Financial traceability risk measurement and analysis method and system based on dynamic entropy transfer

Abstract

The invention discloses a financial traceability risk measurement and analysis method and system based on dynamic entropy transfer, and the method comprises the steps: constructing a dynamic entropy transfer graph through combining with various types of structure information, such as local guiding entropy, path exploration entropy and behavior collaborative entropy; the method can effectively describe the propagation path and the structure level of the risk factor in the complex financial network while keeping the calculation controllable. According to the method, the edge behavior sequence is constructed through the Gaussian kernel function on the basis of the node behavior time sequence, and the multi-scale permutation entropy is combined to model the inter-edge time sequence collaborative change, so that the expression ability of the system to the microscopic interaction behavior is remarkably improved, and the method has good adaptability and interpretability. The method can achieve the positioning of a potential high-influence risk source and the reconstruction of a propagation chain, is suitable for a plurality of scenes, such as financial supervision, risk early warning and abnormal path tracking, is high in processing efficiency, and is stable and reliable in result.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of financial technology and complex network analysis, and particularly relates to a financial traceability risk measurement and analysis method and system based on dynamic entropy transfer. BACKGROUND

[0002] With the continuous evolution of the financial market, the interaction relationship between market subjects is increasingly complex, showing multi-relationship, multi-scale and time sequence characteristics. The traditional single relationship network model has been difficult to accurately depict the real structure and evolution law of the financial system. Therefore, constructing a complex multi-relationship time sequence network that can simultaneously fuse multiple types of financial behavior relationships and reflect the dynamic changes of time has become a key direction in current financial network analysis. Such network model is helpful to comprehensively understand the interaction mechanism between various participants in the financial market, and support in-depth analysis of the system risk propagation path and source. In the stability and risk assessment of the financial system, information entropy is gradually applied to network feature measurement because it can measure the uncertainty and complexity of the system. By analyzing the distribution and evolution of information entropy in the network nodes, the stability of the financial subjects in the system and the potential structural abnormalities can be revealed. When the information entropy of a node fluctuates sharply in a short time, it usually indicates that the state of the node is unstable, and it may become the starting point of risk transmission and spread outward through the network structure.

[0003] However, the existing evaluation methods based on information entropy mostly stay at the static description level, lack modeling of the dynamic transfer process of information entropy in the network structure, and are difficult to truly reflect the generation, amplification and propagation mechanism of risk factors. At the same time, the existing methods usually only focus on a certain structural level of the network, and fail to systematically analyze the risk of nodes from the dual dimensions of macro-structural characteristics and micro-behavior changes, limiting its application ability in system risk source identification and propagation path tracking. Therefore, there is an urgent need for a risk measurement method that can fuse complex multi-relationship time sequence network structure, depict the dynamic transfer behavior of information entropy, and jointly model the macro-structural status and micro-behavior evolution of nodes, in order to realize the accurate identification of potential risk source nodes in the financial system and effective traceability of the risk propagation path. SUMMARY

[0004] The present application aims to overcome the deficiencies of the prior art in the aspect of financial systemic risk traceability analysis, and proposes a financial traceability risk measurement and analysis method based on dynamic entropy transfer, which can accurately identify systemic risk source nodes and quantify the influence propagation path and scope in the complex financial network.

[0005] To achieve the above-mentioned purpose, the present application provides a financial traceability risk measurement and analysis method based on dynamic entropy transfer, the steps of which include:

[0006] A financial network with time series data is constructed, the financial network comprising a node set and an edge set;

[0007] A path probability on a shortest path between nodes is calculated, a target-oriented entropy probability model is constructed based on degree information of nodes in the path, and a local-oriented entropy matrix is generated by normalizing different path lengths;

[0008] A target entropy distribution of all shortest paths between node pairs is counted, a hop number sensitive path probability matrix is constructed by introducing a hop number index modulation function, and a path exploration entropy tensor is aggregated and generated;

[0009] A time delay embedding and symbol reconstruction are performed on a behavior time series of an edge, a frequency of occurrence of a symbol arrangement pattern is counted, a multi-scale permutation entropy value is calculated, and an edge-level sequential co-acting entropy vector group is generated;

[0010] The local-oriented entropy matrix, the path exploration entropy tensor, and the sequential co-acting entropy vector group are fused to construct a dynamic entropy transfer graph, an information transfer path tracking is performed, and a risk factor propagation trajectory atlas is generated; and the dynamic entropy transfer graph is used to complete financial traceability risk measurement and analysis.

