Information processing device, information processing method, and program

Abstract

The invention provides an information processing device, an information processing method, and a program that contribute to visualization of analysis results. According to one embodiment, a processing server is provided with: an embedding unit for embedding data of position information of one or more entities into a Poincare disk; and a drawing unit for drawing the data of the position information embedded in the Poincare disk as the trajectory of the one or more entities by using the data of the time information corresponding to the position information of the one or more entities.

Description

Information processing device, information processing method and program Technical Field

[0001] This invention relates to an information processing device, an information processing method, and a program. Background Technology

[0002] Various methods for analyzing processes are being researched. For example, Patent Document 1 discloses a method for performing process mining on a multi-instance process comprising one or more multi-instance sub-processes. In this method, the event log of the multi-instance process is divided into a main log and one or more sub-logs. For each of the main log and the one or more sub-logs, a flowchart is generated. The generated flowchart is then combined with the combined flowchart.

[0003] Patent Document 1: Japanese Patent Application Publication No. 2023-553220 Summary of the Invention

[0004] In the method described in Patent Document 1, when analyzing multiple objects simultaneously, it may be difficult to visualize the analysis results in a way that is perceptible to the user.

[0005] This invention addresses this problem by providing an information processing device, method, and program that facilitates the visualization of analysis results.

[0006] An exemplary embodiment of the present invention relates to an information processing apparatus comprising: an embedding unit for embedding position information data of one or more entities into a Poincaré disk; and a drawing unit for drawing the position information data embedded in the Poincaré disk as the trajectory of one or more entities by using time information data corresponding to the position information of the one or more entities.

[0007] An exemplary embodiment of the present invention relates to an information processing method in which a computer performs the following processing: embedding location information data of one or more entities into a Poincaré disk; and using time information data corresponding to the location information of one or more entities, depicting the location information data embedded in the Poincaré disk as the trajectory of one or more entities.

[0008] An exemplary embodiment of the present invention relates to a program that causes a computer to perform the following processing: embedding data of position information of one or more entities into a Poincaré disk; and depicting the data of position information embedded in the Poincaré disk as the trajectory of one or more entities by using data of time information corresponding to the position information of the one or more entities.

[0009] Invention Effects

[0010] This invention provides an information processing device, method, and program that facilitates the visualization of analysis results. Attached Figure Description

[0011] Figure 1 is a block diagram showing a structural example of the analysis system according to Embodiment 1.

[0012] Figure 2 is a diagram representing the event log in three-dimensional spacetime.

[0013] Figure 3 is a top view of the spatiotemporal region in Figure 2.

[0014] Figure 4 is a diagram showing the event log inside the Poincaré disk.

[0015] Figure 5 is a compact example of event nodes.

[0016] Figure 6 is a block diagram illustrating an example of the hardware structure of the information processing device according to the present invention. Detailed Implementation

[0017] Implementation Method 1

[0018] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. For clarity, the following description and drawings have been appropriately omitted and simplified. The accompanying drawings are merely illustrative of one or more embodiments. For the purpose of illustrating exemplary embodiments, not all features or processes shown in any of the figures are necessarily required, and some features or processes may be omitted.

[0019] [Structure Description]

[0020] Figure 1 is a block diagram showing an example of the structure of the analysis system. The analysis system S includes a database (DB) 100 and a processing server 200. The DB 100 stores logs (hereinafter also referred to as event logs) indicating the location and time of events that occur, and map information indicating the location. An event represents the movement of any object in space over time. The processing server 200 selects a specified event log from the DB 100 and displays the event based on the selected event log. The events that are the objects of analysis are events within any spatial area (e.g., within a factory). The processing server 200 has a log selection unit 201, an event processing unit 202, an embedding unit 203, a rendering unit 204, an output unit 205, and a resolution specification unit 206. The processing of each unit will be described below.

