CN113922823B - Social media information propagation graph data compression method based on constraint sparse representation - Google Patents
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Abstract
The invention discloses a social media information propagation graph data compression method based on constraint sparse representation, which comprises the following steps: s1, data sampling: sampling each node of the propagation network to obtain a self-centering network of each node in the network; s2, data preprocessing: the self-centering network is expressed in a form of an adjacent matrix, and a dictionary matrix and a sparse code matrix are obtained; s3, extracting atoms representing the network from the dictionary matrix; s4, performing high-frequency atomic analysis according to the sparse code matrix; s5, selecting high-frequency atoms to construct an alternative set; s6, matching in a network by using a self-centering network in the alternative set; s7, reconstructing a network and analyzing results. According to the method, the complex network sparse representation result is used as a guide, constraint representation is carried out by combining the characteristics of the social network propagation network, so that the data compression of the social media information propagation graph is realized, and the aim of recovering the original social network graph data structure can be achieved by using a small number of atoms.
Description
Technical Field
The invention relates to a social media information propagation graph data compression method based on constraint sparse representation.
Background
With the development of the internet, social network platforms are rapidly developing. Whether information is acquired, living interests are shared or communicated with people, the social network is not separated, and the social network becomes an essential part of life of people.
The social network data preprocessing is to process the data acquired by data acquisition, so that the storage is convenient. In reality, most data are incomplete, inconsistent and redundant dirty data before processing, if the data are directly stored and processed later, the storage burden is increased, and meanwhile, the experimental result is seriously influenced. Currently, data preprocessing is mainly focused on filling in blank data, processing redundant data, and the like.
The social network propagation network is large in general scale, and the structural characteristics of the social network propagation network cannot be found by manual observation. Network parameters such as average degree, average path length, average clustering coefficient, node number, edge number and the like can describe the propagation network to a certain extent, but the frequently occurring obvious structural features in the network cannot be found.
This problem can be solved using sparse representation techniques of graph data structures. The technique can decompose a large network with graph data structures, extracting atoms therein as significant local structures, representing the original network as a linear combination of multiple atoms. In the complex network sparse representation, the concept of a self-centering network is used, and when the whole network is not focused any more, but the property of a single node is focused, the self-centering network is used, the network node consists of only one center node and the neighbor of the node, and the edge only comprises the edge between the center node and the neighbor and between the neighbor and the neighbor. The self-centering network can represent structural information of one node.
Sparse representation of the graph data structure can describe the characteristics of the network structure by carrying out sampling decomposition on the original graph structure and extracting the atomic structure of the network by using the sparse representation, and meanwhile, the atoms extracted by the sparse representation can be used for analysis of the network structure, such as network similarity measurement, network classification, identification and the like. This technique allows the characterization of complex networks, but it produces too many atoms, many of which are actually less frequent in the original network, i.e., these atoms are not high frequency atoms and do not contribute much to the overall network. For these atoms, a certain storage cost is required, and at the same time, the accuracy of the characterization of these atoms is not enough, which is disadvantageous for the analysis of the subsequent network structure. In addition, the characterization technique cannot clearly indicate which atoms a certain local structure in the original propagation network is composed of, which is unfavorable for structural analysis of the network.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a data compression technology for the social media information propagation graph, which takes a graph data structure sparse representation result as a guide and combines a social network propagation network to carry out constraint representation, so that the network storage space is reduced, and the aim of recovering the original social network graph data structure can be achieved by using a small number of atoms.
The aim of the invention is realized by the following technical scheme: a social media information propagation graph data compression method based on constraint sparse representation comprises the following steps:
s1, data sampling: sampling each node of the propagation network to obtain a self-centering network of each node in the network;
s2, data preprocessing: the self-centering network is expressed in a form of an adjacent matrix, and a dictionary matrix and a sparse code matrix are obtained;
s3, extracting atoms representing the network from the dictionary matrix;
s4, performing high-frequency atomic analysis according to the sparse code matrix;
s5, selecting high-frequency atoms to construct an alternative set;
s6, matching in a network by using a self-centering network in the alternative set;
s7, reconstructing a network and analyzing results.
