selection device described in Appendix 15, characterized in that it is a route selection device.

[0084] (Note 20) The selection process includes a process of selecting the second set of state transition paths based on the probability density of the first state among the states included in each of the first set of state transition paths. The route selection device described in Appendix 15, characterized in that it is a route selection device. [Explanation of Symbols]

[0085] 10 Server devices 11. Communication Control Unit 13 Storage section 13A Graph Information 15 Control Unit 15A Acquisition Department 15B Extraction part 15C Specific part 15D Selection Section 15E Output Section 30 client terminals

Claims

1. Extract multiple representative points from the probability distribution of the target state, Identify a first set of state transition paths between the aforementioned set of representative points, From the first set of state transition paths, a second set of state transition paths is selected based on the probability density of each of the first set of state transition paths. A route selection program characterized by having a computer perform the processing.

2. The extraction process includes extracting the maximum points of a Gaussian mixture distribution corresponding to the probability distribution of existence of the target state as representative points. The route selection program according to feature 1.

3. The process of identifying the above includes a process of identifying a fully connected graph, which includes nodes corresponding to each of the plurality of representative points and includes edges connecting all nodes, as the first plurality of state transition paths. The route selection program according to feature 1.

4. The process of identifying the above includes a process of identifying the portion of the fully connected graph that corresponds to the minimum spanning tree, which includes nodes corresponding to each of the multiple representative points and edges connecting all nodes, as the first multiple state transition paths. The route selection program according to feature 1.

5. The selection process includes a process of selecting the second set of state transition paths based on the difference between the maximum and minimum probability densities along each of the first set of state transition paths. The route selection program according to feature 1.

6. The selection process includes a process of selecting the second set of state transition paths based on the probability density of the first state among the states included in each of the first set of state transition paths. The route selection program according to feature 1.

7. The selection process includes selecting the second set of state transition paths based on the difference between the probability density of the first state and the probability density of the second state among the states included in each of the first set of state transition paths. The route selection program according to feature 1.

8. Extract multiple representative points from the probability distribution of the target state, Identify a first set of state transition paths between the aforementioned set of representative points, From the first set of state transition paths, a second set of state transition paths is selected based on the probability density of each of the first set of state transition paths. A route selection method characterized by having a computer perform the processing.

9. Extract multiple representative points from the probability distribution of the target state, Identify a first set of state transition paths between the aforementioned set of representative points, From the first set of state transition paths, a second set of state transition paths is selected based on the probability density of each of the first set of state transition paths. A route selection device including a control unit that performs processing.

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