CN-122027486-A - Time sequence network key node identification method based on spectrum normalization propagation accumulation

CN122027486ACN 122027486 ACN122027486 ACN 122027486ACN-122027486-A

Abstract

The invention relates to the technical field of time sequence network processing, in particular to a time sequence network key node identification method based on spectrum normalization propagation accumulation. The method comprises the steps of extracting interactive node pairs in each continuous period, constructing a weighted adjacent matrix based on a full-time domain node union, ensuring that the interactive time sequence characteristic and node integrity are considered, calculating a self-adaptive propagation gain coefficient by means of the accumulated adjacent matrix spectrum radius, adapting to the overall network interaction strength without manual parameter adjustment, avoiding overamplification or underestimation of propagation effect, guaranteeing calculation stability, calculating propagation states by time-division iteration and accumulating to obtain total propagation states, accurately describing the transmission and accumulated reinforcement characteristics of node influence in time sequence evolution, and effectively improving the identification precision of key nodes.

Inventors

LV LINYUAN
Shi Menfeng
FAN TIANLONG
GUO CHANG
MAO ZIANG

Assignees

中国科学技术大学

Dates

Publication Date: 20260512
Application Date: 20260414

Claims (10)

1. The method for identifying the key nodes of the time sequence network based on spectrum normalization propagation accumulation is characterized by comprising the following identification steps: extracting node pairs interacted in each continuous period in the original record of the target time sequence network, and storing the node pairs in a node set of a corresponding period; Taking the union set of all node sets, and constructing a weighted adjacent matrix of each node set based on the union set, wherein each element in the weighted adjacent matrix is the sum of interaction times of corresponding node pairs in the corresponding time period; accumulating all weighted adjacent matrixes to obtain an accumulated adjacent matrix, and calculating a propagation gain coefficient alpha=1/(r+beta) by taking the spectrum radius r of the accumulated adjacent matrix, wherein beta is a constant for preventing zero division; The propagation states of all nodes in all time periods are calculated and concentrated respectively according to x (n) =(I+αA (n) )x (n-1) , the total propagation states of all nodes are obtained through accumulation, the nodes corresponding to the first K total propagation states are selected to serve as key nodes after descending order, x (n) 、x (n-1) is a propagation state vector formed by combining the propagation states of all nodes in the nth time period and the n-1 time period in a parallel mode respectively, I is an identity matrix, and A (n) is a weighted adjacent matrix in the nth time period.
2. The method for identifying key nodes of a time sequence network based on spectrum normalization propagation accumulation according to claim 1 is characterized in that if a target time sequence network is a directed network, a weighted adjacent matrix is an asymmetric matrix, matrix elements only correspond to the sum of interaction times of a certain node pointing to another node, and if the target time sequence network is an undirected network, the weighted adjacent matrix is a symmetric matrix, and the matrix elements are the sum of interaction times between two nodes.
3. The method for identifying the key nodes of the time sequence network based on spectrum normalization propagation accumulation according to claim 1 is characterized in that when the original interaction weight of the interaction event is contained in the target time sequence network, the sum of interaction times is replaced by the sum of the original interaction weights of corresponding node pairs in corresponding time periods, and if the interaction event has no original interaction weight, the original interaction weight of the interaction event is 1.
4. A method of identifying critical nodes of a time-series network based on spectral normalized propagation accumulation according to any of claims 1-3, characterized in that the initial propagation state vector x (0) is a full 1 vector.
5. A method for identifying a time-series network key node based on spectral normalized propagation accumulation according to any of claims 1-3, wherein β has a value of 10 -12 .
6. A method for identifying critical nodes of a time-series network based on spectral normalized propagation accumulation as claimed in any of claims 1-3, wherein the time period is a time window divided by a fixed time step Δt, and the time interval of the nth time window is Wherein The starting time of observation for the original record, n=1, 2.
7. A method for identifying key nodes of a time-series network based on spectral normalization propagation accumulation according to any one of claims 1-3, wherein K takes a value of 1% -10% of the total number of nodes.
8. A method for identifying critical nodes of a time-series network based on spectral normalized propagation accumulation according to any of claims 1-3, further comprising preprocessing steps of de-duplication, error correction, time stamp unification and node identification standardization of the original record before extracting the interactive node pairs.
9. A timing network key node identification system based on accumulated adjacency matrix spectral radius, characterized by being configured to perform a method for identifying a timing network key node based on spectral normalized propagation accumulation as claimed in any one of claims 1-8, comprising: The data preprocessing and extracting module is used for preprocessing the original record of the target time sequence network by performing de-duplication, error correction, unified time stamp and standardized node identification, extracting node pairs which interact in each continuous period and storing the node pairs in a node set of a corresponding period; The weighted adjacent matrix construction module is used for acquiring a union set of all node sets, constructing a weighted adjacent matrix of each time period based on the union set, wherein matrix elements are the sum of interaction times or the sum of original interaction weights of node pairs in the corresponding time period; if the target time sequence network is a directed network, the weighted adjacent matrix is an asymmetric matrix, and if the target time sequence network is an undirected network, the weighted adjacent matrix is a symmetric matrix; The propagation gain coefficient calculation module is used for accumulating all the weighted adjacent matrixes to obtain an accumulated adjacent matrix, extracting the spectrum radius r of the accumulated adjacent matrix and calculating the propagation gain coefficient alpha; The propagation state iteration and accumulation module is used for taking the full 1 vector as an initial propagation state vector x (0) , iteratively calculating the propagation state of each node in each period according to x (n) =(I+αA (n) )x (n-1) , and accumulating to obtain the total propagation state of each node; and the key node screening module is used for sequencing the total propagation states in a descending order, determining K according to the accuracy requirement of the target application scene, and selecting the first K corresponding nodes as key nodes.
10. An electronic device comprising a processor, a memory, and a computer program stored on the memory, wherein the processor implements the method of spectrum normalized propagation accumulation based time-critical network node identification of any of claims 1-8 when the computer program is executed.