[0021] The log selection unit 201 specifies the spatial region of the events to be selected by referring to the map information of DB100. Furthermore, the log selection unit 201 specifies the time region of the events to be selected. The log selection unit 201 can automatically specify the spatial and time regions, or it can be done according to user instructions. The log selection unit 201 selects event log data existing in the specified spatial and time regions by referring to DB100. In the following example, a two-dimensional region (x, y) is assumed to be the spatial region. However, the assumed spatial region is not limited to two dimensions; for example, it can also be a three-dimensional region (x, y, z). Furthermore, the log selection unit 201 can limit the event logs to be selected by limiting the types of entities of the selected events. Entities are objects that are the main body of the event, such as humans, moving objects, props, parts, etc. The number of entities that are the objects of analysis is arbitrary. In the following example, multiple entities are used as the objects of analysis, but a single entity can also be used. Furthermore, the log selection unit 201 can perform annotation processing on information (e.g., entity information) from one or more event logs that are the objects of analysis, enabling users to perform searches.

[0022] The event processing unit 202 stores the event log data selected by the log selection unit 201 in a three-dimensional spacetime. In other words, the event log data is represented in a three-dimensional spacetime. The three-dimensional spacetime is represented by two-dimensional space as Euclidean space and one-dimensional time. Furthermore, when the spatial region of the event log is a three-dimensional region, the event processing unit 202 stores the selected event log data in a four-dimensional spacetime. The four-dimensional spacetime is represented by three-dimensional space and one-dimensional time. The processing of the processing server 200 in three-dimensional spacetime will be described below, but the processing server 200 can also perform the same processing in other dimensions of spacetime, such as four-dimensional spacetime.

[0023] Figure 2 illustrates the event log in three-dimensional spacetime. Locations in the three-dimensional spacetime are represented by two-dimensional space and time. The spatial region SR represents the spatial region specified by the log selection unit 201. Furthermore, the log selection unit 201 specifies the region from time t1 to t2 (t2 > t1) as the time region. In Figure 2, the spatial region SR within the region from time t1 to t2 in the three-dimensional spacetime is represented as the spacetime region DR. The log selection unit 201 selects data from the event log shown in Figure 2 by referring to DB100.

[0024] Furthermore, Figure 3 is a top view of the spatiotemporal region DR in Figure 2. Figure 3 is a diagram used to more clearly show the event log existing within the spatiotemporal region DR. The event log will be explained below with reference to Figures 2 and 3.

[0025] In Figures 2 and 3, the entities selected by the log selection unit 201 for the event logs are shown as character H1, character H2, moving body M1, and item T1. In this example, moving body M1 is an Automatic Guided Vehicle (AGV), but it is not limited to this. Figure 2 shows the movement trajectory of each entity as part of the event logs.

[0026] In Figures 2 and 3, character H1 enters spacetime region DR at position P1 and leaves at position P2. The time at position P2 is after the time at position P1. Character H2 enters spacetime region DR at position P3 and leaves at position P4. The time at position P3 is after the time at position P4. Moving body M1 enters spacetime region DR at position P5 and leaves at position P6. The time at position P5 is after the time at position P6. Furthermore, within spacetime region DR, the trajectory of character H2 intersects with the trajectory 1 of moving body M1 at position P11, and the trajectory of character H1 intersects with the trajectory of moving body M1 at position P12. In other words, character H2 and moving body M1 overlap at position P11, and character H2 and moving body M1 overlap at position P12. The time at position P12 is after the time at position P11.

[0027] Furthermore, Figures 2 and 3 also illustrate the following scenario: Character H2 transports item T1 from position P3 to position P11, and then hands item T1 to mobile entity M1 at position P11. Mobile entity M1 transports item T1 from position P11 to position P12. Character H1 receives item T1 from mobile entity M1 at position P12 and transports it to position P2.

[0028] The event processing unit 202, by storing the event log data in a three-dimensional spatiotemporal space, can clearly define the relationships between the entities shown above. These relationships represent, for example, where entities overlap or where multiple entities travel in the same direction. However, the spatiotemporal region DR is an area that extends both spatially and temporally. As the spatiotemporal region DR expands, the effort required to trace the trajectories of each entity within it increases. Furthermore, when multiple entities exist within the spatiotemporal region DR, the effort required to trace their trajectories increases further. Therefore, it is conceivable that users will require considerable time to analyze the event log data. To mitigate this situation, the processing server 200 performs the following processing.

