CN109684314A - A kind of wireless sensor network missing value estimation method based on space structure - Google Patents
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Abstract
The wireless sensor network missing value estimation method based on space structure that the invention discloses a kind of, belongs to wireless sensor network field.The present invention is while carrying out data recovery, the temporal association of WSNs is considered not only, has the characteristics that temporal correlation in conjunction with sensor node data, missing value estimation is carried out to data come the solution space of constraint matrix completion by way of increasing regularization term, the present invention is based on the constraints of the space structure of WSNs, no matter how consecutive miss value changes, and the present invention can have preferable accuracy rate and stability, can significantly improve the accuracy of data recovery.
Description
Technical field
The invention belongs to wireless sensor network fields, more specifically to a kind of wireless biography based on space structure
Sensor network missing value estimation method.
Background technique
Wireless sensor network (Wireless Sensor Networks, WSNs) is a kind of completely new acquisition of information and place
Reason technology is used widely in numerous areas such as military affairs, environmental monitoring, disaster relief, Industry Control, smart homes, is
The research emphasis of message area.Wireless sensor node is generally exposed directly in external environment, weather conditions, sensor component
Self stability, human factor and other reasons can all lead to the frequent disconnecting of communication link, so as to cause collected perception number
The phenomenon that according to there is loss of data or data exception in the transmission.
In general, conventional needle includes three classes to the processing method of missing data: first is that directly deleting missing data；Second is that not right
Data carry out any processing, directly use current algorithm；Third is that being filled to missing data.Although first kind method letter
Single, easy-to-use, but with the arrival of " big data era ", the sparse characteristic of data is increasingly severe, missing data amount is also gradually
Increase, abandon missing data item not only influence the global feature of data, or even can seriously affect data mining as a result, making to operate
Personnel do the judgement to make mistake, cause great artificial loss.And the second class method, then it must face traditional data mining algorithm
It carries out handling this status both for complete data, needs to carry out classic algorithm to be allowed to be suitable for lacking after accordingly modifying
Data are lost, more importantly this modification task is heavy, what some even cannot achieve.Although in addition, occurring at present
Some parsers for fragmentary data, but usually there is the problems such as algorithm complexity is high, treatment effect is bad.Therefore right
Missing data be filled be fragmentary data processing most ideal method.So-called fragmentary data filling refers to passing through other
Known auxiliary information finds out one or more predicted value closest to missing data, Zhi Houyong with ad hoc approach or model
Predicted value is filled missing data, obtains complete data set, and makes data set that should level off to raw data set as far as possible.
In recent years, researcher proposes a series of model and algorithm for the data recovery problem of WSNs, and obtains
It can become effective.As Nan proposes the sensing data restoration methods excavated based on dependency rule；Li et al. people proposes based on physics
With the sensing data restoration methods of statistical model；2010, Pan Liqiang et al. proposed the sensing data based on temporal and spatial correlations and estimates
Calculating method.It is noted that having stronger correlation, such as temperature sensor and light between the adjacent time point of WSNs data
According to there is a degree of relevance between the surrounding time point of intensity sensor, and this smooth evolution on a timeline
Effect can be typical low-rank structure in mathematical model.In general, this low-rank structure can pass through in WSN data
The method of matrix decomposition obtain using, as rich et al. the data that just WSNs is collected into using the method for Non-negative Matrix Factorization of coroner into
Row compression, and achieve good effect.It is to be noted, however, that in addition to sensing there are other than temporal association in WSNs
There is also being associated with spatially between device node and node, for example, the sensor being positioned adjacent in temperature sensor compared to interval compared with
Remote sensor, temperature changing regularity will be increasingly similar, therefore when shortage of data occurs in this temperature sensor, neighbouring
The numerical value of sensor obviously has more reference role.
Matrix complementing method is the effective ways for estimating missing values, but is not yet led at present in view of the continuity between data
Cause evaluated error larger.Therefore, it is the integrality for guaranteeing data in wireless sensor network, is deposited in the transmission for perception data
The loss of data the problem of, structural constraint spatially how is combined, carrying out estimation to missing values is the one of current urgent need to resolve
Big problem.
