CN103209005A - Hopping sequence prediction system based on graphical model - Google Patents
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Abstract
The invention discloses a hopping sequence prediction system based on a graphical model. The system comprises a preprocessing module, a prediction module and a feedback adjusting module, wherein the preprocessing module is used for removing noise and bandwidth from an intercepted original hopping sequence; the prediction module is connected with the preprocessing module and used for reconstructing a phase space and constructing a prediction model; and the feedback adjusting module is connected with the preprocessing module and the prediction model and used for precision detection, feedback and model adjustment. According to the system, embedded dimension m and time delay phi are solved by adopting a Cao method and an autocorrelation method, and then the phase space is reconstructed; and the Markov boundary of query nodes is learnt on the basis of an improved Microsoft malware protection center (MMPC) algorithm, and then the prediction model is constructed. The embedded dimension m and the time delay phi are two key parameters for reconstructing the phase space, and the parameters acquired by using the autocorrelation method and the Cao method are stable and reliable; and a Bayesian network model is simplified through the Markov boundary, so that the prediction efficiency is high.
Description
Technical field
The invention belongs to the frequency hop sequences electric powder prediction, relate in particular to a kind of frequency hop sequences prognoses system based on graphical model.
Background technology
Existing Chaotic time series forecasting method is, original chaos time sequence is embedded into m dimension phase space, its essence is a plurality of different delay points that utilize certain sequence of points in the original series and it under delay time T, to generate, in the common reconstruct m dimension phase space one point mutually, because it is interrelated that the choosing of time delay τ can be guaranteed between these time delay points, so can utilize Bayesian network to portray this relevance;
Phase space after the reconstruct is expressed as the matrix of a m * n dimension, exists between each row vector to rely on associate feature, the prior art scheme:
(1) with the variable of each row vector as Bayesian network, adopt the K2 algorithm to carry out bayesian network structure learning, and then construct the directed acyclic graph that contains m node, directed acyclic graph is used diagrammatic representation intuitively to relation of interdependence between each row vector in the phase space;
(2) with maximal possibility estimation study Bayesian network parameter, namely determine the conditional probability distribution table at each node place, wherein the probable value in the probability distribution table embodies the dependence intensity between each row vector, and then finishes the structure of bayes predictive model;
(3) phase space after the reconstruct is carried out τ step continuation, the phase space after the continuation is as follows:
To point mutually in future
X (n+l)=[x
N+l, x
N+l+ τ..., x
N+l+ (m-2) τ, x
N+l+ (m-1) τ]
TThe prediction of (1≤l≤τ, n=N-(m-1) τ), be exactly target of prediction be m component x of cenotype point
N+l+ (m-1) τValue because the value of preceding m-1 component of l cenotype point is known, then can be used as the evidence variable, namely
E={X
1=x
n+l,X
2=x
n+l+τ,…,X
m-1=x
n+l+(m-2)τ}。
Obtain maximum a posteriori probability P (X
m=f
iE) Dui Ying value f
i, this is worth f
iBe
Predicted value, again by l≤τ as can be known the maximum predicted step of the Bayesian network forecast model set up of prior art scheme be τ, wherein τ is the time of delay of frequency hop sequences;
(4) more real τ new sequential value is extended for point mutually, and adds in the phase space, updating network parameters is predicted, the circulation of undated parameter goes on again, finishes until prediction;
The research object of prior art scheme is chaos time sequence, and the value number of chaos time sequence is less than 64.When research object is changed into frequency hop sequences, the time delay τ of the C-C method assessment frequency hop sequences in the prior art scheme and embedding window width τ
wConsuming time of a specified duration, unstable result; Utilize Cao method and correlation method to find the solution and embed dimension m and time delay τ, behind phase space reconfiguration, the Bayesian network node number that remains to be learnt equals to embed dimension m, and m 〉=5, node value number equals the frequency hopping code value number of frequency hop sequences, and generally greater than 64, the K2 algorithm in the prior art scheme can't utilize the Bayesian network sample D study bayesian network structure that obtains after the frequency hop sequences reconstruct.。
Summary of the invention
The purpose of the embodiment of the invention is to provide a kind of frequency hop sequences prognoses system based on graphical model, be intended to solve when the value condition of frequency hop sequences for a long time, the C-C method evaluation time postpones τ and embeds window width τ in the prior art
wConsuming time of a specified duration, unstable result, and the problems such as K2 algorithm inefficacy of learning network structure.