Description

Time sequence network key node identification method based on spectrum normalization propagation accumulation Technical Field The invention relates to the technical field of time sequence network processing, in particular to a time sequence network key node identification method based on spectrum normalization propagation accumulation. Background The time sequence network is used as a complex system modeling framework for describing the dynamic evolution of interaction relation along with time, and is widely applied to actual scenes such as crowd contact monitoring, communication network scheduling, online social platform interaction and the like. Compared with a static network which only focuses on the connection relation among nodes, the occurrence period, the sequence and the accumulation frequency of interaction events in a time sequence network directly determine the final result of system dynamics behaviors such as information diffusion, propagation and the like, namely the interaction modes of the same group of nodes in different periods, and possibly cause distinct propagation effects. Therefore, accurately identifying key nodes in the timing network that can trigger significant propagation effects is a core problem for timing network analysis and propagation dynamics research. Currently, the time-series network key node identification methods are mainly divided into two types. The first type is a static aggregation strategy, and the method directly aggregates time sequence interaction data in the full time domain into a single static diagram or simply synthesizes the time sequence interaction data after the centrality is independently calculated on the snapshot of each time segment. However, the time sequence accumulation characteristic of the interaction event and the propagation association between time periods are lost in the mode, only the instant connection state of the nodes can be reflected, the accumulation effect of the node interaction intensity in the whole time domain cannot be described, and obvious deviation exists in the identification of the continuously-propagated key nodes. The second type is a centrality method driven by a time sequence path, node influence is measured by traversing a propagation path meeting time constraint, but the method faces the problems of high calculation complexity, sensitivity to parameters such as path length and the like, and lacks self-adaptive adaptation capability to the overall interaction strength of a network, and propagation related parameters need to be manually adjusted, so that the stability is poor in time sequence networks with different densities and different interaction frequencies, and the method is difficult to popularize and apply on a large scale. In addition, the conventional method for identifying the key nodes of the time sequence network has the key defects that firstly, the accumulated interaction intensity of an all-time domain is not fully utilized to calibrate the propagation gain, the quantification of the propagation effect is lack of network adaptability, the manually set parameters are easy to cause excessive amplification or underestimation of influence, secondly, the transmission and accumulated reinforcement characteristics of the influence of the nodes in different time periods are reflected without a mode of carrying out iterative calculation and accumulating propagation states in time periods, the continuous propagation capability of the nodes in time sequence evolution is difficult to accurately describe, thirdly, the adaptability to a directional/non-directional network is insufficient, quantification calculation logic matched with the interaction directivity is not formed, and the accuracy of key node identification is further influenced. Therefore, a method for identifying key nodes of a timing network is needed, which solves the problems of time sequence information loss, parameter sensitivity, insufficient expandability and the like existing in the existing method and provides efficient and reliable technical support for the key node identification of various dynamic interaction systems. Disclosure of Invention In order to solve the technical problem that the conventional time sequence network key node identification method loses the interaction time sequence accumulation characteristic and causes low identification precision, the invention provides the time sequence network key node identification method based on spectrum normalization propagation accumulation, and the identification precision is effectively improved by integrating full-time domain accumulated interaction strength, self-adaptive calibration propagation gain and time-period iteration accumulated propagation state. Based on the method, the invention also provides a time sequence network key node identification system based on the accumulated adjacency matrix spectrum radius and electronic equipment. In order to achieve the above purpose, the pr