Summary of the invention
1. technical problems to be solved by the inivention
There is loss of data perception data in the present invention, provide a kind of based on space structure in the transmission
Wireless sensor network missing value estimation method, the present invention have considered not only the WSNs time while carrying out data recovery
On association, have the characteristics that temporal correlation in conjunction with sensor node data, constrained by way of increasing regularization term
The solution space of matrix completion carries out missing value estimation to data.
2. technical solution
In order to achieve the above objectives, technical solution provided by the invention are as follows:
A kind of wireless sensor network missing value estimation method based on space structure, steps are as follows:
Step 1, the sparsity using singular values of a matrix recover original matrix according to known matrix Partial Elements；
Structural information in sensor network data is converted into graph structure mathematically by step 2, is based on structural constraint pair
The original matrix of step 1 carries out matrix completion, increases regularization term, and the solution space of constraint matrix completion obtains matrix missing values
Optimal solution.
Further, the step of step 1 is as follows:
Partial data M in step 1.1, given sparse data set Ωij:(i,j)∈Ω∈{1,...,m}×{1,...,
N }, look for out m × n value of matrix M, MijSensing data is abstracted into a low-rank matrix by ∈ M, and low-rank matrix completion is then
By solving completion of the minimization problem realization to unknown element, the matrix completion problem description of standard are as follows:
Wherein, AΩ(X)=(Mij∈Ω) indicate observing matrix M；
Step 1.2 replaces rank of matrix with the nuclear norm of matrix, and formula is as follows:
Wherein, σkFor k-th of the singular value arranged from small to large；
According to above formula, the formula in step 1.1 relaxes are as follows:
When observing data by influence of noise, above formula is then are as follows:
Wherein, γnFor coefficient, coefficient l is determined according to noise class.
Further, using least square method to the formula in step 1.2
It is fitted.
Further, the step of step 2 is as follows:
Step 2.2, by the abstract mathematical model being as follows of sensor network: give undirected weighted network G=(V, E,
W), wherein vertex V={ 1 ..., n }, sideIt is indicated by nonnegative curvature matrix W.For a matrix, column
Vector is m dimensional vector, is expressed as X=(x1,...,xn)；Its row vector is n-dimensional vector, is expressed as X=((x1)T,...,(xm)T)；
Step 2.3 defines train value x1,...,xnFor the value of vertex V, when (j, j ') ∈ E is then smooth, it is assumed that meet xj≈xj′,
That is:
Wherein, L=D-W,For the Laplacian Matrix for scheming G；
Step 2.4, according to above formula, when the observation data in step 1.2 are by influence of noise, the matrix completion of standard is asked
Topic will be converted as follows:
Further, in the step 2.4 formula separable function are as follows:
Wherein, F (X)=γn||X||*,γn、γr、γc
It is coefficient, Augmented Lagrangian Functions are as follows:
Further, using alternating direction multipliers method in the step 2.4 can not differential term solve.
Further, the alternating direction multipliers method is iterated solution, the iteration by variable alternating update mode
Solving method is as follows:
Zk+1=Zk+ρ(Xk+1-Yk+1)
FormulaClosed approximation solution be
Wherein, U, V, Λ are respectively the singular value decomposition of H, are expressed as H=U Λ VT, and H is H=Yk-ρ-1Zk；According to described
Iterative solution method, formula conversion in step 2.4 are as follows:
Wherein, H=Xk+1+ρ-1Zk
Above-mentioned formula is iterated, the optimal solution of matrix missing values is obtained.
3. beneficial effect
Compared with existing well-known technique, the invention has the benefit that
(1) a kind of wireless sensor network missing value estimation method based on space structure of the invention, in classical matrix
On the basis of low-rank decomposition, the structure feature constraint of sensor network is increased, to estimate perception data missing values.
When carrying out data recovery by matrix complementing method, based on network structure, addition time relationship is constraint, is considered not only
WSNs temporal association, and it is added to structural constraint spatially, the present invention can significantly improve the standard of data recovery
Exactness；
(2) a kind of wireless sensor network missing value estimation method based on space structure of the invention, it is contemplated that perception
The missing peak time of data is the principal element for influencing algorithm performance, in order to which test data missing time interval is to algorithm performance
Influence, the present invention test time interval be 1~30min algorithm performance, it is found that the different data missing peak time
Under, the error of inventive algorithm is smaller, so missing time interval does not produce bigger effect the performance of inventive algorithm,
This is that the present invention considers the spatial structure characteristic of WSNs, and the accuracy rate of algorithm also more relies on the spatial coherence of data.
