CN112347425A - Method and system for dense subgraph detection based on time sequence - Google Patents
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Abstract
The application relates to a method and a system for dense subgraph detection based on time series, wherein the method for dense subgraph detection based on time series comprises the following steps: constructing a three-dimensional transaction matrix, a time set and a user set; then, calculating according to the three-dimensional transaction matrix to obtain a time-dimension transaction sum matrix and a user-dimension transaction sum matrix, and summing the transaction sums to obtain a first sum value; then averaging the first summation value through a time set and a user set to obtain an initial dense subgraph abnormal value; and finally, iteratively calculating and updating the abnormal value of the intensive subgraph by a greedy algorithm, recording the obtained maximum abnormal value of the intensive subgraph, and outputting a time set and a user set corresponding to the maximum abnormal value of the intensive subgraph as detection results. The method solves the problems of low accuracy and long calculation time consumption of fund transaction abnormal dense subgraph detection in the prior art, and improves the abnormal detection precision and the calculation speed.
Description
Technical Field
The present application relates to the field of computers, and more particularly, to a method and system for dense subgraph detection based on time series.
Background
With the rapid development of information technology, people increasingly use electronic banks to perform fund operation conveniently and rapidly, however, various phishing, telephone fraud, short message fraud and the like are generated, these various forms of fund fraud behaviors are becoming more and more serious, and based on these problems, the behavior of how to detect abnormal fund transaction of users such as banks, finance and the like has been more and more aroused by people.
In the related art, the fund transaction anomaly detection algorithms are all based on users and commodities and anomaly consideration between the users, such as algorithms like Fraudar, Dspot and FlowScope, and the algorithms cannot detect and obtain feedback results of fund anomaly transactions in real time, and the problems of large calculation amount and long time consumption exist.
At present, no effective solution is provided for the problems of low accuracy rate of abnormal and dense subgraph detection of fund transactions and long time consumption of calculation in the related technology.
Disclosure of Invention
The embodiment of the application provides a time-series-based dense subgraph detection method and a time-series-based dense subgraph detection system, which at least solve the problems of low accuracy and long calculation time consumption of abnormal fund transaction dense subgraph detection in the related technology.
In a first aspect, an embodiment of the present application provides a method for dense subgraph detection based on a time series, where the method includes:
constructing a three-dimensional transaction matrix, a time set and a user set, wherein the dimensionality of the three-dimensional transaction matrix comprises the following steps: transaction time and user, the elements of the three-dimensional transaction matrix comprising: a transaction amount;
calculating to obtain a time-dimension transaction sum matrix and a user-dimension transaction sum matrix according to the three-dimensional transaction matrix, and summing the transaction sums in the elements to obtain a first sum value;
averaging the first summation value through the time set and the user set to obtain an initial dense subgraph abnormal value;
and iteratively calculating and updating the dense subgraph abnormal value through a greedy algorithm, recording the obtained maximum dense subgraph abnormal value, and outputting a time set and a user set corresponding to the maximum dense subgraph abnormal value as detection results.
In some of these embodiments, the summing of the transaction amounts in the elements results in a first summed value
：
Wherein the content of the first and second substances,
is a set of transaction times that are,
is a set of users who transfer money,
is a collection of users that are to be paid,
is a three-dimensional matrix of transactions and,
is the empirical anomaly score.
In some of these embodiments, the empirical anomaly score comprises:
the experience anomaly score is related to the transaction time and the user, wherein the transaction is anomalous within a preset time, the experience anomaly score is greater than 0, and when the user is a white list user, the experience anomaly score is less than 0.
Therein is provided withIn some embodiments, the averaging of the first summation values by the time set and the user set results in an initial dense subgraph outlier
：
Wherein the content of the first and second substances,
is a set of transaction times that are,
is a set of users who transfer money,
is a collection of users that are to be paid,
is the first summation value.
In some embodiments, the iteratively calculating and updating the dense subgraph outliers by a greedy algorithm comprises:
acquiring a minimum element in the time-dimension transaction sum matrix and the user-dimension transaction sum matrix to obtain a minimum value;
screening out the corresponding elements of the minimum elements in the time set or the user set to obtain a new time set or a new user set;
calculating to obtain a second summation value through the minimum value, and averaging the second summation value through the new time set and the user set to obtain an updated dense subgraph abnormal value;
and recalculating the three-dimensional transaction matrix, and recalculating the new time-dimension transaction sum matrix and the user-dimension transaction sum matrix through the new three-dimensional transaction matrix.
In some of these embodiments, after recalculating the transaction sum matrix for the new time dimension and the transaction sum matrix for the user dimension, the method includes:
judging whether an empty set exists in the transaction sum matrix of the new time dimension and the transaction sum matrix of the user dimension;
in the case where there is an empty set, the iterative computation terminates.
