A graph layout optimization method and system based on force model parameter automatic search

Abstract

The application provides a graph layout optimization method and system based on force model parameter automatic search, acquires graph data, generates an initial graph layout result for the graph data, calculates the shortest path length between any pair of nodes in the graph, acquires the specified graph readability index of the user for the given graph data, generates a graph layout result satisfying the specified graph readability index according to the graph layout optimization method based on parameter automatic search, reuses the solved force model to new graph data to generate a layout result, and acquires the selection result of the user for the subgraph of interest in the layout result to perform local optimization on the subgraph corresponding to the selection result. The application can simultaneously satisfy the generation of corresponding visualization results according to the specified graph readability index and aesthetic criteria, so as to better show the structural characteristics of data, and simultaneously allows the user to perform interactive data exploration centered on analysis tasks according to requirements.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of data visualization, and particularly relates to a graph layout optimization method and system based on automatic search of force model parameters. BACKGROUND

[0002] The statements in this section merely provide background information related to the present application and do not necessarily constitute prior art.

[0003] In the data visualization technology, the node connection graph is the most commonly used graph visualization method, which abstracts entities in data into nodes in the graph and describes the relationship between entities as edges in the graph, so as to intuitively show the relationship between entities and facilitate human understanding. However, as the size of graph data increases, a large number of entities and relationships will cause node overlap and edge crisscrossing, inevitably causing visual clutter and making it difficult for users to observe and analyze. The visualization field generally uses graph layout methods to find appropriate positions for each node in the graph data, which can clearly and intuitively display the complex relationship between nodes, thereby improving the readability of graph data.

[0004] After more than half a century of development, a large number of graph layout methods have emerged in the field of graph layout. These methods can be mainly summarized into three categories: model-based methods, index optimization-based methods and hybrid methods:

[0005] 1) Model-based methods

[0006] Mainly generate graph layouts for node connection graphs by simulating two physical models: spring-charge model and stress model. Later, researchers combined the stress model and the spring-charge model, but the design principles of these methods mainly come from physical models rather than specifically optimizing readability indicators and aesthetic criteria. Therefore, these graph layout methods cannot directly optimize the layout results according to readability indicators and aesthetic criteria, nor can they fully exploit the structure information of data, and there are limitations in fully revealing the structure information of the graph and helping users understand and analyze.

[0007] 2) Index optimization-based methods

[0008] Take the readability indicators and aesthetic criteria of the graph as the objective function to directly optimize the position coordinates of all nodes in the graph. Initially, researchers designed a series of optimization algorithms, but only for specific indicators. Later, in order to be able to optimize multiple aesthetic indicators in a unified way, researchers proposed a general optimization framework that can generate layout results that meet aesthetic indicators by simply replacing the loss function. However, this type of framework only supports differentiable aesthetic indicators, although they choose differentiable approximation functions for some non-differentiable aesthetic criteria, but it is difficult to extend to other readability indicators and user-defined loss functions.

[0009] 3) Mixing methods

[0010] Extending the optimization of aesthetic criteria to model-based layout methods, such as force-directed layout methods, can be done by representing each criterion as a new force. However, all such methods are currently built on top of existing models and thus can only support a small range of aesthetic criteria. SUMMARY

[0011] To solve the above problems, the present application provides a graph layout optimization method and system based on automatic search of force model parameters, which can generate corresponding visual results according to specified graph readability indicators and aesthetic criteria to better show the structural characteristics of data, and allows users to perform interactive data exploration centered on analysis tasks according to requirements.

[0012] According to some embodiments, the present application adopts the following technical solutions:

[0013] A graph layout optimization method based on automatic search of force model parameters, comprising the following steps:

[0014] Obtaining graph data, generating an initial graph layout result for the graph data for subsequent graph layout solving;

[0015] Calculating the shortest path length between any pair of nodes in the graph for subsequent force model calculation;

[0016] Obtaining the specified graph readability indicators of the user for the given graph data, and generating a graph layout result satisfying the specified graph readability indicators according to the graph layout optimization method based on automatic search of parameters;

[0017] Reusing the solved force model to new graph data to generate a layout result;

[0018] Obtaining the selection result of the subgraph of interest of the user in the layout result, and performing local optimization on the subgraph corresponding to the selection result.

