CN110210658A - Prophet and Gaussian process user network method for predicting based on wavelet transformation - Google Patents
Prophet and Gaussian process user network method for predicting based on wavelet transformation Download PDFInfo
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Abstract
The present invention provides a kind of Prophet based on wavelet transformation and Gaussian process user network method for predicting.The complex characteristics such as the non-stationary, time variation for user network flow-time sequence carry out Preprocessing to user network flow-time sequence using wavelet transformation.High frequency subsequence and low frequency subsequence are obtained after wavelet transformation, its medium-high frequency subsequence reflect user network flow-time sequence mutability and irregular fluctuation feature, and low frequency subsequence then reflect user network flow-time sequence periodicity and long-term dependency characteristic.The characteristics of present invention is for high frequency subsequence and low frequency subsequence, Prophet model prediction low frequency subsequence is applied respectively, with Gaussian process forecast of regression model high frequency subsequence, discrete wavelet inverse transform is finally carried out again, and reconstruct obtains final predicting network flow result.Prediction technique proposed by the invention can effectively improve user network volume forecasting accuracy.
Description
Technical field
The invention belongs to wireless communication technology fields, and in particular to a kind of Prophet based on wavelet transformation and Gauss mistake
Journey user network data traffic prediction technique.
Background technique
In recent years, mobile communications industry develops rapidly, so that user radio access demand increases substantially.Number of users surge makes
It obtains network traffic demand to increase, the use perception of user declines therewith.How to guarantee that overall network is stablized, ensures QoE
(Quality of Experience, user experience) becomes the huge challenge that mobile communication network operator faces.To individual
The Accurate Prediction of user's future traffic helps to realize the self-optimizing of wireless network, improves efficiency, and provides top quality user's body
It tests.Existing is relatively mostly autoregressive moving-average model to customer flow prediction technique.However the more applicable stationary sequence of this method
Short-term forecast, personal user's network flow data are usually present bursty nature, and it is not very high for causing the accuracy of prediction.
Summary of the invention
Technical problem to be solved by the present invention lies in for deficiency pointed by background technique, provide a kind of based on small echo
The Prophet of transformation and personal user's network flow prediction method of Gaussian process, for high frequency subsequence and low frequency subsequence
The characteristics of, Prophet model prediction low frequency subsequence is applied respectively, with Gaussian process forecast of regression model high frequency subsequence, most
Carry out discrete wavelet inverse transform again afterwards, reconstruct obtains final predicting network flow as a result, can effectively improve user network stream
Measure prediction accuracy.
The present invention is implemented with the following technical solutions to solve above-mentioned technical problem:
A kind of Prophet based on wavelet transformation and Gaussian process user network method for predicting, steps are as follows:
Step 1 carries out Data Preprocessing to user network flow-time sequence using wavelet transformation, obtains high frequency
Sequence and low frequency subsequence, medium-high frequency subsequence be used to reflect the mutability of user network flow-time sequence with it is irregular
Fluctuation feature, low frequency subsequence be used for reflect user network flow-time sequence periodicity and long-term dependency characteristic；
Step 2, with Prophet model prediction low frequency subsequence, with Gaussian process forecast of regression model high frequency subsequence；
Step 3 carries out discrete wavelet inverse transform, and reconstruct obtains final predicting network flow result.