In addition, the missing value estimation precision of temperature can't further increase after interval time being more than 15min, illustrate that the present invention exists
After sample size reaches 30min, as a result tend towards stability；
(3) a kind of wireless sensor network missing value estimation method based on space structure of the invention, space structure
Wireless sensor network missing value estimation method, it is contemplated that consecutive miss value quantity is to influence another factor of algorithm performance.
The present invention compares the performance of each algorithm when perception data consecutive miss number is 1 to 30.It can be found that with consecutive miss value
The increase error of quantity also increases, this is because the present invention needs the non-missing data in view of missing values adjacent to the moment.When scarce
The time interval that mistake is worth non-missing perception data adjacent thereto increases, between missing values non-missing perception data adjacent thereto
Temporal correlation reduce, so that the evaluated error of algorithm increases.Similarly, the reduction of the degree of correlation also results in inventive algorithm
Accuracy rate reduce, but the present invention is constrained with the space structure of WSNs, therefore no matter how consecutive miss value changes, the present invention
Can have preferable accuracy rate and stability.
Detailed description of the invention
Fig. 1 is data set experiment scene figure provided by the invention；
Fig. 2 is that different missing time interval arithmetic performances provided by the invention compare figure；
Algorithm performance compares figure when Fig. 3 is different consecutive miss value quantity provided by the invention.
Specific embodiment
In order to make the object, technical scheme and advantages of the embodiment of the invention clearer, below in conjunction with the embodiment of the present invention
In attached drawing, technical scheme in the embodiment of the invention is clearly and completely described.Wherein, described embodiment is
A part of the embodiment of the present invention, instead of all the embodiments.Therefore, below to the embodiment of the present invention provided in the accompanying drawings
Detailed description be not intended to limit the range of claimed invention, but be merely representative of selected embodiment of the invention.
A kind of wireless sensor network missing value estimation method based on space structure of the invention, the steps include:
Step 1, matrix completion, the target of matrix completion are that the matrix reconstruction lacked from element goes out original full matrix.
In many particular problems, data often carry out tissue with a matrix type.But due to originals such as sampling limitation, noise pollutions
The problems such as cause, these matrixes usually face shortage of data, data exception.In order to solve these problems, compressive sensing theory is expanded
Exhibition is to space of matrices, using the sparsity of singular values of a matrix, the i.e. low-rank of matrix, the case where according to known matrix Partial Elements
Recover original matrix；
Step 2, the matrix completion based on structural constraint, low-rank structure mean to exist between the row and column of matrix M linear
Correlation, but this correlation is not usually structuring.Therefore when matrix M is there are when certain structural relation, we can pass through
The mode for increasing regularization term carrys out the solution space of constraint matrix completion, it is made to be more nearly true value.In the biography that the present invention faces
In sensor network data, the natural structural constraint having spatially, and mathematically, we can be by this structural information
It is expressed as graph structure；
Further, the implementation procedure of step 1 is as follows:
Step 1.1, the matrix completion problem of standard are usually described as: the matrix completion problem of standard is commonly described as: given
Partial data M in sparse data set Ωij: (i, j) ∈ Ω ∈ { 1 ..., m } × { 1 ..., n } looks for out m × n of matrix M
Value, Mij∈M.It is all continuously to record, therefore have very between the data of adjacent time point by sensing data in WSNs data
Strong similitude, this just constitutes a low-rank matrix.Low-rank matrix completion can be realized by solving minimization problem to unknown
The matrix completion problem of the completion of element, standard is commonly described as:
Wherein, AΩ(X)=(Mij∈Ω) indicate observing matrix M.Due to matrix AΩ(X) order is a non-convex function, formula
It (1) is np complete problem.Therefore we need to go the solution of approximation problem using an approximate convex function.