The embodiment of the invention is achieved in that a kind of frequency hop sequences prognoses system based on graphical model, it is characterized in that, comprises based on the frequency hop sequences prognoses system of graphical model:
Pretreatment module is used for the original frequency hop sequences of intercepting and capturing is carried out denoising, goes bandwidth etc., chooses one section an amount of frequency hop sequences { x
i, i=1,2 ..., N is as the training set data of model construction, the M of a training set data rear adjacent frequency hopping code as the model testing data;
Prediction module is connected with described pretreatment module, is used for phase space reconstruction and makes up forecast model;
The feedback adjusting module is connected with prediction module with described pretreatment module, is used for accuracy detection, feedback and model adjustment.
Further, phase space reconstruction adopts Cao method and correlation method to find the solution and embeds dimension m and time delay τ.
Further, make up forecast model and adopt Markov border based on the improvement algorithm study query node of MMPC, and the Markov border as Bayes's localized network structure.
Further, described pretreatment module also comprises:
Intercept and capture the frequency hop sequences data collection module of original frequency hop sequences with reconnaissance receiver; Be used for removing the data processing unit of original frequency hop sequences noise, bandwidth etc., be connected with described frequency hop sequences data collection module; The training set data unit that is used for phase space reconstruction and model through normalization obtains is connected with described data processing unit; Be used for the detection model check data unit that precision of prediction detection, feedback and model are adjusted, be connected with described data processing unit; The evidence data cell that is used for prediction through phase space τ step continuation obtains is connected with described training set data unit.
Further, described prediction module also comprises:
The phase space data cell of utilizing training set data study to obtain is connected with described training set data unit; , be connected with described phase space data cell through the Bayesian network unit that partial structurtes are learnt and parameter learning obtains on the phase space reconstruction basis; Utilize the prediction ordered series of numbers unit of Bayesian network model prediction frequency hop sequences, be connected with the evidence data cell with described Bayesian network unit.
Another object of the present invention is to provide a kind of frequency hop sequences Forecasting Methodology based on graphical model, described frequency hop sequences Forecasting Methodology may further comprise the steps:
As the data sample D that is used for Bayesian network study, the scale of data sample D is n;
Step 4, the prediction step η of model=τ, τ are time delay, according to Bayes's aposterior reasoning algorithm, calculate
Wherein the span of l is 1≤l≤η, and namely l is the l time prediction of prediction in the η step prediction, and E (n+l) is query node X
mThe Markov boundary set in the value of each node.When P is maximum, f
iBe exactly x
N+lPredicted value;
Step 5, after every η step prediction finishes, preserve the frequency hopping code of prediction, and model is detected in the data corresponding true frequency hopping code be extended for and put X (n+l) l=1 mutually ..., η, and add in the phase space, updating network parameters forwards step 4 to, finishes until the predicted back of M frequency hopping code of training set data rear adjacent;
Further, the delay values ri of trying to achieve at correlation method
dOn the basis, time delay τ can regulate downwards, and namely the span of time delay τ is 2≤τ≤τ
d
Further, the node number that the Markov border comprises is α, and the span of parameter alpha is 2≤α≤5.
Frequency hop sequences prognoses system based on graphical model of the present invention, embed dimension m and time delay τ by adopting Cao method and correlation method to find the solution, based on the Markov border of the improvement algorithm of MMPC study query node, and then phase space reconstruction and structure forecast model.Embedding dimension m of the present invention and time delay τ are two key parameters of phase space reconfiguration, and correlation method and Cao method make that to try to achieve parameter more reliable and more stable, utilize the Markov border to simplify Bayesian network model, make forecasting efficiency higher.
Description of drawings
Fig. 1 is the structural representation based on the frequency hop sequences prognoses system of graphical model that the embodiment of the invention provides.
Fig. 2 is three inscape schematic diagrames of the Bayesian network that provides of the embodiment of the invention;
Fig. 3 is that the chaos time sequence that the embodiment of the invention provides is mapped to higher-dimension phase space schematic diagram;
Fig. 4 is that the phase space that provides of the embodiment of the invention is as Bayesian network sample D schematic diagram;
Fig. 5 is the figure that predicts the outcome of the Bayesian network forecast model that provides of the embodiment of the invention;
Fig. 6 is the prediction accuracy analogous diagram of the Bayesian network forecast model that provides of the embodiment of the invention.