[0019] As an optional implementation, the specific process of generating a graph layout result satisfying the specified graph readability indicators according to the graph layout optimization method based on automatic search of parameters includes:

[0020] According to the given weighted graph readability indicators, calculating the loss function of the graph readability indicators;

[0021] Describing the graph layout force model using attractive and repulsive force-related parameters;

[0022] Solving the force model using stochastic gradient descent iteration to obtain a layout with the minimum loss function;

[0023] Searching for the optimal model parameter to optimize the graph layout result.

[0024] As a further implementation, the process of computing a loss function of graph readability indicators according to given weighted graph readability indicators includes: for given graph data and given m weighted graph readability indicators Li(X), the loss function value ψ(X) of layout X with respect to this set of weighted indicators is computed using the following formula:

[0025]

[0026] Given L i (X) is a graph readability indicator including some of stress error, neighborhood preservation, edge crossing, and ideal edge length, w i is the weight of the corresponding indicator.

[0027] As a further implementation, the process of describing a graph layout force model using attractive and repulsive related parameters includes: the graph layout force model supports defining any combination of forces, each force including a force range, a force weight, and a force exponent, both attractive and repulsive forces are applied between any two nodes in the graph, and an energy function of the graph layout force model is constructed, the energy function being a function of model parameters θ.

[0028] As a further implementation, the specific process of searching for optimal model parameters to optimize graph layout results includes: the problem of searching for model parameters θ is formulated as a unified optimization problem, the problem is defined as finding a force model with appropriate parameters θ that can produce a layout X with the lowest loss function ψ with respect to the corresponding indicators:

[0029]

[0030] For this optimization problem, the layout quality is continuously improved by iteratively updating the layout X and updating θ, the initial parameters θ and layout X are substituted into the force model, and a new layout X is obtained by solving the force model + , then X + is used to update θ + , and the process is repeated until the loss function ψ(X) converges.

[0031] As an alternative implementation, for readability indicators that do not have analytical partial derivatives, the graph layout optimization method based on automatic search of force model parameters uses numerical partial derivatives to approximate analytical partial derivatives, estimates the partial derivative of the readability indicator objective function with respect to the parameter by adding an increment δθ in each dimension of the parameter, uses forward difference to calculate the numerical partial derivative, and uses a simulated annealing cooling schedule to adjust δθ during the calculation process.

[0032] As an alternative implementation, the specific process of reusing the solved force model to new graph data to generate a layout result includes:

[0033] For a new graph G * , the graph kernel is used to measure the topological similarity between the input graph and the graph corresponding to the existing force model, and the k most similar graphs G si , i<k;

[0034] The force model corresponding to G si is applied to the new graph G * , and multiple meaningful layouts for the new graph are quickly generated.

[0035] As a further, the force model is pre-computed according to a set of graph data.

[0036] As an alternative implementation, the specific process of local optimization of the subgraph corresponding to the selection result includes:

[0037] Mirror flipping operations are performed on the layout generated by the subgraph in the horizontal and vertical directions;

[0038] An affine transformation including translation, rotation and scaling is found using the iterative closest point algorithm to map the flipped variant to the node coordinates of the subgraph;

[0039] The variant with the minimum cost when mapped to the original layout is selected as the final layout.

[0040] A graph layout optimization system based on force model parameter automatic search includes:

[0041] A preliminary layout module configured to obtain graph data and generate an initial graph layout result for the graph data;

[0042] A shortest distance length calculation module configured to calculate the shortest path length between any pair of nodes in the graph;

[0043] A graph layout optimization module configured to obtain a user-specified graph readability index for given graph data, and to generate a graph layout result that satisfies the specified graph readability index according to a graph layout optimization method based on parameter automatic search;

[0044] A reuse module configured to reuse the solved force model to new graph data to generate a layout result;

[0045] A local optimization module configured to obtain a user's selection result of a subgraph of interest in the layout result, and to perform local optimization on the subgraph corresponding to the selection result.

[0046] A computer-readable storage medium for storing computer instructions, which, when executed by a processor, perform the steps in the above method.

[0047] An electronic device includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, perform the steps in the method described above.

[0048] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0049] 1. This invention proposes a general method for automatically searching for graph layout models based on force models according to readability indicators and aesthetic criteria, and generating layout results that meet optimization objectives for given graph data. Compared with traditional graph layout methods based on readability indicators and aesthetic criteria, this method is more efficient and produces better layout quality.

