CN112988760B - Tensor decomposition-based traffic space-time big data missing completion method - Google Patents
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Abstract
The invention discloses a tensor decomposition-based traffic space-time big data missing completion method, which is characterized in that on the basis of sparse data information acquired by a reconnaissance platform, the sparse data is subjected to reasoning completion by fully utilizing the distribution rule and the variation trend of historical space-time data information, the accuracy and the effectiveness of the completed data information are improved as much as possible, and finally, the target sea area global data information is output in real time to achieve the purpose of sensing the sea area situation in real time.
Description
Technical Field
The invention belongs to the technical field of traffic space-time big data reasoning and completion, and particularly relates to a tensor decomposition-based traffic space-time big data missing and completion method.
Background
In the process of maintenance and law enforcement of the sea police department, data is a core factor influencing and deciding the establishment of action strategies, and the acquisition, updating and processing capabilities of the data determine whether the data can occupy the dominant position of an action site. The enemy and my strength information, sea area meteorological hydrological information and the like acquired by various reconnaissance platforms play a role in the command center of the party in a data form, and how to acquire, process and fuse the large data with multiple sources and various structures and a great variety is the key point of attention in the field of large data in traffic space and time. The information source of the sea area space-time big data technology at the present stage is mainly a water reconnaissance platform, and a large number of reconnaissance platforms comprehensively patrol in the designated sea area, collect various information data in the sailing process and transmit the information data to a command center in real time for subsequent processing and fusion work so as to guarantee real-time grasp of the target sea area space-time data.
However, in practical situations, because the target sea area is usually wide, and the number of reconnaissance platforms is small, the full coverage of the sea area cannot be guaranteed, only some data information in the sea area can be obtained at the same time, and the command center cannot realize real-time global data perception of the target sea area due to other missing data information. In order to improve the condition that a large amount of data values are lost at the same time in the current stage, a space-time big data reasoning and complementing technology needs to be developed urgently, so that a command center can carry out reasoning and complementing on the lost partial data through past historical data and the collected partial data values, and the global real-time data perception of a target sea area is achieved.
Disclosure of Invention
In order to overcome the defects that the existing sea area data sensing technology cannot acquire global data information at the same time and the situation calculation result is low in accuracy, the invention provides a tensor decomposition-based traffic space-time big data missing completion method. The specific technical scheme of the invention is as follows:
a traffic space-time big data missing completion method based on tensor decomposition comprises the following steps:
s1: dividing a target sea area space;
s1-1: taking a square target sea area, dividing the square target sea area into squares with equal size, wherein the side length of each square is 1 nautical mile;
s1-2: filling a target sea area with the grids, setting the target sea area as a rectangular sea area with the width of m nautical miles and the length of n nautical miles, wherein the target sea area can be divided into m multiplied by n grids, representing single data information in a single grid by a number, and constructing an m multiplied by n dimensional data matrix in the target sea area by each data type;
s1-3: after the construction is successful, constructing x m multiplied by n rectangular grids in every x data categories in the target sea area, wherein x m multiplied by n dimensional data matrixes are correspondingly arranged;
s2: situation awareness data integration;
the data information collected in the target sea area is transmitted back to a command center in real time, the collected information is filled into a data matrix by taking each square as a minimum area, each 12-hour time slice is taken, the data information in the same time slice is calculated to obtain a data matrix, and if the data information of k time slices exists, k x m x n-dimensional data matrices are obtained;
s3: constructing a situation data tensor;
constructing k × X m × n dimensional data matrices obtained by calculation in step S2 into a four dimensional tensor, where the first dimension is a data category dimension, and the first dimension is a time dimension by taking X data categories, that is, a four dimensional tensor is composed of X three dimensional tensors, and a three dimensional tensor composed of k m × n dimensional sparse data matrices can be formed by k sequential time slices, so as to finally form a four dimensional spatio-temporal data tensor X;
s4: taking the three-dimensional tensor of the ith data category in X as
Wherein i is more than or equal to 1 and less than or equal to x; for all
The first dimension of the x-th data type is sliced from 1 to 7 to obtain data information of the x-th data type from the 1 st time slice to the 7 th time slice, and the data information is recorded as a three-dimensional tensor
；
S5: decomposing tensor data;
for three-dimensional tensor
The decomposition is carried out, wherein,
，
a three-dimensional real number tensor representing 7 x m x n; according to the three-dimensional tensor decomposition formula:
s6: optimizing tensor data;
adding a regularization term to the decomposed expression of step S5
All elements of D are 1; the tensor decomposition becomes:
Designing a loss function:
wherein the content of the first and second substances,
f norm of the number of fingers will
The index set of the observed elements is noted as
Let us order
Represents an action on
Is defined as:
wherein the content of the first and second substances,
representing an element with three-dimensional tensor coordinates (i, j, k), wherein i and j are numerical values of two dimensions respectively;
a random gradient descent method is used, the specific values of the elements of the regular term D are adjusted in a self-adaptive manner through cyclic calculation, and finally the loss function F (D) reaches the global minimum value;
s7: will three-dimensional tensor
Sequentially extending backward in time dimension for a time slice, taking as
Repeating the step S5 and the step S6 to realize fine adjustment of the regular term D on the value of each element, and repeating the same operation until the calculation is completed
Finally obtaining a regular term D with the best completion effect after optimization;
s8: completing the situation data in real time;
s8-1: repeating the steps S4 to S7 for the three-dimensional tensors of other data categories except the ith data category in the X to obtain X different regular terms;
s8-2: each time the command center receives data information in a new time slice, the three-dimensional tensor corresponding to each data category is extended by one time slice in the time dimension, and the data tensor after final completion is obtained through repeated circulation;
s8-3: and further calculating and processing the supplemented data tensor to obtain the universe real-time situation of the whole target sea area.