Embodiment
In order to make purpose of the present invention, technical scheme and advantage clearer, below in conjunction with embodiment, the present invention is further elaborated.Should be appreciated that specific embodiment described herein only in order to explaining the present invention, and be not used in restriction the present invention.
Fig. 1 shows the frequency hop sequences prognoses system structure based on graphical model provided by the invention.For convenience of explanation, only show part related to the present invention.
Frequency hop sequences prognoses system based on graphical model of the present invention comprises:
Pretreatment module is used for the frequency hop sequences of intercepting and capturing is carried out denoising, goes processing such as bandwidth;
Prediction module is connected with described pretreatment module, is used for phase space reconstruction and makes up forecast model;
The feedback adjusting module is connected with prediction module with described pretreatment module, is used for accuracy detection, feedback and model adjustment.
The present invention also provides a kind of frequency hop sequences Forecasting Methodology based on graphical model, and described frequency hop sequences Forecasting Methodology may further comprise the steps:
As the data sample D that is used for Bayesian network study, the scale of data sample D is n;
Step 4, the prediction step η of model=τ, τ are time delay, according to Bayes's aposterior reasoning algorithm, calculate
Wherein the span of l is 1≤l≤η, and namely l is the l time prediction of prediction in the η step prediction, and E (n+l) is query node X
mThe Markov boundary set in the value of each node.When P is maximum, f
iBe exactly x
N+lPredicted value;
Step 5, after every η step prediction finishes, preserve the frequency hopping code of prediction, and model is detected in the data corresponding true frequency hopping code be extended for and put X (n+l) l=1 mutually ..., η, and add in the phase space, updating network parameters forwards step 4 to, finishes until the predicted back of M frequency hopping code of training set data rear adjacent;
As a prioritization scheme of the embodiment of the invention, phase space reconstruction adopts Cao method and correlation method to find the solution and embeds dimension m and time delay τ.Wherein, time delay τ only can influence the Euclidean geometry shape of the attractor of reconstruct when not getting optimum delay, and then the calculating of influence embedding dimension m, and the attractor that does not influence reconstruct does not have the kinetic property of ambiguity ground reaction system.Therefore, the delay values ri of trying to achieve at correlation method
dOn the basis, time delay τ can regulate downwards, and the span of τ is 2≤τ≤τ
d
As a prioritization scheme of the embodiment of the invention, make up forecast model and adopt Markov border based on the improvement algorithm study query node of MMPC, and the Markov border as Bayes's localized network structure.Wherein, the node number that the Markov border of query node comprises is α, parameter alpha and model training data volume close relation, and the parameter alpha value is more big, and it is more big to make up the required model training data volume of Bayesian network model.And in the actual environment of communication countermeasures, need model to accept a spot of frequency hop sequences and can set up forecast model and implement interference prediction.Therefore, regulate the value of parameter alpha according to circumstances, and the span of parameter alpha is 2≤α≤5.
As a prioritization scheme of the embodiment of the invention, pretreatment module also comprises:
Intercept and capture the frequency hop sequences data collection module of original frequency hop sequences with reconnaissance receiver; Be used for removing the data processing unit of original frequency hop sequences noise, bandwidth etc., be connected with described frequency hop sequences data collection module; The training set data unit that is used for phase space reconstruction and model through normalization obtains is connected with described data processing unit; Be used for the detection model check data unit that precision of prediction detection, feedback and model are adjusted, be connected with described data processing unit; The evidence data cell that is used for prediction through phase space τ step continuation obtains is connected with described training set data unit.
As a prioritization scheme of the embodiment of the invention, prediction module also comprises:
The phase space data cell of utilizing training set data study to obtain is connected with described training set data unit; , be connected with described phase space data cell through the Bayesian network unit that partial structurtes are learnt and parameter learning obtains on the phase space reconstruction basis; Utilize the prediction ordered series of numbers unit of Bayesian network model prediction frequency hop sequences, be connected with the evidence data cell with described Bayesian network unit.
Below in conjunction with accompanying drawing and concrete enforcement application principle of the present invention is further described.
As shown in Figure 1, the frequency hop sequences prognoses system based on graphical model of the embodiment of the invention comprises: pretreatment module 1, and the frequency hop sequences of intercepting and capturing is carried out denoising, goes processing such as bandwidth, obtain the frequency hop sequences for model construction and prediction; Pretreatment module 1 comprises: frequency hop sequences data collection module 11, data processing unit 12, training set data unit 13, evidence data cell 14, model testing data cell 15.