Further, a kind of Prophet based on wavelet transformation proposed by the invention and Gaussian process user network stream
Prediction technique is measured, step 1 specifically comprises the following steps:
(1) single user's network service traffic data time series are obtained, its flow used in each time slot is counted,
User network flow-time sequence u (t), t=1,2 ..., L are obtained, wherein u (t) is user's flow used in time slot t；
(2) scale compression is carried out to user traffic data, i.e., u (t) is carried out the following processing:
Z (t)=log10(u(t)+1) (1)
In formula, z (t) is the compressed user network flow-time sequence of scale；
(3) carrying out pretreatment to time series z (t) makes mean value 0:
In formula, z ' (t) is zero averaging treated time series,For the average value of time series z (t),
(4) wavelet transform is done to z ' (t), obtains low frequency subsequence c (n) and high frequency subsequence d (n)；
To pretreated user network data on flows sequence z ' (t), t=1,2 ..., L carry out single order wavelet decomposition, obtain
To subsequence c (n) and d (n):
WhereinIt is scaling function and wavelet function respectively with ψ (t), is determined by wavelet basis；C (n) is low frequency subsequence,
Low-frequency information comprising sequence, referred to as approximation coefficient；D (n) is high frequency subsequence, the high-frequency information comprising signal, referred to as details
Coefficient；The high frequency subsequence that obtains after single order wavelet decomposition and low frequency sub-sequence length are L/2, i.e. n=1,2 ...,
L/2。
Further, a kind of Prophet based on wavelet transformation proposed by the invention and Gaussian process user network stream
Prediction technique is measured, step 2 carries out Gaussian process recurrence and prediction to high frequency subsequence d (n), using Gaussian process regression model pair
It is modeled, and obtains the prediction result of high frequency subsequenceIncluding following process:
(1) regression model sample data constructs: to any i=1,2 ..., L/2, the input sample of regression model is xi=
{d(i-m),d(i-m+1),...,d(i-1)}T, i-th of output sample of regression model is d (i)；The wherein specific number of m value view
Depending on；Sample data sets D=(X, d) is constructed as a result, wherein X is input sample set, and d is output sample set；
T indicates transposition operation in formula；
(2) training sample set and test sample set are divided: by before D=(X, d) 80% data as training sample
Set Dtrain=(Xtrain,dtrain), rear 20% is used as test sample set Dtest=(Xtest,dtest)；
(3) Gauss Parameters in Regression Model determines: choosing square index covariance function SE as Gaussian process covariance letter
Number, as follows:
Wherein θ is hyper parameter, can obtain optimal hyper parameter θ with maximum likelihood methodML:
θML=argmin (- logp (dtrain|Xtrain,θ)) (8)
(4) Gaussian process regression model is established: it is believed that dtrainGaussian process is obeyed, is indicated are as follows:
Wherein, GP indicates Gaussian process,For noise variance, δijFor Kronecker function, as i=j, δij=1；It surveys
Examination set output sample dtestPosterior distrbutionp Gaussian distributed:
dtest|Xtrain,dtrain,Xtest~N (μ test, Σtest)(10)
Wherein μtestThe mean value for gathering output sample for test selects it to gather the estimated value of output sample as test；
ΣtestThe variance for gathering output sample for test, is respectively as follows:
K (X in formulatrain,Xtest)=K (Xtest,Xtrain)TFor test set input sample and training set input sample it
Between covariance matrix, K (Xtest,Xtest) it is XtestThe covariance of itself, InFor unit matrix；A-1Indicate square of inverting to matrix A
Battle array；
(5) predicted value that training set gathers output sample with test is respectively as follows:
Therefore, the predicted value of high frequency subsequence is obtained
Further, a kind of Prophet based on wavelet transformation proposed by the invention and Gaussian process user network stream
Prediction technique is measured, step 2 using Prophet model modeling and predicts the low frequency subsequence c (n) obtained after wavelet decomposition,
Obtain low frequency subsequence prediction result
G (n), s (n), the sum of h (n) are resolved into low frequency subsequence c (n), it may be assumed that
C (n)=g (n)+s (n)+h (n)+εn (15)
Wherein c (n) indicates original low frequency subsequence, and g (n) is the trend term in user network flow-time sequence, indicates
The acyclic variation of user network flow-time sequence, periodic term s (n) portray the change of user network flow-time sequence periodicity
Change, h (n) represents influence of the special holidays to user network flow-time sequential value, error items εnRepresentative model can not capture
Special variation, and assume its Normal Distribution；
Wherein shown in the following formula of trend term g (n):
Wherein C is bearing capacity, refers to the maximum asymptotic value of time-serial position, is led by the data or profession of market scale
Domain knowledge determines；K indicates the rate of rise of curve, and p is offset parameter；
Periodic term s (n) is given by:
Wherein P represents the period of target sequence, clFor the parameter to be estimated of model, 2N is the approximate item number of setting, is used
In control filter strength；
Festivals or holidays h (n) may be expressed as:
Wherein, for i-th of festivals or holidays, DiIt indicates the period that the festivals or holidays have an impact, defines an instruction
Property function 1, indicate moment n whether be in the influencing timeslice of festivals or holidays i；If n ∈ Di, it is otherwise 0；And it is
A parameter κ is arranged in each festivals or holidaysiTo indicate the coverage of festivals or holidays, κi∈N(0,υi 2)；Assuming that there are M festivals or holidays,
Using Prophet algorithm difference fitted trend item, periodic term and the parameter in festivals or holidays, then by fitting resultSummation obtains the predicted value of user network flow low frequency subsequenceThat is:
It respectively indicates.Since the fit procedure of Prophet model is an existing mature technology, details are not described herein.