Further, the specific implementation method of the step S2 is as follows:
s21, representing the self-centering network as a form of an adjacent matrix;
s22, processing each adjacent matrix, and sequentially connecting all column vectors of the matrix end to form a column vector;
s23, splicing all column vectors together to form a sampling matrix, wherein the column number of the sampling matrix is the number of nodes in the propagation network;
s24, decomposing the sampling matrix by using a KSVD algorithm to obtain a dictionary matrix and a sparse code matrix.
Further, the specific implementation method of the step S3 is as follows: each column vector in the dictionary matrix is processed and restored to be adjacent matrix, after a plurality of adjacent matrices are obtained, the adjacent matrix is restored to be a network, and meanwhile, redundant isomer in the adjacent matrix is removed, so that the atoms representing the network are finally obtained.
Further, the specific implementation method of the step S4 is as follows: the atoms, dictionary column matrixes and sparse code matrixes generated in the matrix decomposition process of the KSVD algorithm are used for obtaining the following mapping relation:
(1) Mapping relation between atoms and dictionary matrix array vectors;
(2) Mapping relation between the dictionary matrix array vector and the sparse code matrix row vector;
fusing the two so as to obtain the mapping relation between atoms and the row vectors of the sparse code matrix;
the sparse code matrix itself represents the use condition of the dictionary matrix array vector in the original matrix, and the number of times of using atoms can be obtained by counting the numerical sums of the row vectors of the sparse code matrix mapped by each atom; calculating the use times of atoms, sorting and filtering the atoms according to the use times, and selecting some atoms with the highest contribution to the original network from the atoms, wherein the selected atoms form a main structure of the network;
for a propagation network, where the atomic ratio of the star shape is quite high, the star atoms are the main feature of the propagation network.
Further, the specific implementation method of the step S5 is as follows: 18 star-shaped self-centering networks with node numbers of 3-20 are constructed as alternative sets generated by constraint atoms.
Further, the specific implementation method of the step S6 is as follows:
s61, constructing an atomic use set and an atomic node sequence set, and storing as a matching characterization result;
s62, taking out the self-center network with the maximum node number from the alternative set as a matching network;
s63, in the propagation network, obtaining the degree of all nodes, and taking out the nodes with the degree larger than or equal to the number-1 of the nodes of the matching network according to the sequence from large to small, and waiting for matching;
s64, sequentially matching the nodes to be matched, overlapping the central node of the matching network with the nodes to be matched, and aligning the neighbor nodes according to the sequence from small to large; sequentially recording the aligned first 19 node serial numbers in an atomic node sequence set, and simultaneously writing the size of the current matching network into an atomic use set; deleting edges between the point to be matched and the recorded neighbors;
s65, repeating the operation of S64 until no node to be matched with the number of the nodes of the matching network is greater than or equal to the number-1;
s66, returning to the step S62 until the alternative set is empty.
Further, the specific implementation method of the step S7 is as follows: the method comprises the steps of collecting an atomic use set and an atomic node sequence set to be used as an input of a reconstruction network; traversing the atom use set, and drawing an atom network according to the corresponding atom node sequence; meanwhile, marking atoms with different numbers of nodes with different colors, so that the composition condition taking the atoms as units is displayed in the original network; selecting nodes with high repeated occurrence times from the high-frequency atoms, and observing the same attribute of the nodes; and calculating the ratio of the space size of the atomic set, the atomic use set and the atomic node sequence set to the space size of the adjacent matrix of the original network, namely the compression rate of the compression method.