Principle of the present invention is:
1, phase space reconfiguration technology:
Research object of the present invention is the original frequency hop sequences of intercepting and capturing in the frequency hopping communications, and existing result of study shows: frequency hop sequences has chaotic characteristic, chaotic characteristic shows as the extreme sensitivity dependence to initial value, bigger linear complexity, the trend irregularities of sequence jump etc., and this is the key issue place that frequency hop sequences is difficult to predict;
Phase space reconfiguration is the first step of analyzing Time Chaotic Dynamical Systems, purpose is to recover chaos attractor in the higher-dimension phase space, because chaos attractor is as one of feature of chaos system, embodying the regularity of chaos system, mean that chaos system finally can fall into a certain specific track, phase space after the reconstruct and original system (producing the Time Chaotic Dynamical Systems of frequency hop sequences) are diffeomorphic, in the higher-dimension phase space, carry out the frequency hop sequences prediction, be equivalent to the prediction in lower dimensional space; Concrete steps are to show complicated pseudo-randomness, chaos characteristic such as non-linear according to frequency hop sequences in the lower dimensional space, utilize Cao method and correlation method in the chaology to choose the best dimension m of embedding and time delay τ respectively, the original power of the frequency hop sequences of phase space reconstruction, and then expansion is then learned characteristic.
2, graphical model matching technique:
Bayesian network has solid data reasoning prediction theory as the special graphical model of a class, it is made up of the directed acyclic graph of dependence and the conditional probability table that each node correspondence between the expression variable, arc on the figure is represented internodal dependence qualitatively, and conditional probability table is then given the quantitative portrayal that of dependence.
The study Bayesian network is exactly to determine the network configuration of Bayesian network and parameter correspondingly, and parameter learning has two kinds of basic skills, i.e. maximal possibility estimation and Bayesian Estimation; Common structure learning algorithm has: the K2 algorithm, and climbing method, simulated annealing etc. predict it is by making up on the figure model based at data with existing, according to the new data of probabilistic relation reasoning prediction of parameter based on the reasoning of Bayesian network; " graphical model matching technique " refers on phase space reconfiguration theoretical foundation, a kind of frequency hopping time series multistep forecasting method based on the Bayesian network model prediction is proposed, at first with the phase space after the reconstruct as priori data information, learn bayesian network structure and parameter then, at last by adopting Bayesian network model that chaos time sequence is predicted; Bayesian network in the graphical model is applied to frequency hop sequences prediction, and embedding dimension m and time delay τ is two key parameters of phase space reconfiguration, and correlation method and Cao method make that to try to achieve parameter more reliable and more stable; Because nodes X
mWhen given Markov border, condition independent with other nodes, predict the outcome so Bayes's localized network has identical reasoning with complete Bayesian network, utilize Markov border simplification Bayesian network model, forecasting efficiency is higher.
As shown in Figure 2, Bayesian network is made of a structure chart G and conditional probability distribution P, be designated as B=(G, P).Wherein, structure chart G is made up of set of node V and directed arc collection E, and namely (V E), is a class directed acyclic graph to G=, and namely all directed arc does not constitute the loop of a closure.It is the qualitative part of Bayesian network, and conditional probability P then is its quantitative part, is the prerequisite that the network quantitative reasoning calculates.Node among the set V represents stochastic variable or event, can be discrete or continuous.There is different values in each node in the discrete Bayesian network, is called the state of node, and commonly used is two state of value, and the state more than three is also arranged.Directed arc among the set E is used for connection and has probabilistic relation and causal two variablees or event.Conditional probability P has then shown the degree of this connection.
As shown in Figure 3, the time delay τ of one dimension chaos time sequence=7, embedding dimension m=3, the phase space reconfiguration technology is mapped to this group one-dimensional data in the 3 dimension phase spaces, and then recovers the chaos attractor of original system.Wherein, chaos attractor is embodying the regularity of chaos system as one of feature of chaos system, means that chaos system finally can fall into a certain specific track.Phase space after the reconstruct can be with a matrix notation, and the line number of matrix is and embeds dimension m.Embedding dimension m when phase space〉3 the time, can't utilize solid figure to show its analog image; When the embedding dimension m of phase space≤ 3, the system trajectory that is recovered by phase space can be showed, as chaos attractor among Fig. 3 in solid space.