Further, a kind of Prophet based on wavelet transformation proposed by the invention and Gaussian process user network stream
Prediction technique is measured, discrete wavelet inverse transform is carried out to the prediction result of above-mentioned high frequency subsequence and low frequency subsequence, reconstruct obtains
In formulaWithRespectively indicate the predicted value of low frequency subsequence Yu high frequency subsequence；It is rightEliminate zero-mean
Changing influences simultaneously fetching number, is restored to the original scale of network flow, obtains the final prediction knot of user network flow-time sequence
Fruit
The invention adopts the above technical scheme, has the advantages that compared with prior art
The invention proposes one kind to obtain Prophet and Gaussian process regression combination prediction model based on wavelet transformation, uses
User network data on flows Time Series are to characterize the low frequency part of long-term trend variation and characterize random by wavelet decomposition
The high frequency section of mutation, is further respectively adopted Prophet model and Gaussian process regression model carries out prediction modeling, has
Preferable prediction effect.Compared with traditional autoregressive moving-average model, this method can preferably pull-in time sequence it is prominent
Become characteristic, is more suitable for the volume forecasting of user.
Detailed description of the invention
Fig. 1 is flow chart of the method for the present invention.
Specific embodiment
With reference to the accompanying drawing and specific embodiment, the present invention is described in further detail.
The present invention provides a kind of Prophet based on wavelet transformation and Gaussian process customer flow prediction technique.For with
The complex characteristics such as the non-stationary, time variation of family network flow time series, using wavelet transformation to user network flow-time
Sequence carries out Preprocessing.High frequency subsequence and low frequency subsequence are obtained after wavelet transformation, medium-high frequency subsequence is anti-
The mutability and irregular fluctuation feature of user network flow-time sequence have been reflected, and low frequency subsequence then reflects user
The periodicity of network flow time series and long-term dependency characteristic.The present invention is directed to the spy of high frequency subsequence and low frequency subsequence
Point applies Prophet model prediction low frequency subsequence respectively, with Gaussian process forecast of regression model high frequency subsequence, finally again
Discrete wavelet inverse transform is carried out, reconstruct obtains final predicting network flow result.
As shown in Figure 1, method of the invention specifically comprises the following steps:
Step 1: data prediction, this step includes following process:
(1) single user's network service traffic data time series are obtained.Such as with one hour or one day for a time slot, system
Its flow used in each time slot is counted, obtains user network flow-time sequence u (t), t=1,2 ..., L, wherein u (t)
For user's flow used in time slot t.
(2) scale compression is carried out to user traffic data, i.e., u (t) is carried out the following processing:
Z (t)=log10(u(t)+1) (1)
In formula, z (t) is the compressed user network flow-time sequence of scale.
(3) carrying out pretreatment to time series z (t) makes mean value 0:
In formula, z ' (t) is zero averaging treated time series,For the average value of time series z (t),
Step 2: doing wavelet transform to z ' (t), low frequency subsequence c (n) and high frequency subsequence d (n) are obtained.