[0029] Returning to Figure 1, the explanation continues. The embedding unit 203 embeds all or a portion (one or more) of the event log location information data from the event log data stored by the event processing unit 202 into the Poincaré disk. Embedding the event log location information data into the Poincaré disk means mapping the event log location information data onto the Poincaré disk. The Poincaré disk is represented as used in non-Euclidean geometry in mathematics. Hyperbolic metric is used in the Poincaré disk. The mapped location information data of each event log represents the movement trajectory of each entity within the Poincaré disk. Alternatively, the embedding unit 203 can automatically select event logs from the event logs stored by the event processing unit 202 to be embedded into the Poincaré disk. Alternatively, the embedding unit 203 can select event logs from the event logs stored by the event processing unit 202 to be embedded into the Poincaré disk according to user instructions.

[0030] The depiction unit 204 depicts the position information data of one or more entities embedded in the Poincaré disk as the trajectory of one or more entities. Specifically, the depiction unit 204 depicts the trajectory of an entity by using time information data corresponding to the position information of one or more entities embedded in the Poincaré disk. Furthermore, in this example, one entity is used as the depiction object, but multiple entities can also be used as the depiction object.

[0031] Figure 4 shows the event log of prop T1 within the Poincaré disk. The arcs in the Poincaré disk PD represent geodesics. The spatial region PR is the spatial region SR shown in the three-dimensional spacetime of Figure 2, displayed within the Poincaré disk PD. Furthermore, positions P1 to P4, as well as positions P11 and P12, as shown in Figure 2, are shown within the Poincaré disk PD.

[0032] The embedding unit 203 embeds the location information of the event log of prop T1 from the event log data shown in Figures 2 and 3 into the Poincaré disk PD. As a result, the data with embedded location information, as shown in Figure 4, shows that prop T1 is connected by the line (hereinafter also referred to as line LT) connecting positions P3, P11, P12 and P2.

[0033] In the stage where the embedding unit 203 embeds the position information data of the event log of prop T1 into the Poincaré disk PD, it is not yet clear in which direction prop T1 moves over time within the Poincaré disk PD. Therefore, the depiction unit 204 determines the direction in which prop T1 moves over time on line LT by using the time information data of the event log of prop T1. The determined direction of movement is indicated by an arrow in FIG4. As described above, the position information data of prop T1 is depicted in FIG4 as a trajectory shown by the line LT with an arrow.

[0034] The output unit 205 outputs the trajectory of one or more entities depicted by the drawing unit 204 to a display unit such as a monitor or touch panel. Furthermore, the output unit 205 can also directly output position information within the Poincaré disk PD to the display unit. Position information includes, for example, information indicating the positions of spatial regions PR, positions P1 to P6, and positions P11 and P12 within the Poincaré disk PD. By outputting this information through the output unit 205, the user can visually observe the trajectory of the prop T1 shown in FIG4 through the display unit. In the display unit, positions P3, P11, P12, and P2 on the trajectory are displayed as event nodes where events occur. Furthermore, the edges connecting each position represent the movement path of the entity.

[0035] The resolution specifying unit 206 determines information (hereinafter also referred to as characteristic information) representing the characteristics of each event log by analyzing the event logs of one or more entities depicted by the depiction unit 204. The characteristic information includes, but is not limited to, at least one of the following: the frequency of event log generation (i.e., the number of occurrences), information related to the movement path of the entity within the Poincaré disk PD (e.g., the amount of movement), and the amount of items carried by the entity. The amount of items includes, for example, at least one of the following: the number of items and the weight of the items. The resolution specifying unit 206 outputs the trajectory of one or more entities depicted by the depiction unit 204 corresponding to the event logs, along with the characteristic information of the event logs, from the output unit 205.

[0036] Furthermore, the resolution specifying unit 206 can aggregate at least one of the entity trajectories output by the output unit 205 based on at least one of the trajectory of each entity or the characteristic information of the event log of each depicted entity. Figure 5 shows an example of the aggregated entity trajectory. Figure 5 shows the trajectory corresponding to the event logs of entities M11, M12, and M13 within the Poincaré disk. Entities M11 to M13 represent moving bodies. Moving body M11 travels from position P21 to position P25 via position P22. Moving body M12 travels from position P21 to position P25 via position P23. Moving body M13 travels from position P21 to position P25 via position P24. Here, the trajectory of moving body M11 is recorded as K11, the trajectory of moving body M12 is recorded as K12, and the trajectory of moving body M13 is recorded as K13. Positions P21 to P25 are event nodes on the trajectory.