As shown in Figure 4, according to chaology, can be similar to recovery frequency hop sequences { x by phase space reconfiguration
i, i=1,2 ..., the Nonlinear Dynamical Characteristics of N, the form of expression of phase space can be matrix X,
Each of matrix is classified a point mutually as, and m time delay point arranged in mutually arbitrarily, choose appropriate time delay τ and can guarantee between the time delay point interrelatedly, and this relevance can utilize Bayesian network to portray, so whole X (t)=[x that put mutually in the phase space
t, x
T+ τ..., x
T+ (m-2) τ, x
T+ (m-1) τ]
T, t=1,2, n can be used as priori data information and carries out Bayesian network study, and each puts a partial data of learning as Bayesian network mutually to be about to phase space, and each i component putting mutually is as a conception of history measured value of i node of Bayesian network.Therefore, the phase space of reconstruct can be used as Bayesian network sample D, on this basis, adopts the Markov border based on the improvement algorithm study query node of MMPC, and the Markov border as Bayes's localized network structure, and then make up the Bayesian network forecast model.
As shown in Figure 5 and Figure 6, at one group of frequency hop sequences with 256 frequency numbers of intercepting and capturing, through processes such as data preliminary treatment, phase space reconfiguration, Bayesian network structure, feedback and model adjustment, can obtain a stable Bayesian network model, and then be used for the frequency hop sequences prediction, and we are with prediction accuracy and the evaluation criterion of prediction Mean Speed as model.Wherein, predict that accuracy refers to predicted value and actual value is identical, do not exist the frequency hopping code number of fluctuation up and down to account for total percentage; The prediction Mean Speed is used average time of the single frequency hopping code of prediction.
Get 1200 frequency hopping codes of frequency hop sequences as the model training data, preceding 1000 frequency hopping codes of this section frequency hop sequences are done training set data, and remaining 200 frequency hopping codes detect data as model.1000 frequency hopping codes of model training data rear adjacent are as forecast set, utilize the phase space data after the reconstruct to carry out Bayesian network study, and according to Bayesian network aposterior reasoning algorithm frequency hop sequences are predicted.In Fig. 5, the red correct frequency hopping code of " o " expression Bayesian network model prediction, blue " * " represents the true frequency hopping code of frequency hop sequences and do not predicted exactly by model.In Fig. 6, the prediction accuracy of blue "-" expression model, its consensus forecast accuracy is 50.8%.The prediction Mean Speed is 4.2 * 10
-4S.
The embodiment of the invention at node value number in the Bayesian network greater than 64, the node number is greater than 4 situation, the time delay τ of C-C method assessment frequency hop sequences and embed window width τ in the prior art
wConsuming time of a specified duration, unstable result; The K2 algorithm of learning network structure can't utilize the Bayesian network sample D study that obtains after the frequency hop sequences reconstruct to obtain Bayesian network; Utilization needs complex calculations when learning complete bayesian network structure based on the learning method of dependence test, and the result is unreliable; The node number that the Markov border of query node comprises is α, the parameter alpha value is more big, it is more big to make up the required model training data volume of Bayesian network model, and in the actual environment of communication countermeasures, need model to accept a spot of frequency hop sequences and can set up forecast model and implement interference prediction.Therefore, utilize the Markov border special nature (in Bayesian network, given query node X
i(the Markov border mb (X of 1≤i≤m)
i), X then
iCondition is independent of all other nodes in the network) the Markov border of study query node, as model structure, simplify Bayesian network model with the Markov border of query node, forecasting efficiency is higher.
The above only is preferred embodiment of the present invention, not in order to limiting the present invention, all any modifications of doing within the spirit and principles in the present invention, is equal to and replaces and improvement etc., all should be included within protection scope of the present invention.
Claims (8)
1. the frequency hop sequences prognoses system based on graphical model is characterized in that, the frequency hop sequences prognoses system of setting up by phase space reconfiguration based on graphical model comprises:
Pretreatment module is carried out denoising, is gone bandwidth etc. the original frequency hop sequences of intercepting and capturing, and chooses one section an amount of frequency hop sequences { x
i, i=1,2 ..., N is as the training set data of model construction, the M of a training set data rear adjacent frequency hopping code as the model testing data;
Prediction module is connected with described pretreatment module, is used for phase space reconstruction and makes up forecast model;
The feedback adjusting module is connected with prediction module with described pretreatment module, is used for accuracy detection, feedback and model adjustment.