(2) present invention replaces rank of matrix using the nuclear norm of Candes et al. matrix proposed, and is defined asWherein σkFor k-th of the singular value arranged from small to large.Therefore, formula (1) can relax
Are as follows:
If without making an uproar or only comprising Gaussian noise in M, and Ω is evenly distributed and sufficiently large, the minimum value of formula (2) it is unique and
It can match with the minimum value of formula (1), can accurately recover objective matrix Ω.If but observation data are by noise shadow
It rings, there are the data of the remote super normal range (NR) in part, formula (2) is then are as follows:
Formula (3) can regard the matrix completion that can portray noise as, that is, the element observed may contain noise, centainly
The influence that noise can be reduced in degree, is fitted with least square, and does not have to the equality constraint of formula (2).Wherein, γnFor
Coefficient, coefficient l are determined according to noise class, if coefficient l is Frobenius norm:(A of the present inventionΩTo see
The matrix measured, ο are Hadamard product).
(3) because solve non-convex problem be it is very difficult, iterative algorithm is easily ensnared into poor locally optimal solution
Perhaps saddle point or needs, which take a substantial amount of time, can just find out relatively good locally optimal solution.Based on problems,
Salakhutdinov and Srebro is proposed using weighting nuclear normWherein p and q
M row and n column distribution are obeyed respectively for observation data.Nuclear norm is weighted compared with unweighted nuclear norm, promotes significant effect, it can be with
Rapidly converge to locally optimal solution；
Further, the process of the matrix completion in step 2 based on structural constraint are as follows:
(1) assume there is the sensor network being made of n sensor, vertex of each sensor as network passes
Relationship such as energy relationship or topological relation between sensor etc. are then the side of network.In the present invention, we select the simplest
Side of single spatial relationship as network connection.It is assumed that depending on the ranks of matrix M are according to the vertex of figure.In sensor network,
Sensor (i.e. the column of matrix M) is the vertex of network, spatial relationship of the relationship between sensor between sensor.
(2) it is as follows to be abstracted as mathematical model for it: give undirected weighted network G=(V, E, W), wherein vertex V=1 ...,
N }, sideIt is indicated by nonnegative curvature matrix W.For a matrix, column vector is m dimensional vector, is expressed as X
=(x1,...,xn)；Its row vector is n-dimensional vector, is expressed as X=((x1)T,...,(xm)T)。
(3) train value x is defined1,...,xnFor the value of vertex V, if (j, j ') ∈ E smoothly assumes to meet xj≈xj′, it may be assumed that
Wherein,L=D-W is the Laplacian Matrix for scheming G.
(4) it is added these smooth items as regularization term in Matrix Solving problem (using l as Frobenius norm),
(5) containing in above formula can not differential term, it is therefore desirable to by alternating direction multipliers method (Alternating
Direction Method of Multipliers, ADMM) it is solved, ADMM carries out the objective function of former problem of equal value
Several subproblems for being easier to find local solution are decomposed into, are to solve separable convex programming to obtain the global solution of former problem
A kind of simple effective method [10] of problem.
The wherein separable function of formula (5) are as follows:
Wherein, F (X)=γn||X||*,γn、γr、γc
It is coefficient, Augmented Lagrangian Functions are as follows:
(6) wherein F (X)=γn||X||*, G (Y)=l (AΩ(X),AΩ(M))+γrtr(XLXT), by being converted into appeal
Form, ADMM replace update mode by variable and are iterated solution, and main iterative solution method is divided into following three step:
Zk+1=Zk+ρ(Xk+1-Yk+1) (10)
(10) formula (8) has a closed approximation solution:Wherein U, V, Λ are respectively the unusual of H
Value is decomposed, and H=U Λ V is expressed asT, and H is H=Yk-ρ-1Zk.Formula (10) is to find out Yk+1, to minimizeSo formula (5) can be rewritten into:
H=Xk+1+ρ-1Zk.Alternately update is carried out according to above-mentioned steps, can converge to formula (5) after the certain number of iteration
Optimal solution.
(11) optimal solution of matrix missing values thus can be obtained, thus completion sensor network, as a number of vertex
For the network of n, it is ordered as the array function (time series of m dimension) of m dimension.