The beneficial effects of the invention are as follows: the invention provides propagation diagram representation under constraint, and exploits a propagation diagram compression method based on complex network sparse representation result guidance. The number of the finally generated atoms is less, the compression rate is high, and the atomic composition condition of the original network can be accurately represented, so that the following beneficial effects can be brought:
(1) Compression of social information propagation network data storage is facilitated;
(2) Compared with the sparse representation of the complex network, the method has the advantages that the number of generated atoms is smaller for a specific social information propagation network, the method has more characteristic significance, and the downstream application is facilitated to carry out network structure analysis;
(3) The composition structure of the original propagation network taking the node as a unit is converted into the composition structure taking the atom as a unit, so that the composition of the social information propagation network can be further explored.
Drawings
FIG. 1 is a flow chart of a social media information propagation graph data compression method based on constrained sparse representation.
Detailed Description
The technical scheme of the invention is further described below with reference to the accompanying drawings.
According to the invention, the representation result of the complex network sparse representation technology on the propagation network is used as a guide, a corresponding structure matching algorithm is constructed, and the structure composition of the original propagation network is researched. As shown in fig. 1, the social media information propagation graph data compression method based on constraint sparse representation comprises the following steps:
s1, data sampling: sampling each node of the propagation network to obtain a self-centering network of each node in the network, thus obtaining a self-centering network set of the propagation network;
s2, data preprocessing: the self-centering network is expressed in a form of an adjacent matrix, and a dictionary matrix and a sparse code matrix are obtained; the specific implementation method comprises the following steps:
s21, the self-centering network is expressed in a form of an adjacent matrix, so that the original abstract network is converted into an actual matrix form, and subsequent mathematical operation is facilitated; an adjacency matrix is a representation of the social network diagram data structure. For a network of N nodes, a adjacency matrix of size N is used for representation, where a ij The value of (2) may be 0 or 1. Alpha when node i and node j have a connecting edge ij 1, otherwise 0. Representing the network as a contiguous matrix may facilitate subsequent mathematical operations.
S22, processing each adjacent matrix, and sequentially connecting all column vectors of the matrix end to form a column vector; e.g. a matrix of dimensions (m, n), which is processed to be converted into a column vector of (m x n, 1);
s23, splicing all column vectors together to form a sampling matrix, wherein the column number of the sampling matrix is the number of nodes in the propagation network;
s24, decomposing the sampling matrix by using a KSVD algorithm to obtain a dictionary matrix and a sparse code matrix.
S3, extracting atoms representing the network from the dictionary matrix; the specific implementation method comprises the following steps: each column vector in the dictionary matrix is processed and restored to be adjacent matrix, after a plurality of adjacent matrices are obtained, the adjacent matrix is restored to be a network, and meanwhile, redundant isomer in the adjacent matrix is removed, so that the atoms representing the network are finally obtained.
Through the steps, the social information propagation network is characterized by using a sparse representation technology of the complex network, and atoms of the propagation network are obtained. Significant local features of the network can be found, and atoms of the original propagation network are acquired, thereby guiding the subsequent steps.
S4, performing high-frequency atomic analysis according to the sparse code matrix; the specific implementation method comprises the following steps: the atoms, dictionary column matrixes and sparse code matrixes generated in the matrix decomposition process of the KSVD algorithm are used for obtaining the following mapping relation:
(1) Mapping relation between atoms and dictionary matrix array vectors;
(2) Mapping relation between the dictionary matrix array vector and the sparse code matrix row vector;
fusing the two so as to obtain the mapping relation between atoms and the row vectors of the sparse code matrix;
the sparse code matrix itself represents the use condition of the dictionary matrix array vector in the original matrix, and the number of times of using atoms can be obtained by counting the numerical sums of the row vectors of the sparse code matrix mapped by each atom; calculating the use times of atoms, sorting and filtering the atoms according to the use times, and selecting some atoms with the highest contribution to the original network from the atoms, wherein the selected atoms form a main structure of the network; the general structure of the network can be composed solely by these atoms, which are collectively referred to herein as the principal features of the network.
By performing the analysis of this step on the propagation network, it can be said that the star-shaped atoms are the main feature of the propagation network, in which the atomic ratio of the star-shaped atoms is considerably high. A star atom is a self-centering network, with the difference that all neighbors of a centering node have no edges to each other.