2. the frequency hop sequences prognoses system based on graphical model as claimed in claim 1 is characterized in that, the embedding dimension m that phase space reconstruction is required and time delay τ adopt Cao method and correlation method to find the solution respectively.
3. the frequency hop sequences prognoses system based on graphical model as claimed in claim 1 is characterized in that, makes up the local network structure of the required Bayesian network of forecast model by learning the Markov border of query node based on the improvement algorithm of MMPC and obtaining.
4. the frequency hop sequences prognoses system based on graphical model as claimed in claim 1 is characterized in that described pretreatment module also comprises:
Intercept and capture the frequency hop sequences data collection module of original frequency hop sequences with reconnaissance receiver;
Be used for removing the data processing unit of original frequency hop sequences noise, bandwidth, be connected with described frequency hop sequences data collection module;
The training set data unit that is used for phase space reconstruction and structure model through normalization obtains is connected with described data processing unit;
Be used for the detection model check data unit that precision of prediction detection, feedback and model are adjusted, be connected with described data processing unit;
The evidence data cell that is used for prediction through phase space τ step continuation obtains is connected with described training set data unit.
5. the frequency hop sequences prognoses system based on graphical model as claimed in claim 1 is characterized in that described prediction module also comprises:
The phase space data cell of utilizing training set data study to obtain is connected with described training set data unit;
On the phase space reconfiguration basis, the Bayesian network unit through partial structurtes are learnt and parameter learning obtains is connected with described phase space data cell;
Utilize the prediction ordered series of numbers unit of Bayesian network model prediction frequency hop sequences, be connected with the evidence data cell with described Bayesian network unit.
6. the frequency hop sequences Forecasting Methodology based on graphical model is characterized in that, described frequency hop sequences Forecasting Methodology may further comprise the steps:
Step 1 is carried out denoising, is gone bandwidth etc. the original frequency hop sequences of intercepting and capturing, and chooses one section an amount of frequency hop sequences { x
i, i=1,2 ..., N is as the training set data of model construction, the M of a training set data rear adjacent frequency hopping code as the model testing data;
Step 2 utilizes correlation method and Cao method to ask time delay τ and the embedding dimension m of phase space reconstruction, then according to these two parameters, training set data is reconstituted the matrix of m * n dimension as phase space X, wherein
As the data sample D that is used for Bayesian network study, the scale of data sample D is n;
Step 3 is based on the improvement algorithm study query node X of MMPC
mThe Markov border, the recycling maximal possibility estimation is learnt the parameter of each node, the final local Bayesian network that obtains to be used for the prediction of multi-frequency point frequency hop sequences;
Step 4, the prediction step η of model=τ, τ are time delay, according to Bayes's aposterior reasoning algorithm, calculate
Wherein the span of l is 1≤l≤η, and namely l is the l time prediction of prediction in the η step prediction, and E (n+l) is query node X
mThe Markov boundary set in the value of each node.When P is maximum, f
iBe exactly x
N+lPredicted value;
Step 5, after every η step prediction finishes, preserve the frequency hopping code of prediction, and model is detected in the data corresponding true frequency hopping code be extended for and put X (n+l) l=1 mutually ..., η, and add in the phase space, updating network parameters forwards step 4 to, finishes until the predicted back of M frequency hopping code of training set data rear adjacent;
Step 6 utilizes model to detect Data Detection model prediction precision, if do not reach required precision, feedback and model adjustment forward step 3 to, if reach required precision, namely obtain stable Bayesian network forecast model, are used for the frequency hop sequences prediction.
7. the parameter of phase space reconstruction as claimed in claim 6 is characterized in that, the delay values ri of trying to achieve at correlation method
dOn the basis, time delay τ can regulate downwards, and the span of τ is 2≤τ≤τ
d
8. as the Markov border of the query node that obtains based on the improvement algorithm study of MMPC as described in the claim 6, it is characterized in that the node number that the Markov border comprises is α, the span of parameter alpha is 2≤α≤5.
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CN105894029A (en) * | 2016-03-31 | 2016-08-24 | 浙江大学 | Self-adaptive movement track data de-noising method based on Fermat point solving |
CN105894029B (en) * | 2016-03-31 | 2019-01-25 | 浙江大学 | A kind of adaptive motion track data denoising method solved based on Fermat point |
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