To pretreated user network data on flows sequence z ' (t), t=1,2 ..., L carry out single order wavelet decomposition, obtain
To subsequence c (n) and d (n):
WhereinIt is scaling function and wavelet function respectively with ψ (t), is determined by wavelet basis.In view of symmetry and just
Then property selects db4 small echo as wavelet basis.C (n) is low frequency subsequence, the low-frequency information comprising sequence, referred to as approximation coefficient.d
It (n) is high frequency subsequence, the high-frequency information comprising signal, referred to as detail coefficients.The high frequency obtained after single order wavelet decomposition
Subsequence and low frequency sub-sequence length are L/2, i.e. n=1,2 ..., L/2.
Step 3: carrying out Gaussian process recurrence and prediction to high frequency subsequence d (n).High frequency subsequence d (n) can consider
Therefore the equal Gaussian distributed of the time sequential value can model it using Gaussian process regression model, obtain high frequency subsequence
Prediction resultThis step includes following process:
(1) regression model sample data constructs.To any i=1,2 ..., L/2, the input sample of regression model is xi=
{d(i-7),d(i-6),...,d(i-1)}T, i-th of output sample of regression model is d (i).Sample data set is constructed as a result,
It closes D=(X, d), wherein X is input sample set, and d is output sample set.
T indicates transposition operation in formula.
(2) training sample set and test sample set are divided.By before D=(X, d) 80% data as training sample
Set Dtrain=(Xtrain,dtrain), rear 20% is used as test sample set Dtest=(Xtest,dtest)。
(3) Gauss Parameters in Regression Model determines.Choose square index covariance function (Squared exponential
Covariance function, SE) it is used as Gaussian process covariance function, as follows:
Wherein θ is hyper parameter, can obtain optimal hyper parameter θ with maximum likelihood methodML:
θML=argmin (- logp (dtrain|Xtrain,θ)) (8)
(4) Gaussian process regression model is established.It can consider dtrainGaussian process is obeyed, is indicated are as follows:
Wherein, GP indicates Gaussian process,For noise variance.δijFor Kronecker function, as i=j, δij=1.
Test set output sample dtestPosterior distrbutionp Gaussian distributed:d test|Xtrain,dtrain,Xtest~N
(μtest,Σtest) (10)
Wherein μtestThe mean value for gathering output sample for test generally selects it to gather the estimation of output sample as test
Value.
ΣtestThe variance for gathering output sample for test, is respectively as follows:
K (X in formulatrain,Xtest)=K (Xtest,Xtrain)TFor test set input sample and training set input sample it
Between covariance matrix, K (Xtest,Xtest) it is XtestThe covariance of itself, InFor unit matrix.A-1Indicate square of inverting to matrix A
Battle array.
(5) predicted value that training set gathers output sample with test is respectively as follows:
Therefore, the predicted value of high frequency subsequence is obtained
Step 4: the low frequency subsequence c (n) obtained after wavelet decomposition using Prophet model modeling and is predicted,
Obtain low frequency subsequence prediction result
G (n), s (n), the sum of h (n) are resolved into low frequency subsequence c (n), it may be assumed that
C (n)=g (n)+s (n)+h (n)+εn (15)
Wherein c (n) indicates original low frequency subsequence, and g (n) is the trend term in user network flow-time sequence, indicates
The acyclic variation of user network flow-time sequence, periodic term s (n) portray the change of user network flow-time sequence periodicity
Change, h (n) represents influence of the special holidays to user network flow-time sequential value.Error items εnRepresentative model can not capture
Special variation, it can be assumed that its Normal Distribution.
Wherein shown in the following formula of trend term g (n):
Wherein C is bearing capacity, refers to the maximum asymptotic value of time-serial position, such as overall market scale, total number of people etc..
This usual value is determined by the data or professional domain knowledge of market scale.K indicates the rate of rise of curve, and p is offset
Parameter is measured, which is generally obtained by Prophet algorithm automatic Fitting.It sets bearing capacity C and uses flow most as user's history
5 times be worth greatly.
Periodic term s (n) is given by:
Wherein P represents the period of target sequence, clFor the parameter to be estimated of model, 2N is the approximate item number of setting, is used
In control filter strength.7 are set by P, corresponding N value is usually 3.