[0011] Preferably, the method for constructing the financial network comprises: acquiring a securities company, a listed company, and an investment subject in a financial market as a node v i ∈V in a complex financial network, each node being associated with a behavior time series, the behavior time series comprising a transaction volume, an asset change, or a credit state continuous time feature A transaction investment behavior is regarded as an edge between nodes.

[0012] Preferably, the behavior time series X ij (t) of the edge is calculated from the behavior sequences of the two end nodes by a Gaussian kernel function:

[0013] X ij (t)=Kern(X i (t),X j (t))

[0014] Wherein, X i (t) and X j (t) are the behavior values of the two end nodes of the edge at time t;

[0015] X ij (t) is mapped to a node reachability y by using an MLP, when y is less than a threshold value a, the nodes are unreachable, and the edge e ij between the node pair (i, j) does not exist.

[0016] Preferably, the generation process of the local-oriented entropy matrix is as follows:

[0017] All reachable shortest path sets p(i, b) are searched by breadth-first search, and target-oriented entropy of each path is defined according to node degree:

[0018]

[0019] Wherein, k j is the out-degree of node j in the path;

[0020] The path length normalization function is used:

[0021] γ(l) = 1 / log(1+l)

[0022] l represents the length of p(i, b); the neighborhood structure sampling sliding window width h is set to limit the path length l < h, and the neighborhood subgraph of node i is intercepted Finally, the sparse matrix M is constructed local ∈R |V|×|V| , which represents the local oriented entropy distribution matrix.

[0023] Preferably, the path exploration entropy tensor construction process is specifically:

[0024] The target entropy distribution of all shortest paths between node pairs is counted, and the search information entropy of each pair of nodes is defined based on the path set:

[0025]

[0026] The node pair set is expanded to the Cartesian product V x V of the whole graph, and the path exploration entropy is calculated:

[0027]

[0028] Wherein, i represents the initial node; b represents the target node; V represents the node set;

[0029] The hop-dependent modulation function is designed:

[0030] ω(d) = exp(-λd)

[0031] Wherein, λ represents the modulation coefficient;

[0032] The structural hierarchy sensitivity is captured, and the probability distribution P' is weighted and modified according to the path hop d, and then the path matrix W after hop weighting is constructed ij , and all path flux tensors T are aggregated global ∈R |V|×|V|×D Wherein, D represents the maximum path length, and the third dimension of the tensor records the path entropy weight of different hop layers.

[0033] Preferably, the step of generating the edge-level sequential co-motion entropy vector group comprises:

[0034] Extracting edge eij Nuclear mapping time series Delay-embedding reconstruction of edge features:

[0035]

[0036] where n is the embedding dimension, τ is the time delay, x ij (k) represents the edge e ij The nuclear mapping feature value at time step k;

[0037] Internal incremental ordering is performed on to obtain the permutation index sequence:

[0038] x ij (k+(q1-1)τ)≤x ij (k+(q2-1)τ)≤…≤x ij (k+(q n -1)τ)

[0039] When equal values appear in the sequence, the index order q n As a supplementary ordering condition, each embedding segment corresponds to a symbol sequence S π =(q1, q2,..., q n ), and the sequence combination of the permutation is n!, and the actual observation K is denoted as K<<n!.

[0040] The frequency P π is counted for the symbol sequence set:

[0041]

[0042] where t represents the starting index of the current time window; T represents the total time length of the behavior time series; S(t) represents the symbol sequence corresponding to the embedding segment starting from time step t;

[0043] The sequential co-motion entropy is represented as:

[0044]

[0045] where P π represents the relative frequency of the symbol sequence π in all embedding segments;

[0046] A plurality of sets of time windows W={w1, w2,..., w n} are set, and the above operations are performed for each window to calculate the sequential co-motion entropy sequence {H w (e ij )} w∈W ; The sequential co-motion entropy sequence combination is taken as the edge-level behavior coordination feature vector group, and the microscopic feature input of the dynamic entropy transfer graph is obtained.