[0050] 2. This invention allows the solved graph layout model to be reused for other graph data, thereby improving the user's graph exploration efficiency;

[0051] 3. This invention supports local optimization of subgraphs, helping users better understand the final graph layout result, thereby enabling interactive graph exploration for analysis tasks.

[0052] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0053] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0054] Figure 1 This is a flowchart of the graph layout optimization method based on automatic search of force model parameters according to the present invention;

[0055] Figure 2 The curves showing the change of the loss function of the method of the present invention and the comparative method when optimizing stress error (SE) are shown.

[0056] Figure 3 (a) and Figure 3 (b) is an example of the graphical layout results produced by the method of the present invention and the comparative method when optimizing stress error (SE);

[0057] Figure 4 (a)-(c) are examples of the results produced by model reuse and local optimization in the method of the present invention. Detailed Implementation

[0058] The application will be further described below with reference to the drawings and embodiments.

[0059] It should be noted that the following detailed description is exemplary in nature and is intended to provide further description of the application. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

[0060] It is to be understood that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments in accordance with the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and / or "comprising," when used in this specification, specify the presence of stated features, steps, operations, elements, components, and / or groups thereof, but do not preclude the presence or addition of one or more other features, steps, operations, elements, components, and / or groups thereof.

[0061] The embodiments in the present application and the features in the embodiments can be combined with each other without conflict.

[0062] Embodiment one

[0063] As described in the background, the existing graph layout method is difficult to meet the following goals: generating corresponding visualization results according to the specified graph readability indicators and aesthetic criteria, so as to better show the structural features of the data, and according to the user's needs, interactive data exploration centered on analysis tasks, which brings inconvenience to the user's analysis and exploration of graph data. In order to meet both user needs at the same time, the embodiment provides a graph layout optimization method based on force model parameter automatic search, which can directly generate corresponding graph layout results for input graph data according to graph readability indicators and aesthetic criteria, and support reuse of existing force models, quickly generate graph layout results for new input data, and also can locally optimize the subgraph selected by the user, produce layout results that meet the user's needs and analysis tasks. As shown in Figure 1 The method comprises the following steps:

[0064] Step 1: receiving graph data, generating an initial graph layout result for the graph data for subsequent graph layout solving.

[0065] Among them, the initial graph layout result can be obtained by randomly assigning coordinate positions to each node in the graph, or it can be generated based on any graph layout method, including force-directed layout, stress layout and hierarchical layout, etc., which is not limited here. The solving of subsequent step 3 is based on this initial layout.

[0066] Step 2: Calculate the shortest path length between any pair of nodes in the graph for subsequent force model calculation.

[0067] The method for calculating the shortest path between all nodes in the graph is not limited, and Dijkstra algorithm or Floyd algorithm can be used.

[0068] Step 3: Receiving the graph readability indicators and aesthetic criteria specified by the user for the given graph data, and generating a graph layout result meeting the specified graph readability indicators and aesthetic criteria according to the graph layout optimization method based on parameter automatic search.

[0069] Regarding the m weighted graph readability indicators L i (X) specified by the user, the loss function value ψ(X) of the layout X with respect to this set of weighted indicators is:

[0070]

[0071] wherein the given L i (X) is not limited, and stress error, neighborhood preservation degree, edge crossing degree, ideal edge length, etc. can be used as the graph readability indicators and aesthetic criteria.

[0072] W={w1,···,w m} is the weight of all m indicators.

[0073] The graph layout optimization method based on parameter automatic search uses the force model Taurus to calculate the graph layout result meeting the graph readability indicators L i (X). Taurus is a general graph layout force model framework supporting the definition of any combination of attractive and repulsive forces, and each force includes 4 parameters: the range R k of the force, the weight ω k of the force, the exponent (α k , β k ) of the force. In order to balance the solving efficiency and layout quality, AutoFDP defaults to select two forces, one attractive force and one repulsive force, and sets the attractive and repulsive forces to be applied between any two nodes in the graph, i.e. the force range is set to V 2 . Therefore, the force model Taurus can be described by 6 parameters: θ=

[0074] {ω a ,α a ,β a ,ω r ,α r ,β r}. Wherein ω a ,α a ,β a represent the weight of the attractive force, the exponent of the Euclidean distance and the exponent of the graph theory distance respectively; ω r ,α r ,β rrespectively represent the weight of repulsive force, the exponent of Euclidean distance and the exponent of graph distance. The graph distance is set as the length of the shortest path. The energy function of force model Taurus The formula is as follows:

[0075]

[0076] When the θ of force model Taurus is determined, a layout X with the minimum loss function can be obtained by solving the force model Taurus, and the graph layout X corresponding to θ θ The solving can be performed by using a stochastic gradient descent solver of force model Taurus:

[0077]

[0078] The graph layout optimization method based on automatic search of parameters optimizes the graph layout result by searching an optimal model parameter θ. The problem of searching the model parameter θ can be expressed as a unified optimization problem, which is defined as finding a force model with a proper parameter θ that can generate a layout X with the lowest loss function ψ of the corresponding index according to the index ψ:

[0079]

[0080] Then, for this optimization problem, the layout quality can be continuously improved by iteratively updating the layout X and updating θ. First, the initial parameters θ and the layout X are substituted into the force model Taurus, and a new layout X is obtained by solving the force model Taurus + , and then X + is used to update θ + , and the process is repeated until the loss function ψ(X) converges. Therefore, the updating process of the parameters θ and the layout X is as follows:

[0081]

[0082] Where λ and ρ are the step sizes of gradient updates. In the alternating optimization process, although the globally optimal layout X(θ) is not obtained in each iteration, when the loss function of the layout converges, the iterative optimization process can guarantee that an X(θ) close to the global optimum is solved.

[0083] For the force model Taurus, by differentiating X, the following can be obtained:

[0084]

[0085] Where e a,ij and e r,ijThese represent the normalized directions of attraction and repulsion, respectively. Then, a fast-converging stochastic gradient descent method is used to update the x-axis of each node. i The location.

[0086] Many readability metrics lack analytical partial derivatives. Therefore, to uniformly solve all readability metrics, the graph layout optimization method based on automatic parameter search of the force model uses numerical partial derivatives to approximate analytical partial derivatives. This is achieved by making small increments δθ in each dimension of the parameter to estimate the partial derivative of the objective function of the readability metric with respect to that parameter. Furthermore, to save time in calculating the numerical partial derivatives, a forward differencing method is chosen.

[0087]

[0088] in:

[0089]

[0090] Calculating numerical partial derivatives using forward differencing is simple and easy to implement, but it can be inaccurate in some cases, especially when the step size δθ is poorly chosen, making it prone to getting trapped in local minima. Therefore, this invention uses a dynamic step size δθ to ensure convergence. Specifically, a larger δθ is chosen in earlier iterations for faster parameter updates, while a smaller δθ is chosen in later iterations to avoid oscillations. Layout It is generated by adding a small perturbation (i.e., dynamic step size) δθ to θ. Considering that θ only contains six parameters, the computational cost of the numerical partial derivatives is still acceptable. To avoid getting trapped in local optima, this invention uses a simulated annealing cooling timetable to adjust the small perturbation δθ. By choosing a suitable decay function for δθ, the convergence of the algorithm can be guaranteed.

[0091] Figure 2 The method of this invention and the comparative method (SGD) are demonstrated. 2 The loss function variation curve when optimizing stress error (SE). Figure 2 There are four curves showing the change of the objective function value, representing the methods of this invention and the comparative method (SGD) using a fixed step size (0.1) δθ, linear decay δθ, and exponential decay δθ. 2 . Figure 2 The results show that the exponentially decaying δθ achieves the best optimization effect, converging to the lowest objective function value, compared to the contrastive method (SGD). 2 It has stronger optimization capabilities.

[0092] Figure 3 The method of this invention and the comparative method (SGD) are demonstrated. 2 Visual representation of the optimization of stress error (SE). Figure 3 (a) and Figure 3(b) are the results of the invented method and the comparative method (SGD) respectively 2 In the visualizations of 1 iteration, 15 iterations, 30 iterations, the invented method reveals the grid structure in the graph better and converges faster. This proves that the invented graph layout optimization method based on automatic search of force model parameters can effectively search for the corresponding graph layout model for the specified indicators and generate a graph layout result that meets the specified graph readability indicators and aesthetic criteria.

[0093] Step 4: Reuse the solved force model to the newly input graph data to quickly generate a layout result.

[0094] The user inputs a graph data to be analyzed, and the invented method finds a force model calculated on data similar in structure to the input graph data, and then reuses this force model to directly solve the input graph data to generate an initial graph layout.