In some embodiments, after obtaining the transaction amount sum matrix in the time dimension and the transaction amount sum matrix in the user dimension, the method includes:
and constructing an N-branch tree of the transaction sum matrix of the time dimension and the transaction sum matrix of the user dimension.
In a second aspect, an embodiment of the present application provides a system for dense subgraph detection based on time series, where the system includes:
the construction module is used for constructing a three-dimensional transaction matrix, a time set and a user set, wherein the dimensionality of the three-dimensional transaction matrix comprises the following steps: transaction time and user, the elements of the three-dimensional transaction matrix comprising: a transaction amount;
a calculation module for calculating a time dimension transaction sum matrix and a user dimension transaction sum matrix according to the three-dimensional transaction matrix, and summing the transaction amounts in the elements to obtain a first sum value,
averaging the first summation value through the time set and the user set to obtain an initial dense subgraph abnormal value;
and the output module is used for iteratively calculating and updating the dense subgraph abnormal value through a greedy algorithm, recording the obtained maximum dense subgraph abnormal value, and outputting a time set and a user set corresponding to the maximum dense subgraph abnormal value as detection results.
In a third aspect, an embodiment of the present application provides an electronic apparatus, including a memory and a processor, where the memory stores a computer program, and the processor is configured to execute the computer program to perform any one of the methods for dense subgraph detection based on time series.
In a fourth aspect, the present application provides a storage medium, where a computer program is stored, where the computer program is configured to execute any one of the methods for dense subgraph detection based on time series described above when running.
Compared with the related technology, the dense subgraph detection method based on the time series provided by the embodiment of the application constructs a three-dimensional transaction matrix, a time set and a user set based on transaction data, wherein the dimensionality of the three-dimensional transaction matrix comprises the following steps: transaction time and user, elements of the three-dimensional transaction matrix include: a transaction amount; then, calculating according to the three-dimensional transaction matrix to obtain a time-dimension transaction sum matrix and a user-dimension transaction sum matrix, and summing the transaction sums in the elements to obtain a first sum value; then averaging the first summation value through a time set and a user set to obtain an initial dense subgraph abnormal value; and finally, iteratively calculating and updating the abnormal value of the intensive subgraph by a greedy algorithm, recording the obtained maximum abnormal value of the intensive subgraph, and outputting a time set and a user set corresponding to the maximum abnormal value of the intensive subgraph as a detection result, so that the problems of low detection accuracy and long calculation time consumption of the abnormal intensive subgraph in the fund transaction in the prior art are solved.
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The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the application and together with the description serve to explain the application and not to limit the application. In the drawings:
fig. 1 is a flowchart of a time-series based dense subgraph detection method according to an embodiment of the application;
FIG. 2 is a block diagram of a dense subgraph detection system based on time series according to an embodiment of the application;
FIG. 3 is a schematic diagram of a screening matrix element according to an embodiment of the present application;
fig. 4 is an internal structural diagram of an electronic device according to an embodiment of the present application.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application will be described and illustrated below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application. All other embodiments obtained by a person of ordinary skill in the art based on the embodiments provided in the present application without any inventive step are within the scope of protection of the present application. Moreover, it should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation-specific decisions must be made to achieve the developers' specific goals, such as compliance with system-related and business-related constraints, which may vary from one implementation to another.
Reference in the specification to "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the specification. The appearances of the phrase in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments. Those of ordinary skill in the art will explicitly and implicitly appreciate that the embodiments described herein may be combined with other embodiments without conflict.
Unless defined otherwise, technical or scientific terms referred to herein shall have the ordinary meaning as understood by those of ordinary skill in the art to which this application belongs. Reference to "a," "an," "the," and similar words throughout this application are not to be construed as limiting in number, and may refer to the singular or the plural. The present application is directed to the use of the terms "including," "comprising," "having," and any variations thereof, which are intended to cover non-exclusive inclusions; for example, a process, method, system, article, or apparatus that comprises a list of steps or modules (elements) is not limited to the listed steps or elements, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus. Reference to "connected," "coupled," and the like in this application is not intended to be limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. Reference herein to "a plurality" means greater than or equal to two. "and/or" describes an association relationship of associated objects, meaning that three relationships may exist, for example, "A and/or B" may mean: a exists alone, A and B exist simultaneously, and B exists alone. Reference herein to the terms "first," "second," "third," and the like, are merely to distinguish similar objects and do not denote a particular ordering for the objects.