[0047] Preferably, the method for constructing the dynamic entropy transfer graph comprises: fusing a local orientation entropy matrix, a global path exploration entropy tensor and a set of edge level sequential co-motion entropy vectors, performing blocking alignment and normalization processing on the three types of features, and constructing an edge weight fusion function:

[0048]

[0049] Wherein, β1+β2+β3=1;M local [i,j] represents the normalized entropy value of the node pair (i,j) in its neighborhood structure based on the oriented path; D represents the set path hop length maximum length; d represents the current path hop level; Tglobal[i,j,d] represents the sum of the exploration entropy values corresponding to all path fluxes of the node pair (i,j) in the level with hop number d; V sync [e ij ] represents the edge e ij The sequential co-motion entropy feature value calculated under the multi-scale time window;

[0050] A dynamic entropy transfer graph is constructed based on the weighted edge weight matrix:

[0051] G dyn =(V,E',W E′ )

[0052] Wherein, W E′ represents an edge weight set; V represents a node set; E represents an edge set.

[0053] Preferably, the generation step of the risk factor propagation trajectory atlas comprises:

[0054] The shortest path search and information transfer tracking algorithm based on weight propagation is performed on the graph G dyn , the information flow path and transfer strength of each node (i,j) are calculated, and the risk factor propagation trajectory atlas is generated:

[0055]

[0056] Wherein, Path(i→j) represents the shortest information transfer path from node i to node j in the graph G dyn ; EntropyFlow ij represents the cumulative information entropy transfer strength in the propagation path from node i to node j.

[0057] The application also provides a financial traceability risk measurement and analysis system based on dynamic entropy transfer, which is used for realizing the above method and comprises a construction module, a calculation module, a statistics module, a generation module and a fusion module.

[0058] The construction module is used for constructing a financial network with time sequence data, the financial network comprising a node set and an edge set;

[0059] The calculation module is used for calculating path probability on a shortest path between nodes, constructing a target-oriented entropy probability model based on degree information of nodes in the path, and performing normalization processing on different path lengths to generate a local-oriented entropy matrix;

[0060] The statistics module is used for statistically calculating target entropy distribution of all shortest paths between node pairs, introducing a hop number index modulation function to construct a hop number sensitive path probability matrix, and aggregating to generate a path exploration entropy tensor;

[0061] The generation module is used for performing time delay embedding and symbol reconstruction on a behavior time sequence of an edge, statistically calculating appearance frequency of a symbol arrangement pattern, calculating a multi-scale arrangement entropy value, and generating an edge-level sequential co-motion entropy vector group;

[0062] The fusion module is used for fusing the local-oriented entropy matrix, the path exploration entropy tensor and the sequential co-motion entropy vector group, constructing a dynamic entropy transfer graph, performing information transfer path tracking, and generating a risk factor propagation trajectory atlas; and using the dynamic entropy transfer graph, completing financial traceability risk measurement and analysis.

[0063] Compared with the prior art, the present application has the following beneficial effects:

[0064] I. Fusion of multi-dimensional structural characteristics, enhancement of modeling precision: the present application combines local-oriented entropy, path exploration entropy and behavior co-motion entropy and other multi-type structural information to construct a dynamic entropy transfer graph, which can effectively depict the propagation path and structural level of a risk factor in a complex financial network while keeping the calculation controllable.

[0065] II. Retention of node behavior dynamics and edge-level interaction information: the present application is based on a node behavior time sequence, constructs an edge behavior sequence through a Gaussian kernel function, and models the time sequence co-motion change between edges by combining multi-scale arrangement entropy, which significantly improves the expression ability of the system to micro-interaction behaviors and has good adaptability and interpretability.

[0066] III. Systematic financial risk traceability analysis, practicality and scalability: the present application can realize positioning of a potential high-impact risk source and reconstruction of a propagation chain, is suitable for multiple scenarios such as financial supervision, risk early warning and abnormal path tracking, has high processing efficiency, and the result is stable and reliable. BRIEF DESCRIPTION OF DRAWINGS

[0067] In order to more clearly illustrate the technical solutions of the present application, the drawings needed in the embodiments are briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor on the basis of these drawings.

[0068] Figure 1 The step flowchart of the embodiment of the present application;

[0069] Figure 2 The financial traceability risk measurement method based on dynamic entropy transfer of the embodiment of the present application. DETAILED DESCRIPTION

[0070] The technical solutions in the embodiments of the present application will be described clearly and completely in the following with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the protection scope of the present application.

[0071] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, the present application will be further described in detail with reference to the drawings and specific embodiments.