Festivals or holidays h (n) can be indicated are as follows:
Wherein, for i-th of festivals or holidays, DiIndicate the period that the festivals or holidays have an impact.Define an instruction
Property function 1, indicate moment n whether be in the influencing timeslice of festivals or holidays i.If n ∈ Di, it is otherwise 0.And it is
A parameter κ is arranged in each festivals or holidaysiTo indicate the coverage of festivals or holidays, κi∈N(0,υi 2).Assuming that there are M festivals or holidays,
Using Prophet algorithm difference fitted trend item, periodic term and the parameter in festivals or holidays, then by fitting resultSummation obtains the predicted value of user network flow low frequency subsequenceThat is:
It respectively indicates.Since the fit procedure of Prophet model is an existing mature technology, details are not described herein.
Step 5: carrying out discrete wavelet inverse transform, reconstruct to the prediction result of above-mentioned high frequency subsequence and low frequency subsequence
It obtains
In formulaWithRespectively indicate the predicted value of low frequency subsequence Yu high frequency subsequence.It is rightEliminate zero-mean
Changing influences simultaneously fetching number, is restored to the original scale of network flow, obtains the final prediction knot of user network flow-time sequence
Fruit
Specific embodiment described herein is only an example for the spirit of the invention.The neck of technology belonging to the present invention
The technical staff in domain can make various modifications or additions to the described embodiments or replace by a similar method
In generation, however, it does not deviate from the spirit of the invention or beyond the scope of the appended claims.
Claims (5)
1. a kind of Prophet based on wavelet transformation and Gaussian process user network method for predicting, which is characterized in that step
It is as follows:
Step 1 carries out Data Preprocessing to user network flow-time sequence using wavelet transformation, obtains high frequency subsequence
With low frequency subsequence, medium-high frequency subsequence is used to reflect the mutability and irregular fluctuation of user network flow-time sequence
Property feature, low frequency subsequence be used for reflect user network flow-time sequence periodicity and long-term dependency characteristic；
Step 2, with Prophet model prediction low frequency subsequence, with Gaussian process forecast of regression model high frequency subsequence；
Step 3 carries out discrete wavelet inverse transform, and reconstruct obtains final predicting network flow result.
2. a kind of Prophet based on wavelet transformation according to claim 1 and Gaussian process user network volume forecasting
Method, which is characterized in that step 1 specifically comprises the following steps:
(1) single user's network service traffic data time series are obtained, its flow used in each time slot is counted, obtains
User network flow-time sequence u (t), t=1,2 ..., L, wherein u (t) is user's flow used in time slot t；
(2) scale compression is carried out to user traffic data, i.e., u (t) is carried out the following processing:
Z (t)=log10(u(t)+1) (1)
In formula, z (t) is the compressed user network flow-time sequence of scale；
(3) carrying out pretreatment to time series z (t) makes mean value 0:
In formula, z ' (t) is zero averaging treated time series,For the average value of time series z (t),
(4) wavelet transform is done to z ' (t), obtains low frequency subsequence c (n) and high frequency subsequence d (n)；
To pretreated user network data on flows sequence z ' (t), t=1,2 ..., L carry out single order wavelet decomposition, obtain son
Sequence c (n) and d (n):
WhereinIt is scaling function and wavelet function respectively with ψ (t), is determined by wavelet basis；C (n) is low frequency subsequence, includes
The low-frequency information of sequence, referred to as approximation coefficient；D (n) is high frequency subsequence, the high-frequency information comprising signal, referred to as detail coefficients；
The high frequency subsequence and low frequency sub-sequence length obtained after single order wavelet decomposition is L/2, i.e. n=1,2 ..., L/2.