The dense subgraph detection method based on the time sequence can be applied to anti-fraud scenes of fund transactions such as banks, finance and the like, and the specific implementation scheme is as follows: constructing a three-dimensional transaction matrix, a time set and a user set based on transaction data, wherein the dimensionality of the three-dimensional transaction matrix comprises: transaction time and user, elements of the three-dimensional transaction matrix include: a transaction amount; then, calculating according to the three-dimensional transaction matrix to obtain a time-dimension transaction sum matrix and a user-dimension transaction sum matrix, and summing the transaction sums in the elements to obtain a first sum value; then, averaging the first summation value through the constructed time set and the user set to obtain an initial dense subgraph abnormal value; and finally, iteratively calculating and updating the abnormal value of the intensive subgraph by a greedy algorithm, recording the abnormal value of the maximum intensive subgraph, outputting a time set and a user set corresponding to the abnormal value of the maximum intensive subgraph as a detection result to obtain an intensive group with abnormal fund transaction, solving the problems of low detection accuracy and long calculation time consumption of the intensive subgraph with abnormal fund transaction in the prior art, automatically segmenting the time dimension by the algorithm when selecting the characteristics, automatically screening abnormal information, more accurately and conveniently detecting the abnormal dimension, improving the accuracy of the analysis result, reducing the financial risk, and quickly calculating a large amount of data on complex linear time by the greedy algorithm to effectively improve the calculation speed.
The present embodiment provides a method for dense subgraph detection based on time series, and fig. 1 is a flowchart of a method for dense subgraph detection based on time series according to an embodiment of the present application, as shown in fig. 1, the flowchart includes the following steps:
step S101, a three-dimensional transaction matrix, a time set and a user set are constructed based on transaction data, wherein the dimensionality of the three-dimensional transaction matrix comprises the following steps: transaction time and user, elements of the three-dimensional transaction matrix include: the transaction amount, optionally, the first dimension of the three-dimensional transaction matrix S is transaction time, which indicates when the user is conducting a transaction; the second dimension is the transfer user and the third dimension is the collection user, wherein the transaction amount is the corresponding value element in the matrix, as shown in table 1, 10 thousands of transfers are made from the transfer user 0 to the collection user 1, and then the transaction amount 10 is input at the corresponding position of the three-dimensional transaction matrix S. Optionally, the time set in this embodiment
Indicating how many transaction times are contained in the current set, and the initial value is to contain all time values. For example, if there are two total transactions at 10:00 and 10:10, respectively, then
(ii) a The user set includes, but is not limited to, a transfer user set and a collection of receiving users, and the transfer user set
Indicating how many users the transfer user currently contains, beginning withThe starting value is the value that contains all users, e.g., the transferring users have 0, 1, 2, 3, respectively, then
(ii) a Collection of payee users
Indicating how many users the payee currently contains, and the initial value contains all users, e.g. the payee has 0, 1, 2, 3, respectively, then
(ii) a Taking a bank transaction as an example, at 10:00, 0 user transfers 10 ten thousands, 9 ten thousands and 8 ten thousands yuan to 1, 2 and 3 users respectively, at 10:10, 2 user transfers 2 ten thousands to 3 user, as shown in table 1 below, a three-dimensional transaction matrix S with a dimension of (2,4,4) is constructed, wherein the first dimension 2 represents that 2 transaction times are 10:00 and 10:10, and the second and third dimensions 4 represent that there are transfer users 0, 1, 2, 3 and collection users 0, 1, 2, 3 respectively, and the matrix S is shown in the following formula (1):
TABLE 1
| Time of day | Transfer user | User of collection | Transfer amount |
| 10:00 | 0 | 1 | 10w |
| 10:00 | 0 | 2 | 9w |
| 10:00 | 0 | 3 | 8w |
| 10:10 | 2 | 3 | 2w |
Compared with the prior art that the fund transaction abnormity detection algorithm is based on users, commodities and abnormity consideration between the users, the feedback result of the fund abnormal transaction cannot be obtained through real-time detection, and the problems of large calculation amount and long consumed time exist, the time dimension is added in the embodiment, when the characteristics are selected, the time dimension is automatically segmented, the abnormal information is automatically screened out, and the detection accuracy of the abnormal group is improved;
step S102, a time-dimension transaction sum matrix and a user-dimension transaction sum matrix are obtained through calculation according to the three-dimensional transaction matrix, and transaction amounts in the three-dimensional transaction matrix are summed to obtain a first sum value. Optionally, the time dimension transaction sum matrix in this embodiment
Meaning the sum of the amounts involved at different transaction times, e.g.,
the sum of the transaction amounts related to the transaction time 0 and the transaction time 1 is respectively 27 ten thousand and 2 ten thousand; user dimension transaction sum matrix including, but not limited to, transfer user dimension transaction sum matrix