[0072] Firstly, the learning partner relationship, online learning partner relationship network and network learning community are defined as follows:

[0073] Definition 1:

[0074] Learning partner relationship: the learning partner relationship between learners is a learning partner relationship between learners, which is interdependent, close cooperation and firm and lasting. Specifically, the feature similarity between learners reaches a threshold value, and the learning material coincidence degree of the same operation performed by learners reaches a threshold value.

[0075] Definition 2:

[0076] Online learning partner relationship network: the online learning partner relationship network is a homogenous information network obtained by projecting the heterogeneous information network of the online knowledge sharing platform mapped by the learning partner relationship extracted by the multi-layer bipartite graph downward. There is only one type of connection between nodes in the network, i.e. the learning partner relationship. The homogenous information network is the online learning partner relationship network.

[0077] Definition 3:

[0078] Network learning community: the network learning community is obtained by using the community discovery method to mine the community structure in the online learning partner relationship network. There is a learning partner relationship between learners in the community, and the existence of the network learning community promotes the learning of learners.

[0079] Embodiment one

[0080] As Figure 1 , Figure 2 indicated, the application provides a financial traceability risk measurement and analysis method based on dynamic entropy transfer, comprising the following steps:

[0081] S1. Construct a financial network with time series data.

[0082] In this embodiment, the financial network includes a node set and an edge set.

[0083] Set the node set V, including entity types such as financial institutions, account subjects, and asset units, define the edge set E, representing credit behavior, transaction behavior, and holding relationship, respectively, to form a multi-relationship heterogeneous network structure. Each node v i ∈V carries a set of behavior time series Record its financial operation behavior in unit time, such as transaction volume, credit change or liquidity indicators. Construct edge set to represent directional financial interaction.

[0084] For any edge e ij ∈E, construct it by kernel mapping of the behavior time series of nodes v i , v j , define the edge level time series as:

[0085] X ij (t)=Kern(X i (t),X j (t))

[0086] Where, Kern(·,·) is a Gaussian kernel function used to measure the instantaneous or time delay correlation of the behaviors of two nodes:

[0087]

[0088] Use MLP to map X ij (t) to node reachability y, when y is less than threshold α, the nodes are not reachable, and the edge e ij between node pair (i,j) does not exist.

[0089] S2. Calculate the path probability on the shortest path between nodes, build a target-oriented entropy probability model based on the degree information of the nodes in the path, and normalize the path length to generate a local oriented entropy matrix.

[0090] Use breadth-first search to search for all reachable shortest path sets P(i,b), and define the target-oriented entropy for each path according to the node degree:

[0091]

[0092] where k j is the out-degree of node j in the path. The path length normalization function is used:

[0093] γ(l) = 1 / log(l + 1)

[0094] l represents the length of p i , b), and the path probability value is length normalized. To avoid redundant aggregation interference, the neighborhood structure sampling sliding window width h is set, and the path length l < h is limited to intercept the neighborhood subgraph of node i Finally, the sparse matrix M local ∈ R |V|×|V| is constructed, which represents the local directed entropy distribution matrix.

[0095] S3. The target entropy distribution of all shortest paths between node pairs is counted, the hop number index modulation function is introduced to construct the hop number sensitive path probability matrix, and the path exploration entropy tensor is aggregated and generated.

[0096] The target entropy distribution of all shortest paths between node pairs is counted, and the search information entropy of each pair of nodes is defined based on the path set:

[0097]

[0098] The node pair set is expanded to the Cartesian product V x V of the whole graph, and the path exploration entropy is calculated:

[0099]

[0100] where i represents the initial node; b represents the target node; λ represents the modulation coefficient, which controls the speed of weight decay with hop number growth; V represents the node set;

[0101] The hop number dependent modulation function is designed:

[0102] ω(d) = exp(-λd)

[0103] Capture the structural level sensitivity, weight the probability distribution P' with the path hop number d, and then construct the path matrix W ij weighted by hop number, and aggregate all path flux tensors T global ∈ R |V|×|V|×D , where D represents the maximum path length, and the third dimension of the tensor records the path entropy weight of different hop number layers.

[0104] S4. Time delay embedding and symbol reconstruction are performed on the behavior time series of the edge, the frequency of symbol arrangement pattern is counted, the multi-scale permutation entropy value is calculated, and the edge-level sequential co-motion entropy vector group is generated.