[0095] Model reuse quickly generates multiple different and high-quality layouts for new input graphs by reusing the already solved force model. Model reuse significantly improves the efficiency of layout generation and provides a intuitive way for users to predict the overall structure of the input graph. In this way, users can see the multi-faceted structural characteristics of the input graph data (such as global skeleton structure, branch structure, hierarchical structure, and cluster partitioning, etc.). The following three steps are taken to reuse the force model obtained from one graph to generate a layout for the input graph data. First, apply steps 1-3 to a set of graph data to optimize multiple indicators and pre-compute a set of force models. Then, for a new input graph G * , use graph kernels to measure the topological similarity between the input graph and the graphs corresponding to the existing force models, and select the k most similar graphs G si (i < k). Finally, the invented method applies the force model corresponding to G si to the new graph G * , thereby quickly generating multiple meaningful layouts for the new input graph.

[0096] Figure 4 is an example of the results produced by the invented method in model reuse and local optimization. Figure 4 (a) of is the layout result of the pre-computed graph data using steps 1-3 and the force model, which can be reused for new input data. Figure 4 (b) of is a new input data that reuses Figure 4 (a) of the force model to generate a layout result. The new input data calculates the graph kernel similarity with the existing graph data, selects a graph data with the highest similarity, and reuses the force model to the new input data, thereby generating a layout for the new input data. The reused graph layout has structural characteristics close to the reused graph, Figure 4 (a) and Figure 4(b) all show the branching structure of the data well, and the path and length of each edge node to the center circle can be clearly seen.

[0097] Step 5: The user selects a subgraph of interest from the layout result.

[0098] In which the user can get a local subgraph of interest as the input of the local optimization layout method by various interactive methods, such as selecting a node and its neighbors by clicking, selecting a range of nodes by framing, or selecting a path of interest.

[0099] Step 6: Local optimization is performed on the subgraph of interest of the user, helping the user to understand the local structure of the data.

[0100] The user interactively selects a subgraph of interest R on the initial graph layout, can specify some task-related indicators for it, and then regenerates the layout of the local subgraph according to the specified indicators through the local optimization method. The node coordinates of the subgraph SG in the region R are X s , and then the user can apply an indicator function ψ s (such as NP for exploring clusters) to the subgraph SG according to the data analysis task to adjust the subgraph layout. By initializing SG with X, we first apply step 3 to generate a layout X s ′ , and then use the iterative closest point (ICP) algorithm to align the layout X s ′ with the reference X s . In the process of local optimization, sometimes a layout may be obtained which is mirror-inverted in the direction of the original layout. In order to find the layout that is closest to the layout X s before optimization, the present application first performs horizontal and vertical mirror-inversion operations on the generated layout X s ′ . Subsequently, an affine transformation including translation, rotation and scaling is found by using the iterative closest point (ICP) algorithm to map the inverted variant X s ′ to X s . Finally, the variant that maps to the original layout with the minimum cost is selected as the final layout. Figure 4 (c) shows the improved layout after performing local stress error (SE) optimization on Figure 4 (b). Stress error (SE) aims to achieve distance preservation results, and it can be seen that through stress error (SE) optimization, Figure 4 the branching of the subgraph in the red box in (c) is clearer, and the connection relationship of the nodes in the subgraph is well displayed;

[0101] The method of the embodiment can be implemented by using a mainstream visual programming language. Since the solution of the optimization equation is slow, a GPU parallel program can be written by using CUDA to speed up. Tests prove that the application can help users to observe the multiple structural features of data and better understand the data.

[0102] Embodiment two

[0103] The embodiment aims to provide a graph layout optimization method based on automatic search of force model parameters.

[0104] To achieve the above object, the embodiment provides a graph layout optimization system based on automatic search of force model parameters, which comprises:

[0105] a module for receiving graph data and generating an initial graph layout result for the graph data;

[0106] a module for calculating the shortest path length between any pair of nodes in the graph;

[0107] a module for receiving the graph readability index and aesthetic criteria specified by a user for given graph data and generating a graph layout result meeting the specified graph readability index and aesthetic criteria according to the graph layout optimization method based on automatic search of parameters;

[0108] a module for reusing the solved force model to newly input graph data to quickly generate a layout result;

[0109] a module for selecting a subgraph of interest from the layout result;

[0110] a module for performing local optimization for the subgraph of interest of the user to help the user to understand the local structure of the data.