3. a kind of Prophet based on wavelet transformation according to claim 2 and Gaussian process user network volume forecasting
Method, which is characterized in that step 2 carries out Gaussian process recurrence and prediction to high frequency subsequence d (n), returns using Gaussian process
Model models it, obtains the prediction result of high frequency subsequenceIncluding following process:
(1) regression model sample data constructs: to any i=1,2 ..., L/2, the input sample of regression model is xi={ d (i-
m),d(i-m+1),...,d(i-1)}T, i-th of output sample of regression model is d (i)；Wherein m value regard specific data and
It is fixed；Sample data sets D=(X, d) is constructed as a result, wherein X is input sample set, and d is output sample set；
T indicates transposition operation in formula；
(2) training sample set and test sample set are divided: by before D=(X, d) 80% data as training sample set
Dtrain=(Xtrain,dtrain), rear 20% is used as test sample set Dtest=(Xtest,dtest)；
(3) Gauss Parameters in Regression Model determines: choosing square index covariance function SE as Gaussian process covariance function, such as
Shown in lower:
Wherein θ is hyper parameter, can obtain optimal hyper parameter θ with maximum likelihood methodML:
θML=argmin (- logp (dtrain|Xtrain,θ)) (8)
(4) Gaussian process regression model is established: it is believed that dtrainGaussian process is obeyed, is indicated are as follows:
Wherein, GP indicates Gaussian process,For noise variance, δijFor Kronecker function, as i=j, δij=1；Test set
Close output sample dtestPosterior distrbutionp Gaussian distributed:
dtest|Xtrain,dtrain,Xtest~N (μtest,Σtest) (10)
Wherein μtestThe mean value for gathering output sample for test selects it to gather the estimated value of output sample as test；ΣtestFor
The variance of test set output sample, is respectively as follows:
K (X in formulatrain,Xtest)=K (Xtest,Xtrain)TBetween test set input sample and training set input sample
Covariance matrix, K (Xtest,Xtest) it is XtestThe covariance of itself, InFor unit matrix；A-1It indicates to matrix A finding the inverse matrix；
(5) predicted value that training set gathers output sample with test is respectively as follows:
Therefore, the predicted value of high frequency subsequence is obtained
4. a kind of Prophet based on wavelet transformation according to claim 2 and Gaussian process user network volume forecasting
Method, which is characterized in that step 2 is for the low frequency subsequence c (n) that obtains after wavelet decomposition, simultaneously using Prophet model modeling
Prediction, obtains low frequency subsequence prediction result
G (n), s (n), the sum of h (n) are resolved into low frequency subsequence c (n), it may be assumed that
C (n)=g (n)+s (n)+h (n)+εn (15)
Wherein c (n) indicates original low frequency subsequence, and g (n) is the trend term in user network flow-time sequence, indicates user
The acyclic variation of network flow time series, periodic terms(n) variation of user network flow-time sequence periodicity, h are portrayed
(n) influence of the special holidays to user network flow-time sequential value, error items ε are representednThe spy that representative model can not capture
Different variation, and assume its Normal Distribution；
Wherein shown in the following formula of trend term g (n):
Wherein C is bearing capacity, refers to the maximum asymptotic value of time-serial position, is known by the data or professional domain of market scale
Know to determine；K indicates the rate of rise of curve, and p is offset parameter；
Periodic term s (n) is given by:
Wherein P represents the period of target sequence, clFor the parameter to be estimated of model, 2N is the approximate item number of setting, for controlling
Filter strength；
Festivals or holidays h (n) may be expressed as:
Wherein, for i-th of festivals or holidays, DiIt indicates the period that the festivals or holidays have an impact, defines an indicative function
1, indicate whether moment n is in the influencing timeslice of festivals or holidays i；If n ∈ Di, it is otherwise 0；It and is each section
A parameter κ is arranged in holidayiTo indicate the coverage of festivals or holidays, κi∈N(0,υi 2)；Assuming that there are M festivals or holidays,
Using Prophet algorithm difference fitted trend item, periodic term and the parameter in festivals or holidays, then by fitting resultSummation obtains the predicted value of user network flow low frequency subsequenceThat is:
5. a kind of Prophet based on wavelet transformation according to claim 2 and Gaussian process user network volume forecasting
Method, which is characterized in that discrete wavelet inverse transform, reconstruct are carried out to the prediction result of above-mentioned high frequency subsequence and low frequency subsequence
It obtains
In formulaWithRespectively indicate the predicted value of low frequency subsequence Yu high frequency subsequence；It is rightEliminate zero averaging shadow
Simultaneously fetching number is rung, the original scale of network flow is restored to, obtains the final prediction result of user network flow-time sequence
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