Transaction sum matrix with payee dimension
Wherein the transaction amount sum matrix of the transfer user dimension
Indicates the total amount of transaction money transferred by the different transfer users, for example,
representing the sum of the money transferred by the transfer users 0, 1, 2 and 3 respectively; transaction amount sum matrix of payee dimensions
Indicating the total amount of the transaction received by the different payee users, e.g.,
representing the total amount of the transaction received by the respective payee 0, 1, 2, 3; first sum value
Representing the sum of the transaction amounts involved in the time dimension, transfer user dimension and collection user dimension of the three-dimensional transaction matrix, resulting in a total transaction amount, e.g.,
the first sum is the sum of the transaction amount of 10 thousands, 9 thousands and 8 thousands transferred from the transfer user 0 to the receiving users 1, 2 and 3 respectively and 2 thousands transferred from the transfer user 2 to the receiving user 3 at the transaction time 0 and 129；
And step S103, averaging the first summation values through the time set and the user set to obtain an initial dense subgraph abnormal value. Optionally, in this embodiment, the first summation value obtained in step S102 is averaged through the total number of elements in the time set and the user set to obtain an initial dense subgraph abnormal value, for example, the time set obtained through calculation is obtained
User collection of account transfers
And collection of payee users
2+4+4=10, on the first summation value obtained in step S102
Averaging to obtain initial dense subgraph abnormal values
；
Step S104, performing iterative computation and updating of the initial dense subgraph abnormal value through a greedy algorithm, recording the maximum dense subgraph abnormal value therein, and outputting a time set and a user set corresponding to the maximum dense subgraph abnormal value as a detection result, optionally, in the embodiment, the initial dense subgraph abnormal value is updated through the iterative computation of the greedy algorithm, wherein the iterative computation step includes: acquiring a minimum element in a time-dimension transaction sum matrix and a user-dimension transaction sum matrix to obtain a minimum value; then, screening out the corresponding elements of the minimum elements in the time set or the user set to obtain a new time set or a new user set; then, a second summation value is obtained through the minimum value calculation, and the second summation value is averaged through a new time set and a user set to obtain an updated dense subgraph abnormal value; and finally, reconstructing the three-dimensional transaction matrix, recalculating through the newly-established three-dimensional transaction matrix to obtain a new time-dimension transaction sum matrix and a user-dimension transaction sum matrix, and iteratively calculating the steps until one of the time-dimension transaction sum matrix and the user-dimension transaction sum matrix is an empty set. After the iterative computation is completed, recording a maximum dense subgraph abnormal value obtained in the iterative computation, wherein a time set and a user set corresponding to the maximum dense subgraph abnormal value are final abnormal dense groups, and high-risk abnormal operation exists;
in some embodiments, the specific iterative computation process for updating the initial dense subgraph abnormal value by greedy algorithm iterative computation is as follows: taking bank transaction as an example, a time-dimension transaction sum matrix is obtained
Transaction amount sum matrix of transfer user dimension
Transaction sum matrix with payee dimension
Since there is the same minimum element 0, the matrix is randomly selected
The second element 0 in (1) is the total transaction amount transferred by the transfer user 1, corresponding to the user 1 in the transfer user set, and the minimum value is obtained
；
Then, the corresponding element of the minimum element 0 in the transfer user set is screened out: user 1, get a new set of transfer users
The change is not changed;
finally passes through the minimum
Calculating to obtain a second summation value
As shown in the following formula (5):
set of transit times
Collection of users
And a new set of transfer users
Averaging the second summation values to obtain updated dense subgraph abnormal values
As shown in the following formula (6):
wherein the content of the first and second substances,
is the value of the second sum and,
is a set of users who have new money transfers,
is a collection of users that are to be paid,
is a transaction time set;
calculating to obtain updated dense subgraph abnormal values
Then, before the maximum dense subgraph abnormal value in the updated dense subgraph abnormal values is recorded, a three-dimensional transaction matrix S is reconstructed, and the maximum dense subgraph abnormal value in the matrix S is recorded
All rows in (1) are set to 0, i.e.
And recalculating to obtain a time-dimension transaction sum matrix through the newly-established three-dimensional transaction matrix S
Transaction amount sum matrix of transfer user dimension
Transaction sum matrix with payee dimension
Using the obtained new time dimension transaction sum matrix
Transaction amount sum matrix of transfer user dimension
Transaction sum matrix with payee dimension
Repeating the iterative calculation process until the transaction sum matrix of the time dimension
Transaction amount sum matrix of transfer user dimension
Transaction sum matrix with payee dimension
Until at least one of them is empty, e.g.