[0111] Embodiment three

[0112] The embodiment aims to provide an electronic device.

[0113] To achieve the above object, the embodiment provides an electronic device, which comprises a memory, a processor and a computer program stored in the memory and executable on the processor, and the processor implements the following steps when executing the program, comprising:

[0114] receiving graph data and generating an initial graph layout result for the graph data;

[0115] calculating the shortest path length between any pair of nodes in the graph;

[0116] receiving the graph readability index and aesthetic criteria specified by a user for given graph data and generating a graph layout result meeting the specified graph readability index and aesthetic criteria according to the graph layout optimization method based on automatic search of parameters;

[0117] reusing the solved force model to new input graph data to quickly generate layout results;

[0118] user selects subgraph of interest from the layout results;

[0119] performing local optimization on the subgraph of interest to help user understand local structure of the data.

[0120] Embodiment Four

[0121] The embodiment aims to provide a computer-readable storage medium.

[0122] To achieve the above object, the embodiment provides a computer-readable storage medium, which stores a computer program, and the program is executed by a processor to perform the following steps:

[0123] receiving graph data, and generating an initial graph layout result for the graph data;

[0124] calculating the shortest path length between any pair of nodes in the graph;

[0125] receiving graph readability index and aesthetic criteria specified by a user for given graph data, and generating a graph layout result satisfying the specified graph readability index and aesthetic criteria according to a graph layout optimization method based on parameter automatic search;

[0126] reusing the solved force model to new input graph data to quickly generate layout results;

[0127] user selects subgraph of interest from the layout results;

[0128] performing local optimization on the subgraph of interest to help user understand local structure of the data.

[0129] The steps involved in the above embodiments two, three and four correspond to embodiment one, and the specific implementation can refer to the relevant description part of embodiment one. The term "computer-readable storage medium" should be understood as including a single medium or multiple media of one or more instruction sets; it should also be understood as including any medium capable of storing, encoding or carrying instruction sets for execution by a processor and causing the processor to perform any method in the present application.

[0130] Those skilled in the art will appreciate that embodiments of the present application can be devised for a variety of applications. FIG. 1 illustrates an example of a system 100 that can implement an embodiment of the present application. As shown in FIG. 1, system 100 includes a host computer 110 that is configured to communicate via one or more wired or wireless communication links 120 with one or more remote devices, such as a user terminal 130. Host computer 110 can be configured to communicate with user terminal 130 directly or via one or more intermediary devices. For example, host computer 110 can be configured to communicate with user terminal 130 via one or more core networks 140, one or more core network 140, and / or one or more networks 150. By way of example, network 150 can include one or more wireless access networks and / or one or more core networks, and host computer 110 and / or user terminal 130 can be configured to communicate data and / or signaling over the air interface and through one or more base stations with one or more remote devices, such as user terminal 130. Host computer 110 can be configured to communicate with user terminal 130 according to a protocol, such as a Global System for Mobile Communications (GSM) protocol, a code division multiple access (CDMA) protocol, a Long Term Evolution (LTE) protocol, a 5G protocol, a 6G protocol, and / or the like.

[0131] The present application is described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and / or block in the flowchart illustrations and / or block diagrams, and combinations of flows and / or blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general purpose computer, special purpose computer, embedded processing device or other programmable data processing device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing device, create means for implementing the functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flow or flows and / or blocks. Figure 1 one or more functions specified in the flow or flows and / or blocks.

[0132] These computer program instructions can also be stored in a computer- readable memory that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instructions which implement the flow or flows and / or blocks. Figure 1 one or more functions specified in the flow or flows and / or blocks. Figure 1 one or more functions specified in the flow or flows and / or blocks.

[0133] These computer program instructions can also be loaded onto a computer or other programmable data processing device to cause a series of operational steps to be performed on the computer or other programmable device to produce a computer-implemented process such that the instructions which execute on the computer or other programmable device provide steps for implementing the functions specified in the flow or flows and / or blocks. Figure 1 one or more functions specified in the flow or flows and / or blocks. Figure 1 one or more functions specified in the flow or flows and / or blocks.

[0134] The foregoing is merely illustrative of the principles of this application and various modifications can be made by persons skilled in the art without departing from the scope and nature of the teachings herein. Any modification, equivalent replacement, improvement, etc. made by those skilled in the art without departing from the spirit and principle of the present application shall fall within the scope of the present application.