(1) data introduction
In order to measure the validity of experimental method, the present invention uses Inter Indoor of Intel's Berkeley laboratory
The actual sensor data set (http://db.lcs.mit.edu/labdata/labdata.html) of mesh acquisition is tested,
Fig. 1 is the data set experiment scene.Inter Indoor project is passed in 54 Mica2Dot of indoor deployment of 40m × 30m
Sensor acquires a perception data every 30s.Fig. 1 is data set experiment scene figure.The data sample that Berkeley laboratory is collected
There are eight attributes, including temperature, humidity, illumination and voltage value, date etc..The present invention selects temperature data to test, experiment
Data are shown in Table 1:
The description of 1 Intel's Berkeley laboratory related data of table
Since original perception data is concentrated containing the missing values that can not be restored, needed during the experiment from original
Data acquisition system in select the one piece of data of the node containing less missing values, that is, selecting data with respect to intact part is test number
The average value adjacent to moment perception data is replaced with according to collection, and by wherein missing values, and then forms a complete test data
Collection.
(2) structure matrix constructs
Structure matrix reflection is the compactness contacted between node and node, this compactness is refered in particular in the present invention
It is its natural positional relationship.Because containing respective positions information, position in sensing data of the present invention
The relationship of setting can be embodied by the Euclidean distance in space.It will be appreciated, however, that this distance matrix is the matrix connected entirely, this will
It will increase the noise of the Laplacian Matrix of figure, and then influence the result of optimization.Therefore this distance matrix must be carried out dilute
Thinization processing.
In the present invention, the method that we have selected two kinds of LS-SVM sparseness respectively: (1) threshold method, it will be in distance matrix
Two nodes greater than certain threshold value are considered as there is no connection (it is 0.35 that the present invention, which obtains threshold value), thus only remain node
It is middle that there are the connections of close relation.(2) nearest neighbor method chooses node periphery and connects most close K node according to distance matrix
Building connection, it is important to note that the structure matrix constructed in this way, the degree of each of which node is all k.In addition, optimizing for convenience
On the contrary journey, the structure matrix for the building that the present invention selects not Weight have that connect the connection side be 1, then be 0.
(3) result of implementation
The present invention is also by mentioned algorithm and classical LM (the Linear interpolation based on temporal correlation
Model, LM) algorithm and traditional arest neighbors interpolation method NNI (Nearest Neighbor Interpolation, NNI) reality
Effect is tested to compare.It is missing values by the known temperature data that random labelling test data is concentrated, then distinguish in experiment
Missing values are estimated using three kinds of algorithms, to evaluate the validity of various algorithms.
In view of problem to be solved by this invention be how accurately to estimate missing data, therefore the present invention with algorithm to lack
Standard of the accuracy of mistake value estimation as measure algorithm performance, using the root-mean-square error (Root of estimated value and original value
Mean Square Error, RMSE) as evaluation measurement.RMSE is smaller, and expression restores better to missing data.
Wherein, yitFor true non-missing data value,To assume yitThe estimated value obtained after missing by algorithm, mean
It is then expressed as marking the data for being to carry out estimation and be averaging its residual values to all.
On the one hand, the missing peak time of perception data is the principal element for influencing algorithm performance.In order to which test data lacks
Influence of the time interval to algorithm performance is lost, the present invention tests the algorithm performance that time interval is 1~30min, and Fig. 2 is experiment
As a result.It can be found that the error of inventive algorithm is respectively less than NNI and LM algorithm under the different data missing peak time, so lacking
Time interval is lost there is no producing bigger effect to the performance of inventive algorithm, is that inventive algorithm considers the space of WSNs
Structure feature, the accuracy rate of algorithm also more rely on the spatial coherence of data.In addition, after interval time being more than 15min, temperature
The missing value estimation precision raising effect of degree significantly reduces, illustrate inventive algorithm after sample size reaches 30min, algorithm
As a result it has tended towards stability.
On the other hand, consecutive miss value quantity is to influence another factor of algorithm performance.Present invention experiment compares sense
The performance of primary data consecutive miss number each algorithm when being 1 to 30, Fig. 3 is experimental result.As can be seen from Figure 3, with continuous
The increase of missing values quantity, each Algorithm Error increase.The reason is that, these three algorithms require in view of missing values adjacent to when
The non-missing data carved.When the time interval of missing values non-missing perception data adjacent thereto increases, missing values are adjacent
Non- missing perception data between temporal correlation reduce, so as to cause NNI and LM algorithm evaluated error increase.Equally
Ground, the accuracy rate that the reduction of the degree of correlation also results in inventive algorithm reduces, but inventive algorithm has the space structure of WSNs
Constraint, therefore no matter how consecutive miss value changes, inventive algorithm can have preferable accuracy rate and stability.