[0037] The resolution specifying unit 206 can choose to directly output the trajectories of each entity shown in FIG. 5 to the output unit 205, or to output them to the output unit 205 after aggregation. The resolution specifying unit 206 can perform any of the following processes.

[0038] (1) For example, the resolution specifying unit 206 compares the generation frequency of each trajectory K11, K12, and K13 with a predetermined threshold by referring to the characteristic information of each event log. In this case, it is assumed that the generation frequency of trajectory K11 is less than the predetermined threshold, and the generation frequencies of trajectories K12 and K13 are above the predetermined threshold. In this case, the resolution specifying unit 206 determines that the importance of trajectory K11 is lower than that of other trajectories, and trajectory K11 can be aggregated into any other trajectory. The resolution specifying unit 206 compares the proximity of trajectory K11 to trajectory K12 and the proximity of trajectory K11 to trajectory K13, and determines which of trajectory K12 or K13 is closer to trajectory K11. In this example, trajectory K12 is closer to trajectory K11 than trajectory K13. Therefore, the resolution specifying unit 206 is set to output from the output unit 205 in the form of trajectory K11 aggregated into trajectory K12. When trajectory K11 is reduced to trajectory K12, the user can visually recognize trajectories K12 and K13 in Figure 5 on the display unit, but cannot visually recognize trajectory K11. As another example, trajectory K11 can be displayed on the display unit in a less conspicuous form compared to trajectories K12 and K13 (e.g., as a dashed line or a light color). Position P22 can also be displayed on the display unit in a less conspicuous form compared to other positions.

[0039] (2) The resolution designation unit 206 refers to the characteristic information of each event log and compares the ratio of the generation frequency of each trajectory K11, K12, and K13 to the generation frequency of the entire trajectory within the Poincaré disk with a predetermined threshold. In this example, it is assumed that the ratio of the generation frequency of trajectory K11 is less than the predetermined threshold, while the ratios of the generation frequencies of trajectories K12 and K13 are greater than the predetermined threshold. In this case, the resolution designation unit 206 also determines that the importance of trajectory K11 is lower than that of other trajectories, and trajectory K11 can be aggregated into any other trajectory. After the determination, the processing performed by the resolution designation unit 206 is the same as that shown in (1).

[0040] (3) The resolution designation unit 206 refers to the characteristic information of each event log and compares the quantity of items carried by the entities involved in each event log with a predetermined threshold. As mentioned above, the quantity of items can be the number of items or the weight of the items. In this example, it is assumed that the quantity of items carried by the mobile body M11 is less than the predetermined threshold, while the quantity of items carried by the mobile bodies M12 and M13 is greater than or equal to the predetermined threshold. In this case, the resolution designation unit 206 also determines that the importance of trajectory K11 is lower than that of other trajectories, and trajectory K11 can be reduced to any other trajectory. After the determination, the processing performed by the resolution designation unit 206 is the same as the processing shown in (1).

[0041] (4) The resolution specifying unit 206 can compare the proximity of trajectory K11 and trajectory K12 with a predetermined reference related to proximity. Furthermore, the resolution specifying unit 206 can compare the proximity of trajectory K11 and trajectory K13 with a predetermined reference related to proximity. In this example, the resolution specifying unit 206 determines that the proximity of trajectory K11 and trajectory K12 is closer than the predetermined reference, and the proximity of trajectory K11 and trajectory K13 is closer than the predetermined reference. At this time, the resolution specifying unit 206 can be set to output from the output unit 205 in the form of trajectory K11 compressed into trajectory K12. Alternatively, the resolution specifying unit 206 can further perform the comparison processing related to the generation frequency shown in (1) or (2). If the generation frequency of trajectory K11 is less than a predetermined threshold or the ratio of the generation frequency of trajectory K11 is less than a predetermined threshold, the resolution specifying unit 206 can be set to output from the output unit 205 in the form of trajectory K11 compressed into trajectory K12. As another example, the resolution designation unit 206 can refer to the characteristic information of each event log to further compare the amount of items carried by the entities involved in each event log with a predetermined threshold. If the amount of items carried by the mobile body M11 is less than the predetermined threshold, and the amount of items carried by the mobile body M12 is greater than or equal to the predetermined threshold, the resolution designation unit 206 can be set to output from the output unit 205 in the form of trajectory K11 being reduced to trajectory K12.