Claims

1. A graph layout optimization method based on automatic search of force model parameters, characterized in that, Includes the following steps: Acquire graph data and generate an initial graph layout result for the graph data; Calculate the shortest path length between any pair of nodes in the graph; Obtain the user's specified graph readability index for the given graph data, and generate a graph layout result that meets the specified graph readability index according to the graph layout optimization method based on parameter automatic search; The solved force model is reused on new graph data to generate layout results; Obtain the selection results of the sub-graphs that the user is interested in from the layout results, and perform local optimization on the sub-graphs corresponding to the selection results; The specific process of generating a graph layout that meets a specified graph readability index based on a parameter-based automatic search graph layout optimization method includes: Calculate the loss function of the graph readability index based on the given weighted graph readability index; The force model is described by describing the diagram layout using parameters related to gravity and repulsion. The force model is solved iteratively using stochastic gradient descent to obtain a layout with the minimum loss function; Search for the optimal model parameters to optimize the graph layout results; The process of calculating the loss function of a graph readability index based on a given weighted graph readability index includes: for a given graph data and m specified weighted graph readability indices Li(X), the loss function value ψ(X) of the layout X for this set of weighted indices is calculated using the following formula: ； Given The graph readability metrics include several of the following: stress error, neighborhood preservation, edge crossover, and ideal edge length. The weights of the corresponding indicators; The process of describing the graph layout force model using gravity and repulsion parameters includes: the graph layout force model supports defining any combination of forces, each force including the range of the force, the weight of the force, and the exponent of the force; setting both gravity and repulsion to be applied between any two nodes in the graph; and constructing the energy function of the graph layout force model, the energy function being a function of the model parameter θ. The specific process of searching for the optimal model parameter optimization graph layout results includes: the problem of searching for model parameters θ is formulated as a unified optimization problem, defined as finding a force model with appropriate parameters θ based on the index ψ, which can produce a layout X with the lowest loss function ψ for the corresponding index: ； For this optimization problem, the layout quality is continuously improved by iteratively updating the layout X and θ alternately. The initial parameters θ and layout X are substituted into the force model, and a new layout is obtained by solving the force model. Then use Update This process is repeated until the loss function ψ(X) converges; For readability metrics that lack analytical partial derivatives, the graph layout optimization method based on automatic search of force model parameters approximates analytical partial derivatives using numerical partial derivatives by adding an increment to each dimension of the parameter. The partial derivative of the objective function for estimating the readability metric with respect to this parameter is calculated using the forward differencing method, and the cooling time of simulated annealing is used to adjust the calculation process. .

2. The graph layout optimization method based on automatic search of force model parameters as described in claim 1, characterized in that, The specific process of reusing the solved force model onto new graphical data to generate layout results includes: For the new diagram A graph kernel is used to measure the topological similarity between the input graph and the graphs corresponding to existing force models, and the k most similar graphs are selected. , i < k; will with The corresponding force model is applied to the new drawing. This allows for the rapid generation of multiple meaningful layouts for a new graph.

3. The graph layout optimization method based on automatic search of force model parameters as described in claim 2, characterized in that, The force model is calculated in advance based on a set of graphical data.

4. The graph layout optimization method based on automatic search of force model parameters as described in claim 1, characterized in that, The specific process of performing local optimization on the subgraph corresponding to the selection result includes: Perform horizontal and vertical mirroring operations on the layout generated from the subgraph; The iterative nearest point algorithm is used to find an affine transformation that includes translation, rotation, and scaling, and the flipped variant is mapped to the node coordinates of the subgraph for alignment. Choose the variant that has the lowest cost when mapping to the original layout as the final layout.

5. A graph layout optimization system based on automatic search of force model parameters, employing the graph layout optimization method based on automatic search of force model parameters as described in any one of claims 1-4, characterized in that, include: The initial layout module is configured to acquire graph data and generate an initial graph layout result for the graph data; The shortest distance length calculation module is configured to calculate the shortest path length between any pair of nodes in the graph; The graph layout optimization module is configured to obtain the graph readability index specified by the user for the given graph data, and generate a graph layout result that meets the specified graph readability index according to the graph layout optimization method based on parameter automatic search. The reuse module is configured to reuse the solved force model on new graph data to generate layout results; The local optimization module is configured to obtain the user's selection results of the subgraphs of interest in the layout results, and perform local optimization on the subgraphs corresponding to the selection results.

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