Preferably, the data categories in step S2 include the number of my vessels, the number of enemy vessels, the average wave height, the average wind power, the wind direction, and the precipitation in the area.
The invention has the beneficial effects that:
1. the method adopts a tensor completion method to complete the sparse data information, and the tensor has a time dimension, so that the historical data information is fully considered in the tensor completion process, the distribution rule and the variation trend of the historical data information are used for guiding the sparse data information completion at the current moment, and the accuracy and the effectiveness of the completed data tensor are improved.
2. The regular term is added in the tensor decomposition process, so that the overfitting phenomenon in the historical spatiotemporal data learning process can be effectively avoided, the generalization capability of the whole method is greatly improved, and more accurate results can be obtained when the obtained brand new data information is subjected to completion work.
3. The method designs a new loss function aiming at the learning process of historical space-time data, can more effectively evaluate the error between the data obtained after tensor decomposition completion and the original data, and minimizes the error between the completed data obtained after the loss function is minimized and the original data, so that the final result error of the integral tensor decomposition completion method is smaller, and the effect is better.
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In order to illustrate embodiments of the present invention or technical solutions in the prior art more clearly, the drawings which are needed in the embodiments will be briefly described below, so that the features and advantages of the present invention can be understood more clearly by referring to the drawings, which are schematic and should not be construed as limiting the present invention in any way, and for a person skilled in the art, other drawings can be obtained on the basis of these drawings without any inventive effort. Wherein:
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
In order that the above objects, features and advantages of the present invention can be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings. It should be noted that the embodiments of the present invention and features of the embodiments may be combined with each other without conflict.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced in other ways than those specifically described herein, and therefore the scope of the present invention is not limited by the specific embodiments disclosed below.
As shown in fig. 1, a tensor decomposition-based traffic spatiotemporal big data missing completion method includes the following steps:
s1: dividing a target sea area space;
s1-1: taking a square target sea area, dividing the square target sea area into squares with equal size, wherein the side length of each square is 1 nautical mile;
s1-2: filling a target sea area with the grids, setting the target sea area as a rectangular sea area with the width of m nautical miles and the length of n nautical miles, wherein the target sea area can be divided into m multiplied by n grids, and representing single data information in a single grid by using a number, so that each data type is constructed into an m multiplied by n dimensional data matrix in the target sea area, and subsequent processing is facilitated;
s1-3: after the construction is successful, constructing x m multiplied by n rectangular grids in every x data categories in the target sea area, wherein x m multiplied by n dimensional data matrixes are correspondingly arranged;
s2: situation awareness data integration;
the data information collected in the target sea area is transmitted back to a command center in real time, the collected information is filled into a data matrix by taking each square as a minimum area, each 12 hour is taken as a time slice, the data information in the same time slice is calculated to obtain a data matrix, the obtained matrix is a sparse matrix because the global data information of the target sea area cannot be obtained in 12 hours, most of the data in the squares are missing, and k x m x n dimensional data matrices are obtained if the data information of k time slices exists;
s3: constructing a situation data tensor;
constructing k × X m × n dimensional data matrices obtained by calculation in step S2 into a four dimensional tensor, where the first dimension is a data category dimension, and the first dimension is a time dimension by taking X data categories, that is, a four dimensional tensor is composed of X three dimensional tensors, and a three dimensional tensor composed of k m × n dimensional sparse data matrices can be formed by k sequential time slices, so as to finally form a four dimensional spatio-temporal data tensor X;
s4: taking the three-dimensional tensor of the ith data category in X as
Wherein i is more than or equal to 1 and less than or equal to x; for all
The first dimension of the x-th data type is sliced from 1 to 7 to obtain data information of the x-th data type from the 1 st time slice to the 7 th time slice, and the data information is recorded as a three-dimensional tensor
；
S5: decomposing tensor data;
for three-dimensional tensor
The decomposition is carried out, wherein,
，
a three-dimensional real number tensor representing 7 x m x n; according to the three-dimensional tensor decomposition formula:
s6: optimizing tensor data;
adding to the decomposed equation of step S5Upper regularization term
All elements of D are 1; the tensor decomposition becomes:
recalculating the obtained H, A, B, C and D according to the formula to obtain the complemented three-dimensional tensor
；
Designing a loss function:
wherein the content of the first and second substances,
f norm of the number of fingers will
The index set of the observed elements is noted as
Let us order
Represents an action on
Is defined as:
wherein the content of the first and second substances,
representing an element with three-dimensional tensor coordinates (i, j, k), wherein i and j are numerical values of two dimensions respectively;
a random gradient descent method is used, the specific values of the elements of the regular term D are adjusted in a self-adaptive manner through cyclic calculation, and finally the loss function F (D) reaches the global minimum value;
s7: will three-dimensional tensor
Sequentially extending backward in time dimension for a time slice, taking as
Repeating the step S5 and the step S6 to realize fine adjustment of the regular term D on the value of each element, and repeating the same operation until the calculation is completed
Finally obtaining a regular term D with the best completion effect after optimization;
s8: completing the situation data in real time;
s8-1: repeating the steps S4 to S7 for the three-dimensional tensors of other data categories except the ith data category in the X to obtain X different regular terms;
s8-2: each time the command center receives data information in a new time slice, the three-dimensional tensor corresponding to each data category is extended by one time slice in the time dimension, and the data tensor after final completion is obtained through repeated circulation;
s8-3: and further calculating and processing the supplemented data tensor to obtain the universe real-time situation of the whole target sea area.