[0042] As shown above, the resolution specifying unit 206 functions as a consolidation unit capable of changing the granularity of the displayed traces related to the event log. In the case of consolidation, the resolution specifying unit 206 controls the output unit 205 to perform display, thereby consolidating information related to low-importance event logs into information related to high-importance event logs.

[0043] Additionally, the resolution specification unit 206 can switch the display on the display unit between the state where the event log has been aggregated and the state where it has not been aggregated, based on the user's operation on the processing server 200. For three or more tracks of an entity, they can also be aggregated into one track using the same method as in the examples shown in (1) to (4). The specified thresholds or benchmarks used in the determinations in (1) to (4) can be changed by the user.

[0044] Furthermore, after performing convergence, the resolution specifying unit 206 can display at least one of the convergence count of the trajectory in the entire Poincaré disk or the convergence count of the trajectory of each event node after convergence on the display unit. For example, the user inputs specific information about the event nodes or edges to be displayed on the display unit into the processing server 200. Then, the resolution specifying unit 206 displays the determined convergence count of the event nodes or edges on the display unit.

[0045] [Explanation of Effects]

[0046] In the processing server 200 of the present invention, the embedding unit 203 embeds location information data of one or more entities into a Poincaré disk. The depiction unit 204 depicts the location information data embedded in the Poincaré disk as the trajectory of one or more entities using time information data corresponding to the location information of the one or more entities. By depicting the trajectory, the user can track and understand events related to the entities. The user can visually recognize and understand event-related information such as the trajectory and characteristic information of each entity. For example, in manufacturing operations, distribution, etc., the user can analyze and determine which entity transported which part to which place at what time. Thus, the processing server 200 can facilitate the visualization of entity-related analysis results.

[0047] Furthermore, users can perform searches by inputting information from one or more event logs that are the objects of analysis into the processing server 200. The output unit 205 can display the trajectory and characteristic information of entities related to the input event logs on the display unit. Therefore, the processing server 200 can more clearly define the interaction between the processes of multiple events. The interaction between the processes of events may be, for example, the intersection of the trajectories of entities or their proximity above a predetermined benchmark. By using statistical methods such as time series analysis and Granger causality analysis, users can perform detailed analysis of the relationships between multiple events extracted through the search.

[0048] Furthermore, the embedding unit 203 embeds the spatial region of the analysis object in Euclidean space into the Poincaré disk, and the depiction unit 204 can depict the trajectory of one or more entities within this spatial region embedded in the Poincaré disk. Compared to the usual case of storing the spatial region of the analysis object in three-dimensional spatiotemporal space, the processing server 200 can reduce the size of the spatial region that the user considers the analysis object. Therefore, the user can easily visually identify the trajectory of the entity. This effect is particularly pronounced when there are multiple entities and the event logs interact with each other in a complex manner. It also reduces the need for the user to zoom in or out on the display scale of the entity's trajectory. Moreover, when the user searches for information from one or more event logs that are the analysis object, the processing server 200 can zoom out on the search object more quickly. Therefore, the user can effectively analyze events.

[0049] Furthermore, the resolution specifying unit 206 can combine two or more trajectories of multiple entities into one trajectory based on at least one of the trajectories of multiple entities or characteristic information related to multiple entities. For example, the processing server 200 can combine information related to complex event logs into simpler information related to high-importance event logs. Therefore, users can easily identify high-importance event logs. Moreover, by performing the combination, the number of event logs that become the object of computation in the processing server 200 is reduced. Therefore, the processing server 200 can reduce processing costs such as computing resources and time. That is, the processing server 200 can improve scalability. Users can perform detailed analysis of events by visually recognizing specific information about the number of combinations.

[0050] Furthermore, by specifying the spatial area of ​​events to be selected through the log selection unit 201, users can easily grasp information related to the events being analyzed. Moreover, by limiting the logs of selected events to specific event logs or enabling users to perform searches through the log selection unit 201, users can further easily grasp information related to the events.

[0051] The structure of the processing server 200 is not limited to the hardware structure shown above. The processing of the processing server 200 can also be achieved by having a computer processor execute computer programs.

[0052] Figure 6 is a block diagram illustrating an example of the hardware structure of an information processing apparatus (in other words, a computer) that performs the processing of the processing server 200. Referring to Figure 6, the information processing apparatus 90 includes a signal processing circuit 91, a processor 92, and a memory 93.