；
After the iterative computation is completed, recording the maximum dense subgraph abnormal value obtained in the iterative computation, wherein the maximum dense subgraph abnormal value is determined by judging conditions, namely the updated dense subgraph abnormal value is obtained in the iterative computation
Comparison of
And
if the numerical value in between
Is greater than
Then remain updated
For example, comparing the initial dense subgraph abnormal values obtained in step S2
And the new dense subgraph abnormal value obtained by updating in the step S5
Due to the magnitude of
Greater than initially
Is thus recorded
And carrying out iterative comparison in such a way until the whole iterative computation is finished, recording a finally reserved value which is the maximum dense subgraph abnormal value, and recording a time set corresponding to the maximum dense subgraph abnormal value
User collection of account transfers
And collection of payee users
The three obtained sets are final abnormal dense groups;
in this embodiment, a transaction sum matrix of time dimensions is iteratively screened through a greedy algorithm
Transaction amount sum matrix of transfer user dimension
Transaction sum matrix with payee dimension
Calculating the minimum value of the data to obtain an updated dense subgraph abnormal value until the updated dense subgraph abnormal value is obtained
、
And
one of the three matrixes is an empty set, iteration is finished, and the maximum dense subgraph abnormal value obtained in iterative computation is recorded. Compared with the prior art that the subgraph is solved by violence, the time complexity is
The embodiment screens through a greedy algorithm
、
And
the minimum value in the sub-graph is deleted and then the sub-graph is solved, and the complexity of the computation time is
The method has the advantages that the complexity of linear time is obviously reduced, the calculation time is greatly reduced, the calculation of a large amount of data is greatly advantageous, the calculation time and memory resources can be effectively saved, and the calculation speed is increased. In addition, the abnormal intensive group with high-risk operation can be effectively screened out through the iterative computation, so that the monitoring of abnormal users and abnormal operation by financial institutions such as banks and the like is facilitated, and the financial risk is reduced.
Through the steps S101 to S104, compared with the prior art, the fund transaction anomaly detection algorithm is based on the user and the commodity, and the anomaly consideration between the user and the user, and there are problems that the feedback result of the fund anomaly transaction cannot be detected in real time, the calculation amount is large, and the consumed time is long. The embodiment detects an abnormally-dense subgraph in a time dimension, and constructs a three-dimensional transaction matrix, a time set and a user set based on transaction data, wherein the dimension of the three-dimensional transaction matrix comprises: transaction time and user, elements of the three-dimensional transaction matrix include: a transaction amount; then, calculating according to the three-dimensional transaction matrix to obtain a time-dimension transaction sum matrix and a user-dimension transaction sum matrix, and summing the transaction sums in the elements to obtain a first sum value; then, averaging the first summation value through the constructed time set and the user set to obtain an initial dense subgraph abnormal value; and finally, iteratively calculating and updating the abnormal value of the intensive subgraph by a greedy algorithm, recording the obtained maximum abnormal value of the intensive subgraph, outputting a time set and a user set corresponding to the maximum abnormal value of the intensive subgraph as a detection result to obtain an intensive group with abnormal fund transaction, solving the problems of low detection accuracy and long calculation time consumption of the intensive subgraph with abnormal fund transaction in the prior art, automatically segmenting the time dimension by the algorithm when selecting the characteristics, automatically screening abnormal information, more accurately and conveniently detecting the abnormal dimension, improving the accuracy of the analysis result, reducing the financial risk, quickly calculating a large amount of data on complex linear time by the greedy algorithm, and effectively improving the calculation speed.
In some embodiments, all elements in the three-dimensional transaction matrix are summed to obtain a first summation value
As shown in the following formula (2):
wherein the content of the first and second substances,
is a set of transaction times that are,
is a set of users who transfer money,
is to receiveA set of users, S is a three-dimensional transaction matrix,
is an empirical anomaly score, optionally an empirical anomaly score
And the transaction time
Related to the user, wherein the transaction is abnormal within a preset time, and the experience abnormal score is
If the user is a white list user, the experience abnormal score is larger than 0
Less than 0, the specific value is determined empirically, e.g., if 0-6 transactions are at a higher risk, then the time period
A value greater than 0, wherein if the transaction spans a time period, such as transaction times of 10:00 and 1:00, then 1:00 is at a time period with a greater risk of transaction between 0 and 6 points, the first summation value
Needs to add one
Values, e.g. user-defined
And when the 10:00 is not in the time period with larger transaction risk of 0-6 points, the addition is not needed; for some users considered normal, such as white-listed users, the risk of white-listed users is lower, so
Can be customized to be negative, e.g., if B1 is a white-listed user among users { A1, A2, A3, B1}, then the first summation value is calculated
When necessary, a negative one is added
Value, e.g.
(ii) a Conversely, if it is a blacklisted user, it is self-defined because of the higher risk
Is positive and the value can be set higher, e.g., B1 is a blacklisted user among users { A1, A2, A3, B1}, then the first summation value is calculated
When necessary, a positive one is added
Value, e.g.
(ii) a Further, if black and white users exist among all users, such as users B1 and B2 among users { A1, A2, A3, B1, B2, C1} are white users and C1 is a black list user, the first sum value is calculated
When necessary to add
Has a value of
And
the sum of the values,
namely, it is
(ii) a If the black-and-white list users exist in the users in the time period with the transaction time of 0-6 points and the transaction risk is large, the users in the black-and-white list exist
，
，
All need to be customized according to the above rules, and sum is carried out to obtain the final product
Value is added to the first summation value
In the formula (2).