Shortage of data problem is the intrinsic problem in sensor network.To reduce missing values to the shadow of wireless sensor network
It rings, the present invention proposes a kind of missing value estimation method based on space structure, on the basis of classical matrix low-rank decomposition, increases
The structure feature of sensor network constrains, to estimate perception data missing values.Pass through what is acquired in actual sensor
The simulation results show estimated on data set using temperature value, this method accuracy with higher and stability.
Schematically the present invention and embodiments thereof are described above, description is not limiting, institute in attached drawing
What is shown is also one of embodiments of the present invention, and actual structure is not limited to this.So if the common skill of this field
Art personnel are enlightened by it, without departing from the spirit of the invention, are not inventively designed and the technical solution
Similar frame mode and embodiment, are within the scope of protection of the invention.
Claims (4)
1. a kind of wireless sensor network missing value estimation method based on space structure, it is characterised in that: steps are as follows:
Step 1, the sparsity using singular values of a matrix recover original matrix according to known matrix Partial Elements；
Structural information in sensor network data is converted into graph structure mathematically by step 2, based on structural constraint to step
1 original matrix recovered carries out matrix completion:
In sensor network, sensor is the vertex of sensor network, space of the relationship between sensor between sensor
Relationship；It is as follows to be abstracted as mathematical model: giving undirected weighted network G=(V, E, W), wherein vertex V={ 1 ..., n },
SideIt is indicated by nonnegative curvature matrix W；For a matrix, column vector is m dimensional vector, is expressed as X=
(x1,...,xn)；Its row vector is n-dimensional vector, is expressed as X=((x1)T,...,(xm)T)；Define train value x1..., xj...,
xnFor the value of vertex V, if (j, j') ∈ E is obtained:
Wherein,L=D-W is the Laplacian Matrix for scheming G；
It is added smooth item obtained above as regularization term in Matrix Solving problem:
Solution obtains the optimal solution of matrix missing values, completion sensor network.
2. wireless sensor network missing value estimation method according to claim 1, it is characterised in that: the step 1
Steps are as follows:
Partial data M in step 1.1, given sparse data set Ωij: (i, j) ∈ Ω ∈ { 1 ..., m } × { 1 ..., n } is looked for
Seek out m × n value of matrix M, MiijSensing data is abstracted into a low-rank matrix by ∈ M, real by solving minimization problem
Now to the completion of unknown element, the matrix completion problem of standard is described are as follows:
Wherein, AΩ(X)=(Mij∈Ω) indicate observing matrix M；
Step 1.2 replaces rank of matrix with the nuclear norm of matrix, and formula is as follows:
Wherein, σkFor k-th of the singular value arranged from small to large；
According to above formula, the formula in step 1.1 relaxes are as follows:
When observing data by influence of noise, above formula is then are as follows:
Wherein, γnFor coefficient, coefficient l is determined according to noise class.
3. wireless sensor network missing value estimation method according to claim 2, it is characterised in that: use least square
Method is to the formula in step 1.2It is fitted.
4. wireless sensor network missing value estimation method according to claim 1, it is characterised in that: use alternating direction
Multiplier method in Matrix Solving problem in the step 2 can not differential term solve, obtain separable function are as follows:
Wherein, F (X)=γn||X||*,γn、γr、γcIt is
Coefficient, Augmented Lagrangian Functions are as follows:
Wherein, G (Y)=l (AΩ(X),AΩ(M))+γrtr(XLXT), the alternating direction multipliers method passes through variable alternating update side
Formula is iterated solution, and the iterative solution method is as follows:
Zk+1=Zk+ρ(Xk+1-Yk+1)
FormulaClosed approximation solution be
Wherein, U, V, Λ are respectively the singular value decomposition of H, are expressed as H=U Λ VT, and H is H=Yk-ρ-1Zk；According to the iteration
Solving method converts Matrix Solving problem are as follows:
Wherein, H=Xk+1+ρ-1Zk
Above-mentioned formula is iterated, the optimal solution of matrix missing values is obtained.
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| CN111881413A (en) * | 2020-07-28 | 2020-11-03 | 中国人民解放军海军航空大学 | Multi-source time sequence missing data recovery method based on matrix decomposition |
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