[0053] The signal processing circuit 91 is a circuit that processes signals according to the control of the processor 92. Additionally, the signal processing circuit 91 may include communication circuitry for transmitting or receiving signals from other devices.

[0054] Processor 92 is connected to memory 93 and performs the processing of the system described in the above embodiments by reading from memory 93 and executing computer programs. Processor 92 has one or more processors. As an example of processor 92, a central processing unit (CPU), a microprocessor (MPU), a field-programmable gate array (FPGA), a digital signal processor (DSP), or an application-specific integrated circuit (ASIC) can be used.

[0055] The memory 93 is composed of volatile memory, non-volatile memory, or a combination of volatile and non-volatile memory. The memory 93 is not limited to one unit; multiple units may be provided. Furthermore, the volatile memory may be, for example, dynamic random access memory (DRAM), static random access memory (SRAM), or other random access memory (RAM). The non-volatile memory may be, for example, programmable random only memory (PROM), erasable programmable read only memory (EPROM), other read only memory (ROM), flash memory, or a solid state drive (SSD).

[0056] The memory 93 is used to store one or more commands. Here, one or more commands are stored as a program in the memory 93. The processor 92 can perform the processing described in the above embodiment by reading from the memory 93 and executing the stored program. The memory 93 can be located either externally or internally to the processor 92.

[0057] As explained above, each system or device in the above embodiments has one or more processors that execute one or more programs comprising command groups. A command group is a set of commands used to cause a computer to perform the algorithms described in the accompanying drawings. By executing the program, the information processing described in the embodiments can be realized.

[0058] When a program is read into a computer, it includes a set of commands or software code for causing the computer to perform one or more functions described in the embodiments. The program may be stored in a non-transitory computer-readable medium or a tangible storage medium. By way of example, and not limitation, a computer-readable medium or a tangible storage medium includes memory technologies such as Random Access Memory (RAM), Read Only Memory (ROM), Flash Memory, and Solid State Drive (SSD). Furthermore, a computer-readable medium or a tangible storage medium may include optical disc storage devices such as Compact Disc Read-Only Memory (CD-ROM), Digital Versatile Disk (DVD), and Blu-ray discs. Moreover, a computer-readable medium or a tangible storage medium may include magnetic tape cassettes, magnetic tape, disk storage, and magnetic storage devices. The program may be transmitted on a temporary computer-readable medium or a communication medium. By way of example, and not limitation, a temporary computer-readable medium or communication medium includes propagating signals such as electricity, light, and sound. Temporary computer-readable media can provide programs to a computer via wired or wireless communication paths such as wires and optical fibers.

[0059] The present invention has been described above with reference to the embodiments described above, but the present invention is not limited to the above embodiments. Various modifications that can be understood by those skilled in the art can be made to the structure or details of the present invention within the scope of the present invention.

[0060] Symbol Explanation

[0061] 10-Analysis system, 100-DB, 200-Processing server, 201-Log selection unit, 202-Event processing unit, 203-Embedding unit, 204-Description unit, 205-Output unit, 206-Resolution specification unit.

Claims

1. An information processing device, characterized in that, It comprises: an embedding unit for embedding position information data of one or more entities into a Poincaré disk; and a drawing unit for drawing the position information data embedded in the Poincaré disk as the trajectory of one or more entities by using time information data corresponding to the position information of the one or more entities.

2. The information processing device according to claim 1, characterized in that, The embedding part embeds a defined spatial region in Euclidean space into the Poincaré disk, and the drawing part draws the trajectory of one or more entities within the defined spatial region embedded in the Poincaré disk.

3. The information processing apparatus according to claim 1 or 2, characterized in that, It also includes: a convergence unit, which converges two or more trajectories of the multiple entities into one trajectory based on at least one of the trajectories of the multiple entities or information related to the multiple entities.

4. An information processing method, characterized in that, The computer performs the following processing: embedding location information data of one or more entities into a Poincaré disk; and using time information data corresponding to the location information of one or more entities, depicting the location information data embedded in the Poincaré disk as the trajectory of one or more entities.

5. A program, characterized in that, The computer performs the following processing: embedding location information data of one or more entities into a Poincaré disk; and using time information data corresponding to the location information of one or more entities, depicting the location information data embedded in the Poincaré disk as the trajectory of one or more entities.

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