Taking the bank transaction mentioned in steps S101 and S102 as an example, summing all the elements in the three-dimensional transaction matrix S to obtain a first sum value
In some embodiments, the obtained first summation value is averaged through the time set and the user set to obtain a first dense subgraph abnormal value
As shown in the following formula (3):
wherein the content of the first and second substances,
is a set of transaction times that are,
is a set of users who transfer money,
is a collection of users that are to be paid,
is a first summation value;
taking the bank transaction mentioned in steps S101 and S102 as an example, the first summation value obtained by averaging the total number of elements in the time set and the user set is used to obtain a first dense subgraph abnormal value
As shown in the following formula (4):
wherein the numerator is a first summation value
And denominators are the total number 10 of elements of the time set element number 2, the transfer user set element number 4 and the receipt user set element number 4.
In some of these embodiments, after the time dimension transaction amount sum matrix and the user dimension transaction amount sum matrix are obtained, an N-ary tree of the time dimension transaction amount sum matrix and the user dimension transaction amount sum matrix is constructed. Optionally, a node and an N-ary tree corresponding to the node are constructed, when other nodes are removed, the node corresponding to the node is updated, the node corresponding to the minimum element can be found more conveniently and rapidly by searching the matrix in the tree construction mode, the calculation efficiency is improved, and in addition, the node corresponding to the minimum element can also be found in a direct table searching modeFind the smallest element in the matrix. Preferably, the matrix of transaction sums over a time dimension
Constructing a binary tree by using the matrix, and constructing a transaction sum matrix of the dimensions of the transfer users
Constructing a quadtree, when removed
When the second element in the matrix is 0, updating the score corresponding to the node to obtain
，
And
。
it should be noted that the steps illustrated in the above-described flow diagrams or in the flow diagrams of the figures may be performed in a computer system, such as a set of computer-executable instructions, and that, although a logical order is illustrated in the flow diagrams, in some cases, the steps illustrated or described may be performed in an order different than here.
The embodiment also provides a system for dense subgraph detection based on time series, which is used for implementing the above embodiments and preferred embodiments, and the description of the system is omitted. As used hereinafter, the terms "module," "unit," "subunit," and the like may implement a combination of software and/or hardware for a predetermined function. Although the means described in the embodiments below are preferably implemented in software, an implementation in hardware, or a combination of software and hardware is also possible and contemplated.
Fig. 2 is a block diagram of a dense subgraph detection system based on time series according to an embodiment of the present application, and as shown in fig. 2, the system includes a construction module 21, a calculation module 22, and an output module 23:
a building module 21, configured to build a three-dimensional transaction matrix, a time set, and a user set based on transaction data, where dimensions of the three-dimensional transaction matrix include: transaction time and user, elements of the three-dimensional transaction matrix include: a transaction amount; the calculation module 22 is used for calculating a transaction sum matrix of a time dimension and a transaction sum matrix of a user dimension according to the three-dimensional transaction matrix, summing transaction sums in the elements to obtain a first sum value, and averaging the first sum value through the time set and the user set to obtain a first dense subgraph abnormal value; and the output module 23 is configured to iteratively calculate and update the dense subgraph abnormal value through a greedy algorithm, record the maximum dense subgraph abnormal value in the updated dense subgraph abnormal value, and output a time set and a user set corresponding to the maximum dense subgraph abnormal value as detection results.
Through the system, compared with the prior art that the fund transaction abnormity detection algorithm is based on users, commodities and abnormity consideration between the users, the feedback result of the fund abnormal transaction cannot be obtained through real-time detection, the problems of large calculation amount and long consumed time exist, the time dimension is added in the embodiment, when the characteristics are selected, the time dimension is automatically segmented, the abnormity information is automatically screened out, and the detection accuracy of the abnormity group is improved; the calculation module 22 calculates a time-dimension transaction sum matrix and a user-dimension transaction sum matrix according to the three-dimensional transaction matrix, sums the transaction amounts in the elements to obtain a first sum value, and averages the first sum value through a time set and a user set to obtain a first dense subgraph abnormal value; compared with the prior art in which subgraph is solved by violence, the output module 23 needs time complexity of
This example screens through a greedy algorithm
、
And
the minimum value in the sub-graph is deleted and then the sub-graph is solved, and the complexity of the computation time is
The method has the advantages that the complexity of linear time is obviously reduced, the calculation time is greatly reduced, the calculation of a large amount of data is greatly advantageous, the calculation time and memory resources can be effectively saved, and the calculation speed is increased. In addition, the abnormal intensive group with high-risk operation can be effectively screened out through the iterative computation, so that the monitoring of abnormal users and abnormal operation by financial institutions such as banks and the like is facilitated, and the financial risk is reduced.