S5, selecting high-frequency atoms to construct an alternative set;
for a propagation network, under the guidance of a complex network sparse representation result, the composition condition of the network can be described by adopting star atoms without using other structures.
The invention aims to perform representation under the constraint of the original propagation network, uses star atoms under the guidance of the sparse representation result of the complex network as an alternative set, and constrains the atomic generation in the representation process to make the star atoms. In the sparse representation technology of the complex network, the generation of atoms is unconstrained, the atoms are generated in iteration according to the actual situation of a sampling matrix, however, the actual use frequency of a large number of generated atoms is not great, and the contribution to the original network is not great.
In the characterization process, the invention restricts the generation of atoms so that the atoms can only be generated from the pre-constructed candidate set. In order to control the size of atoms, the network size of atoms is defined to be 20 or less in total nodes without infinitely enlarging the atoms. Thus, 18 star-shaped self-centering networks with node numbers of 3-20 are constructed as candidate sets generated by constraint atoms.
S6, matching in a network by using a self-centering network in the alternative set;
the present invention does not employ a adjacency matrix to represent each sampled self-centering network during the constraint characterization step, although this is quite effective in complex network sparse characterization. The reason is that the number of adjacency matrices of different isomers of the same network is large, and especially when the upper limit of the size of a given atom is 20, the number of adjacency matrices is more various. This can lead to significant time complexity, affecting the practical usability of the present invention.
The invention does not adopt an adjacent matrix to represent the network, but directly uses the network itself, and uses the star-shaped self-center network in the alternative set to match in the network, so as to gradually decompose the network into a plurality of different combinations of the star-shaped self-center networks, and simultaneously generate corresponding star-shaped atoms. The specific implementation method comprises the following steps:
s61, constructing an atomic use set and an atomic node sequence set, and storing as a matching characterization result;
s62, taking out the self-center network with the maximum node number from the alternative set as a matching network;
s63, in the propagation network, obtaining the degree of all nodes, and taking out the nodes with the degree larger than or equal to the number-1 of the nodes of the matching network according to the sequence from large to small, and waiting for matching;
s64, sequentially matching the nodes to be matched, overlapping the central node of the matching network with the nodes to be matched, and aligning the neighbor nodes according to the sequence from small to large; sequentially recording the aligned first 19 node serial numbers in an atomic node sequence set, and simultaneously writing the size of the current matching network into an atomic use set; deleting edges between the point to be matched and the recorded neighbors;
s65, repeating the operation of S64 until no node to be matched with the number of the nodes of the matching network is greater than or equal to the number-1;
s66, returning to the step S62 until the alternative set is empty.
S7, reconstructing a network and analyzing results; the specific implementation method comprises the following steps: the method comprises the steps of collecting an atomic use set and an atomic node sequence set to be used as an input of a reconstruction network; traversing the atom use set, and drawing an atom network according to the corresponding atom node sequence; meanwhile, marking atoms with different numbers of nodes with different colors, so that the composition condition taking the atoms as units is displayed in the original network; the nodes with high repeated occurrence times are selected from the high-frequency atoms, the nodes have high influence on the network, and the same attribute of the nodes is observed, so that the condition of the network can be known more in an ascending way; and calculating the ratio of the space size of the atomic set, the atomic use set and the atomic node sequence set to the space size of the adjacent matrix of the original network, namely the compression rate of the compression method. Through the steps, the original propagation network component structure with the nodes as units is converted into the component structure with the atoms as units. Those of ordinary skill in the art will recognize that the embodiments described herein are for the purpose of aiding the reader in understanding the principles of the present invention and should be understood that the scope of the invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific modifications and combinations from the teachings of the present disclosure without departing from the spirit thereof, and such modifications and combinations remain within the scope of the present disclosure.