[0105] The kernel mapping time series of edge e ij is extracted delayed embedding reconstruction is performed on the edge features:

[0106]

[0107] where n is the embedding dimension, τ is the time delay, x ij (k) represents the edge e ij The kernel mapping feature value at time step k.

[0108] The internal incremental order is sorted to obtain the permutation index sequence:

[0109] x iij (k+(q1-1)τ)≤x ij (k+(q2-1)τ)≤……≤x ij (k+(q n -1)τ)

[0110] When equal values appear in the sequence, the index order q n As a supplementary ordering condition, each embedding segment corresponds to a symbol sequence S π =(q1, q2,..., q n ), and the sequence combination of the permutation is n!, and the actual observation K is denoted as K<<n!.

[0111] The frequency P π is counted for the symbol sequence set:

[0112]

[0113] where t represents the starting index of the current time window, T represents the total time length of the behavior time sequence, and S(t) represents the symbol sequence corresponding to the embedding segment starting from time step t.

[0114] The sequential co-motion entropy is represented as:

[0115]

[0116] where P π represents the relative frequency of the symbol sequence π in all embedding segments.

[0117] A plurality of sets of time windows W={w1, w2,..., w m} are set, and the above operations are performed on each window to calculate the sequential co-motion entropy sequence {H w (e ij )} w∈W ; The sequential co-motion entropy sequence combination is used as the edge-level behavior coordination feature vector group, and the micro feature input of the dynamic entropy transfer graph is obtained.

[0118] ​S5. Fuse the local orientation entropy matrix, path exploration entropy tensor and sequential co-motion entropy vector group, construct a dynamic entropy transfer graph, perform information transfer path tracking, and generate a risk factor propagation trajectory map; and use the dynamic entropy transfer graph to complete the financial traceability risk measurement and analysis.

[0119] Fuse the local orientation entropy matrix, global path exploration entropy tensor, and edge-level sequential co-motion entropy vector group, and perform containment alignment and normalization processing on the three types of features to construct an edge weight fusion function:

[0120]

[0121] Where β1+β2+β3=1; M local [i,j] represents the normalized entropy value of node pair (i,j) in its neighborhood structure based on the guided path; D represents the maximum length of the path hop number set; d represents the current path hop number level; T global [i,j,d] represents the sum of all path flux corresponding exploration entropy values in the level with hop number d; V sync [e ij ] represents the edge e ij Sequential co-motion entropy feature values calculated under a multi-scale time window.

[0122] Based on the weighted edge weight matrix, a dynamic entropy transfer graph is constructed:

[0123] G dyn =(V,E',W E′ )

[0124] Where, W E′ represents the edge weight set; V represents the node set; E represents the edge set.

[0125] The value of node entropy transfer result MLP(X i (t)·ω ij ) represents the risk of the node in the financial network, and the larger the value, the more susceptible the node is to systemic risk.

[0126] Perform shortest path search and information transfer tracking algorithm based on weight propagation on graph G dyn , calculate the information flow path and transfer intensity for each node (i,j), and generate a risk factor propagation trajectory map:

[0127]

[0128] Where Path(i→j) represents the shortest information transfer path from node i to node j in graph G dyn ; EntropyFlow ijdenotes the accumulated information entropy transfer strength in the propagation path from node i to node j.

[0129] The generated risk factor propagation trajectory atlas can be regarded as the core result of the financial systemic risk traceability analysis, supporting the upper risk source identification, path intervention simulation and structure sensitivity analysis tasks.

[0130] Embodiment two

[0131] The embodiment also provides a financial traceability risk measurement and analysis system based on dynamic entropy transfer, including a construction module, a calculation module, a statistics module, a generation module and a fusion module. The construction module is used for constructing a financial network with time series data. The financial network includes a node set and an edge set. The calculation module is used for calculating path probabilities on shortest paths between nodes, constructing a target-oriented entropy probability model based on degree information of nodes in the path, performing normalization processing on different path lengths, and generating a local oriented entropy matrix. The statistics module is used for counting target entropy distributions of all shortest paths between node pairs, constructing a hop number sensitive path probability matrix by introducing a hop number index modulation function, and aggregating to generate a path exploration entropy tensor. The generation module is used for performing time delay embedding and symbol reconstruction on behavior time series of edges, counting frequencies of symbol permutation patterns, calculating multi-scale permutation entropy values, and generating an edge-level sequential co-motion entropy vector group. The fusion module is used for fusing the local oriented entropy matrix, the path exploration entropy tensor and the sequential co-motion entropy vector group, constructing a dynamic entropy transfer graph, performing information transfer path tracking, and generating a risk factor propagation trajectory atlas. The dynamic entropy transfer graph is used to complete financial traceability risk measurement and analysis.