The present invention will be described in detail with reference to the following application scenarios.
The invention aims to provide a method and a system for dense subgraph detection based on a time sequence, and the flow steps of the technical scheme for dense subgraph detection based on the time sequence in the embodiment comprise:
s1, taking bank transaction as an example, as shown in Table 1, a three-dimensional transaction matrix S and a time set are constructed
User collection of account transfers
And collection of payee users
；
S2, calculating the transaction amount according to the transaction time and the user in the three-dimensional transaction matrix to obtain a transaction amount sum matrix of time dimension
Transaction amount sum matrix of transfer user dimension
Transaction sum matrix with payee dimension
And summing all elements in the three-dimensional transaction matrix S to obtain a first summation value
Through time aggregation
User collection of account transfers
And collection of payee users
For the first summation value
Averaging to obtain initial dense subgraph abnormal values
；
S3, obtaining
，
，
The smallest element, if there is the same smallest element, randomly selects one. Selecting
Second inElement 0, get the minimum value
；
S4, due to
The second element in the list corresponds to transfer user 1, so that the transfer users are collected
The second element in the solution is screened out to obtain a new
, 
Invariably, FIG. 3 is a schematic diagram of the elements of the screening matrix according to an embodiment of the application, as shown in FIG. 3, due to the set of transfer users
The second element 1 in (a) is screened out, thus the three-dimensional transaction matrix S neutralizes
All elements concerned are absent and should be removed;
s5, passing through the minimum value
Recalculating to obtain a second sum average
Through a new set of transfer users
Constant, and constant
For the second summation valueLine averaging to obtain updated dense subgraph abnormal value
S6, recalculating the three-dimensional transaction matrix S and dividing the three-dimensional transaction matrix S into S matrices
All rows in (1) are set to 0, i.e.
And then recalculated according to S3
，
，
；
S7, judgment
，
，
Whether or not there is an empty set, e.g.
If not, continuing to execute S3, and if yes, executing S8;
s8, recording the maximum dense subgraph abnormal value obtained in the iterative computation after the iteration is finished, wherein the maximum dense subgraph abnormal value is determined by judging conditions, namely the updated dense subgraph abnormal value is obtained in the iterative computation
Comparison of
And
if the numerical value in between
Is greater than
Then remain updated
E.g., comparing the initial dense subgraph outliers obtained in step S2
And the new dense subgraph abnormal value obtained by updating in the step S5
The numerical value in between, because
Greater than initially
Is thus recorded
The iterative comparison is carried out until the iterative computation from S3 to S7 is finished, and the record retains the final value which is the maximum dense subgraph abnormal value
That is, the final output risk score is obtained, wherein the transfer user set corresponding to the maximum dense subgraph abnormal value
Set of payee users
And time aggregation
Is the exception group that is ultimately output.
Results in the above example:
；
；
；
(ii) a That is, user 0 given 1, 2, 3 transfers at time 0, i.e., 10, is an unusually dense group with a high risk score of 5.4.
The present embodiment also provides an electronic device comprising a memory having a computer program stored therein and a processor configured to execute the computer program to perform the steps of any of the above method embodiments.
Optionally, the electronic apparatus may further include a transmission device and an input/output device, wherein the transmission device is connected to the processor, and the input/output device is connected to the processor.
In addition, in combination with the method for dense subgraph detection based on time series in the above embodiments, the embodiments of the present application may provide a storage medium to implement. The storage medium having stored thereon a computer program; the computer program, when executed by a processor, implements any one of the methods of time-series based dense subgraph detection in the above embodiments.
In one embodiment, fig. 4 is a schematic diagram of an internal structure of an electronic device according to an embodiment of the present application, and as shown in fig. 4, there is provided an electronic device, which may be a server, and its internal structure diagram may be as shown in fig. 4. The electronic device includes a processor, a memory, a network interface, and a database connected by a system bus. Wherein the processor of the electronic device is configured to provide computing and control capabilities. The memory of the electronic equipment comprises a nonvolatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of an operating system and computer programs in the non-volatile storage medium. The database of the electronic device is used for storing data. The network interface of the electronic device is used for connecting and communicating with an external terminal through a network. The computer program is executed by a processor to implement a method of dense subgraph detection based on time series.
Those skilled in the art will appreciate that the configuration shown in fig. 4 is a block diagram of only a portion of the configuration associated with the present application, and does not constitute a limitation on the electronic device to which the present application is applied, and a particular electronic device may include more or less components than those shown in the drawings, or combine certain components, or have a different arrangement of components.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by hardware instructions of a computer program, which can be stored in a non-volatile computer-readable storage medium, and when executed, can include the processes of the embodiments of the methods described above. Any reference to memory, storage, database, or other medium used in the embodiments provided herein may include non-volatile and/or volatile memory, among others. Non-volatile memory can include read-only memory (ROM), Programmable ROM (PROM), Electrically Programmable ROM (EPROM), Electrically Erasable Programmable ROM (EEPROM), or flash memory. Volatile memory can include Random Access Memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms such as Static RAM (SRAM), Dynamic RAM (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDRSDRAM), Enhanced SDRAM (ESDRAM), Synchronous Link DRAM (SLDRAM), Rambus Direct RAM (RDRAM), direct bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).