Claims (3)
1. The social media information propagation graph data compression method based on constraint sparse representation is characterized by comprising the following steps of:
s1, data sampling: sampling each node of the propagation network to obtain a self-centering network of each node in the network;
s2, data preprocessing: the self-centering network is expressed in a form of an adjacent matrix, and a dictionary matrix and a sparse code matrix are obtained;
s3, extracting atoms representing the network from the dictionary matrix; the specific implementation method comprises the following steps: processing each column vector in the dictionary matrix, recovering the column vector into an adjacent matrix, recovering the adjacent matrix into a network after obtaining a plurality of adjacent matrices, and removing redundant isomers in the adjacent matrix, so that the atoms representing the network are finally obtained;
s4, performing high-frequency atomic analysis according to the sparse code matrix; the specific implementation method comprises the following steps: the atoms, dictionary column matrixes and sparse code matrixes generated in the matrix decomposition process of the KSVD algorithm are used for obtaining the following mapping relation:
(1) Mapping relation between atoms and dictionary matrix array vectors;
(2) Mapping relation between the dictionary matrix array vector and the sparse code matrix row vector;
fusing the two so as to obtain the mapping relation between atoms and the row vectors of the sparse code matrix;
the sparse code matrix itself represents the use condition of the dictionary matrix array vector in the original matrix, and the number of times of using atoms can be obtained by counting the numerical sums of the row vectors of the sparse code matrix mapped by each atom; calculating the use times of atoms, sorting and filtering the atoms according to the use times, and selecting some atoms with the highest contribution to the original network from the atoms, wherein the selected atoms form a main structure of the network;
for a propagation network, star atoms are adopted as main characteristics of the propagation network;
s5, selecting high-frequency atoms to construct an alternative set;
s6, matching in a network by using a self-centering network in the alternative set; the specific implementation method comprises the following steps:
s61, constructing an atomic use set and an atomic node sequence set, and storing as a matching characterization result;
s62, taking out the self-center network with the maximum node number from the alternative set as a matching network;
s63, in the propagation network, obtaining the degree of all nodes, and taking out the nodes with the degree larger than or equal to the number-1 of the nodes of the matching network according to the sequence from large to small, and waiting for matching;
s64, sequentially matching the nodes to be matched, overlapping the central node of the matching network with the nodes to be matched, and aligning the neighbor nodes according to the sequence from small to large; sequentially recording the aligned first 19 node serial numbers in an atomic node sequence set, and simultaneously writing the size of the current matching network into an atomic use set; deleting edges between the point to be matched and the recorded neighbors;
s65, repeating the operation of S64 until no node to be matched with the number of the nodes of the matching network is greater than or equal to the number-1;
s66, returning to the step S62 until the alternative set is empty;
s7, reconstructing a network and analyzing results; the specific implementation method comprises the following steps: the method comprises the steps of collecting an atomic use set and an atomic node sequence set to be used as an input of a reconstruction network; traversing the atom use set, and drawing an atom network according to the corresponding atom node sequence; meanwhile, marking atoms with different numbers of nodes with different colors, so that the composition condition taking the atoms as units is displayed in the original network;
selecting nodes with high repeated occurrence times from the high-frequency atoms, and observing the same attribute of the nodes;
and calculating the ratio of the space size of the atomic set, the atomic use set and the atomic node sequence set to the space size of the adjacent matrix of the original network to obtain the compression rate.
2. The social media information propagation graph data compression method based on constraint sparse representation according to claim 1, wherein the specific implementation method of step S2 is as follows:
s21, representing the self-centering network as a form of an adjacent matrix;
s22, processing each adjacent matrix, and sequentially connecting all column vectors of the matrix end to form a column vector;
s23, splicing all column vectors together to form a sampling matrix, wherein the column number of the sampling matrix is the number of nodes in the propagation network;
s24, decomposing the sampling matrix by using a KSVD algorithm to obtain a dictionary matrix and a sparse code matrix.
3. The social media information propagation graph data compression method based on constraint sparse representation according to claim 1, wherein the specific implementation method of step S5 is as follows: 18 star-shaped self-centering networks with node numbers of 3-20 are constructed as alternative sets generated by constraint atoms.
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