In some embodiments, the data categories in step S2 include the number of my vessels, the number of enemy vessels, the average wave height, the average wind, the wind direction, and the precipitation within the area.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (2)
1. A traffic space-time big data missing completion method based on tensor decomposition is characterized by comprising the following steps:
s1: dividing a target sea area space;
s1-1: taking a square target sea area, dividing the square target sea area into squares with equal size, wherein the side length of each square is 1 nautical mile;
s1-2: filling a target sea area with the grids, setting the target sea area as a rectangular sea area with the width of m nautical miles and the length of n nautical miles, wherein the target sea area can be divided into m multiplied by n grids, representing single data information in a single grid by a number, and constructing an m multiplied by n dimensional data matrix in the target sea area by each data type;
s1-3: after the construction is successful, constructing x m multiplied by n rectangular grids in every x data categories in the target sea area, wherein x m multiplied by n dimensional data matrixes are correspondingly arranged;
s2: situation awareness data integration;
the data information collected in the target sea area is transmitted back to a command center in real time, the collected information is filled into a data matrix by taking each square as a minimum area, each 12-hour time slice is taken, the data information in the same time slice is calculated to obtain a data matrix, and if the data information of k time slices exists, k x m x n-dimensional data matrices are obtained;
s3: constructing a situation data tensor;
constructing k × X m × n dimensional data matrices obtained by calculation in step S2 into a four dimensional tensor, where the first dimension is a data category dimension, and the first dimension is a time dimension by taking X data categories, that is, a four dimensional tensor is composed of X three dimensional tensors, and a three dimensional tensor composed of k m × n dimensional sparse data matrices can be formed by k sequential time slices, so as to finally form a four dimensional spatio-temporal data tensor X;
s4: taking the three-dimensional tensor of the ith data category in X as
Wherein i is more than or equal to 1 and less than or equal to x; for all
The first dimension of the x-th data type is sliced from 1 to 7 to obtain data information of the x-th data type from the 1 st time slice to the 7 th time slice, and the data information is recorded as a three-dimensional tensor
；
S5: decomposing tensor data;
for three-dimensional tensor
The decomposition is carried out, wherein,
，
a three-dimensional real number tensor representing 7 x m x n; according to the three-dimensional tensor decomposition formula:
s6: optimizing tensor data;
adding a regularization term to the decomposed expression of step S5
All elements of D are 1; the tensor decomposition becomes:
Designing a loss function:
wherein the content of the first and second substances,
f norm of the number of fingers will
Of the elements observed inIndex set is marked as
Let us order
Represents an action on
Is defined as:
wherein the content of the first and second substances,
representing an element with three-dimensional tensor coordinates (i, j, k), wherein i and j are numerical values of two dimensions respectively;
a random gradient descent method is used, the specific values of the elements of the regular term D are adjusted in a self-adaptive manner through cyclic calculation, and finally the loss function F (D) reaches the global minimum value;
s7: will three-dimensional tensor
Sequentially extending backward in time dimension for a time slice, taking as
Repeating the step S5 and the step S6 to realize fine adjustment of the regular term D on the value of each element, and repeating the same operation until the calculation is completed
Finally obtaining a regular term D with the best completion effect after optimization;
s8: completing the situation data in real time;
s8-1: repeating the steps S4 to S7 for the three-dimensional tensors of other data categories except the ith data category in the X to obtain X different regular terms;
s8-2: each time the command center receives data information in a new time slice, the three-dimensional tensor corresponding to each data category is extended by one time slice in the time dimension, and the data tensor after final completion is obtained through repeated circulation;
s8-3: and further calculating and processing the supplemented data tensor to obtain the universe real-time situation of the whole target sea area.
2. The tensor decomposition-based traffic space-time big data missing completion method as claimed in claim 1, wherein the data categories in the step S2 include the number of my vessels, the number of enemy vessels, the average wave height, the average wind power, the wind direction and the precipitation in the area.
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