[0132] The above-described embodiments are only descriptions of the preferred modes of the present application and do not limit the scope of the present application. Without departing from the design spirit of the present application, various modifications and improvements to the technical solutions of the present application made by those skilled in the art shall fall within the protection scope determined by the claims of the present application.

Claims

1. A financial traceability risk measurement and analysis method based on dynamic entropy transfer, characterized by the following steps: include: Constructing a financial network with time series data, wherein the financial network includes a node set and an edge set; Calculate the path probability on the shortest path between nodes, build a target-oriented entropy probability model based on the degree information of the nodes in the path, and normalize different path lengths to generate a local-oriented entropy matrix; The target entropy distribution of all shortest paths between node pairs is calculated, and a hop-count exponential modulation function is introduced to construct a hop-count sensitive path probability matrix, which is then aggregated to generate a path exploration entropy tensor. Perform time-delay embedding and symbol reconstruction on the edge behavior time series, count the frequency of symbol arrangement patterns, calculate the multi-scale arrangement entropy value, and generate the edge-level sequential co-motion entropy vector group; The local guidance entropy matrix, the path exploration entropy tensor and the sequential collaborative entropy vector group are integrated to construct a dynamic entropy transfer graph, perform information transfer path tracing, and generate a risk factor propagation trajectory map; and use the dynamic entropy transfer graph to complete the financial traceability risk measurement and analysis.

2. The financial traceability risk measurement and analysis method based on dynamic entropy transfer according to claim 1 is characterized in that: The method for constructing the financial network includes: obtaining securities companies, listed companies and investment entities in the financial market as nodes in the complex financial network. i ∈V, each node is associated with a behavioral time series, which includes the continuous time characteristics of transaction volume, asset changes or credit status Transaction and investment behaviors are regarded as edges between nodes.

3. The financial traceability risk measurement and analysis method based on dynamic entropy transfer according to claim 2 is characterized in that: Edge behavior time series X ij (t) is calculated by the behavior sequence of the nodes at both ends through the Gaussian kernel function: X ij (t)=Kern(X i (t),X j (t)) Among them, X i (t), X j (t) are the behavior values ​​of the nodes at both ends of the edge at time t; Use MLP to transform X ij (t) is mapped to the inter-node reachability y. When y is less than the threshold α, the nodes are unreachable, and the edge e of the corresponding node pair (i, j) is ij Does not exist.

4. The method for measuring and analyzing financial traceability risk based on dynamic entropy transfer according to claim 1 is characterized in that: The generation process of the local guided entropy matrix is: Use breadth-first traversal to search all reachable shortest path sets p(i,b), and define the goal-oriented entropy of each path based on the node degree: Among them, k j is the out-degree of node j in the path; Use the path length normalization function: γ(l)=1 / log(1+l) Indicates the length of p(i, b); sets the neighborhood structure sampling sliding window width h, limits the path length l<h, and intercepts the neighborhood subgraph of node i Finally, construct the sparse matrix M local ∈R |V|×|V| , represents the local guided entropy distribution matrix.

5. The method for measuring and analyzing financial traceability risk based on dynamic entropy transfer according to claim 4 is characterized in that: The specific process of constructing the path exploration entropy tensor is as follows: Count the target entropy distribution of all shortest paths between node pairs, and define the search information entropy of each pair of nodes based on the path set: Expand the node pair set to the full graph Cartesian product V×V and calculate the path exploration entropy: Where i represents the initial node; b represents the target node; V represents the node set; Design a hop-count-dependent modulation function: ω(d)=exp(-λd) Where λ represents the modulation coefficient; Capturing the structural hierarchy sensitivity, the probability distribution P′ is modified by weighting the number of path hops d, and then the hop-weighted path matrix W is constructed. ij , and aggregate all path flux tensors T global ∈R |V|×|V|×D , where D represents the maximum path length, and the third dimension of the tensor records the path entropy weights of different hop layers.