It should be understood by those skilled in the art that various features of the above-described embodiments can be combined in any combination, and for the sake of brevity, all possible combinations of features in the above-described embodiments are not described in detail, but rather, all combinations of features which are not inconsistent with each other should be construed as being within the scope of the present disclosure.
The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.
Claims (10)
1. A method of dense subgraph detection based on time series, the method comprising:
constructing a three-dimensional transaction matrix, a time set and a user set, wherein the dimensionality of the three-dimensional transaction matrix comprises the following steps: transaction time and user, the elements of the three-dimensional transaction matrix comprising: a transaction amount;
calculating to obtain a time-dimension transaction sum matrix and a user-dimension transaction sum matrix according to the three-dimensional transaction matrix, and summing the transaction sums in the elements to obtain a first sum value;
averaging the first summation value through the time set and the user set to obtain an initial dense subgraph abnormal value;
and iteratively calculating and updating the dense subgraph abnormal value through a greedy algorithm, recording the obtained maximum dense subgraph abnormal value, and outputting a time set and a user set corresponding to the maximum dense subgraph abnormal value as detection results.
2. The method of claim 1, wherein summing the transaction amounts in the element results in a first summed value
：
Wherein the content of the first and second substances,
is a set of transaction times that are,
is a set of users who transfer money,
is a collection of payee users, S is a three-dimensional transaction matrix,
is the empirical anomaly score.
3. The method of claim 2, wherein the empirical anomaly score comprises:
the experience anomaly score is related to the transaction time and the user, wherein the transaction is anomalous within a preset time, the experience anomaly score is greater than 0, and when the user is a white list user, the experience anomaly score is less than 0.
4. The method of claim 1, wherein the first summation value is summed over the set of times and the set of usersLine averaging is carried out to obtain an initial intensive subgraph abnormal value
：
Wherein the content of the first and second substances,
is a set of transaction times that are,
is a set of users who transfer money,
is a collection of users that are to be paid,
is the first summation value.
5. The method of claim 1, wherein the iteratively computing and updating the dense subgraph outliers by a greedy algorithm comprises:
acquiring a minimum element in the time-dimension transaction sum matrix and the user-dimension transaction sum matrix to obtain a minimum value;
screening out the corresponding elements of the minimum elements in the time set or the user set to obtain a new time set or a new user set;
calculating to obtain a second summation value through the minimum value, and averaging the second summation value through the new time set and the user set to obtain an updated dense subgraph abnormal value;
and recalculating the three-dimensional transaction matrix, and recalculating the new time-dimension transaction sum matrix and the user-dimension transaction sum matrix through the new three-dimensional transaction matrix.
6. The method of claim 5, wherein after recalculating the transaction sum matrix for the new time dimension and the transaction sum matrix for the user dimension, the method comprises:
judging whether an empty set exists in the transaction sum matrix of the new time dimension and the transaction sum matrix of the user dimension;
in the case where there is an empty set, the iterative computation terminates.
7. The method of claim 1, wherein after obtaining the transaction sum matrix in the time dimension and the transaction sum matrix in the user dimension, the method comprises:
and constructing an N-branch tree of the transaction sum matrix of the time dimension and the transaction sum matrix of the user dimension.
8. A system for dense subgraph detection based on time series, the system comprising:
the construction module is used for constructing a three-dimensional transaction matrix, a time set and a user set, wherein the dimensionality of the three-dimensional transaction matrix comprises the following steps: transaction time and user, the elements of the three-dimensional transaction matrix comprising: a transaction amount;
a calculation module for calculating a time dimension transaction sum matrix and a user dimension transaction sum matrix according to the three-dimensional transaction matrix, and summing the transaction amounts in the elements to obtain a first sum value,
averaging the first summation value through the time set and the user set to obtain an initial dense subgraph abnormal value;
and the output module is used for iteratively calculating and updating the dense subgraph abnormal value through a greedy algorithm, recording the obtained maximum dense subgraph abnormal value, and outputting a time set and a user set corresponding to the maximum dense subgraph abnormal value as detection results.
9. An electronic device comprising a memory and a processor, wherein the memory has stored therein a computer program, and the processor is configured to execute the computer program to perform the method for time-series based dense subgraph detection according to any one of claims 1 to 7.
10. A storage medium, in which a computer program is stored, wherein the computer program is arranged to perform the method for time-series based dense subgraph detection according to any one of claims 1 to 7 when running.
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