6. The method for measuring and analyzing financial traceability risk based on dynamic entropy transfer according to claim 1, characterized in that: The steps of generating the edge-level sequential collaborative entropy vector group include: Extract edge e ij Kernel map time series Perform delayed embedding reconstruction on edge features: Among them, the embedding dimension is n, the time delay is τ, and x ij (k) represents edge e ij The kernel map eigenvalue at time step k; right Perform internal incremental sorting to obtain the permutation index sequence: x ij (k+(q1-1)τ)≤x ij (k+(q2-1)τ)≤…≤x ij (k+(q n -1)t) When equal value items appear in the sequence, the index order q n As a supplementary sorting condition, each embedded segment corresponds to a symbol sequence S π =(q1, q2, ..., q n ), the permuted sequence combination is n!, and the actual observation K is recorded as K<<n!; Statistical frequency P of the symbol sequence set π : Where t represents the starting index of the current time window; T represents the total time length of the behavior time series; S(t) represents the symbol sequence corresponding to the embedded segment constructed with time step t as the starting point; The sequential co-motion entropy is expressed as: Among them, P π represents the relative frequency of the symbol sequence π in all embedded segments; Set multiple groups of time windows W = {w1, w2, ..., w m }, perform the above operation on each window and calculate the sequential co-movement entropy sequence {H w (e ij )} w∈W ; Combining the sequential collaborative entropy sequences as the edge-level behavior collaborative feature vector group to obtain the microscopic feature input of the dynamic entropy transfer graph.

7. The method for measuring and analyzing financial traceability risk based on dynamic entropy transfer according to claim 1 is characterized in that: The method for constructing the dynamic entropy transfer graph includes: fusing the local guidance entropy matrix, the global path exploration entropy tensor and the edge-level sequential collaborative entropy vector group, performing containment alignment and normalization processing on the three types of features, and constructing an edge weight fusion function: Among them, β1+β2+β3=1; M local [i, j] represents the normalized entropy value of the node pair (i, j) in its neighborhood structure based on the guided path; D represents the maximum length of the set path hops; d represents the current path hop level; T global [i, j, d] represents the sum of the exploration entropy values ​​corresponding to all path fluxes of the node pair (i, j) in the level with hop count d; V sync [e ij ] represents edge e ij Sequential co-motion entropy eigenvalues ​​calculated in multi-scale time windows; Based on the weighted edge matrix, a dynamic entropy transfer graph is constructed: G dyn =(V,E',W E′ ) in, W E′ represents the edge weight set; V represents the node set; E represents the edge set.

8. The method for measuring and analyzing financial traceability risk based on dynamic entropy transfer according to claim 7 is characterized in that: The steps of generating the risk factor propagation trajectory map include: In Figure G dyn The shortest path search and information transfer tracking algorithm based on weight propagation is executed, and the information flow path and transfer intensity are calculated for each node (i, j), generating a risk factor propagation trajectory map: Among them, Path(i→j) represents the graph G dyn The shortest information transfer path from node i to node k in EntropyFlow ij It represents the cumulative information entropy transfer intensity in the propagation path from node i to node j.

9. A financial traceability risk measurement and analysis system based on dynamic entropy transfer, the system being used to implement the method according to any one of claims 1 to 8, characterized in that: include: Construction module, calculation module, statistics module, generation module, fusion module; The construction module is used to construct a financial network with time series data, and the financial network includes a node set and an edge set; The calculation module is used to calculate the path probability on the shortest path between nodes, build a target-oriented entropy probability model based on the degree information of the nodes in the path, and normalize different path lengths to generate a local-oriented entropy matrix; The statistical module is used to count the target entropy distribution of all shortest paths between node pairs, introduce a hop index modulation function to construct a hop-sensitive path probability matrix, and aggregate to generate a path exploration entropy tensor; The generation module is used to perform time delay embedding and symbol reconstruction on the edge behavior time series, count the frequency of occurrence of symbol arrangement patterns, calculate multi-scale arrangement entropy values, and generate edge-level sequential co-motion entropy vector groups; The fusion module is used to fuse the local guidance entropy matrix, the path exploration entropy tensor and the sequential collaborative entropy vector group, construct a dynamic entropy transfer graph, perform information transfer path tracking, and generate a risk factor propagation trajectory map; and use the dynamic entropy transfer graph to complete the financial traceability risk measurement and analysis.

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