CN110210658A - Prophet and Gaussian process user network method for predicting based on wavelet transformation - Google Patents

Abstract

The invention provides a wavelet transform-based Prophet and Gaussian process user network traffic prediction method. Aiming at the complex characteristics of user network traffic time series such as non-stationarity and time-varying, wavelet transform is used to preprocess and analyze the user network traffic time series. After wavelet transform, high-frequency subsequences and low-frequency subsequences are obtained. The high-frequency subsequences reflect the abruptness and irregular fluctuation characteristics of the user network traffic time series, while the low-frequency subsequences reflect the user network traffic time series. Cyclical and long-term dependencies. Aiming at the characteristics of high-frequency sub-sequences and low-frequency sub-sequences, the present invention uses the Prophet model to predict the low-frequency sub-sequences, uses the Gaussian process regression model to predict the high-frequency sub-sequences, and finally performs inverse discrete wavelet transform to reconstruct the final network traffic prediction. result. The prediction method proposed by the present invention can effectively improve the prediction accuracy of user network traffic.

Description

Prophet and Gaussian Process User Network Traffic Prediction Method Based on Wavelet Transform

technical field

The invention belongs to the technical field of wireless communication, and in particular relates to a method for predicting the data flow of a user network based on wavelet transform of Prophet and Gaussian process.

Background technique

In recent years, the rapid development of the mobile communication industry has resulted in a substantial increase in the demand for wireless access of users. The surge in the number of users increases the demand for network traffic, and the user's perception of use decreases. How to ensure overall network stability and QoE (Quality of Experience, user experience) has become a huge challenge for mobile communication network operators. Accurate prediction of future traffic of individual users helps to achieve self-optimization of wireless networks, improve efficiency, and provide the best user experience. Most of the existing methods for predicting user traffic are autoregressive moving average models. However, this method is more suitable for short-term prediction of stationary series, and the network traffic data of individual users often has sudden characteristics, resulting in a low prediction accuracy.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to provide a method for predicting network traffic of individual users based on Prophet and Gaussian process based on wavelet transform, aiming at the deficiencies pointed out in the background technology. The model predicts low-frequency subsequences, uses Gaussian process regression model to predict high-frequency subsequences, and finally performs inverse discrete wavelet transform to reconstruct the final network traffic prediction result, which can effectively improve the accuracy of user network traffic prediction.

The present invention adopts the following technical scheme to realize in order to solve the above-mentioned technical problems:

A wavelet transform-based Prophet and Gaussian process user network traffic prediction method, the steps are as follows:

Step 1. Use wavelet transform to perform data preprocessing analysis on the user network traffic time series to obtain high frequency subsequences and low frequency subsequences, where the high frequency subsequences are used to reflect the abruptness and irregular volatility of the user network traffic time series The low-frequency subsequence is used to reflect the periodicity and long-term dependence of the user network traffic time series;

Step 2. Use the Prophet model to predict the low-frequency subsequence, and use the Gaussian process regression model to predict the high-frequency subsequence;

Step 3: Perform inverse discrete wavelet transform and reconstruct to obtain the final network traffic prediction result.

Further, in a method for predicting user network traffic based on wavelet transform based on Prophet and Gaussian process, step 1 specifically includes the following steps:

(1) Obtain the time series of network traffic data of a single user, count the traffic used in each time slot, and obtain the user network traffic time series u(t), t=1,2,...,L, where u (t) is the flow used by the user in time slot t;

(2) Scale the user traffic data, that is, perform the following processing on u(t):

z(t)=log ₁₀ (u(t)+1) (1)

In the formula, z(t) is the time series of user network traffic after scale compression;

(3) Preprocess the time series z(t) to make the mean 0:

In the formula, z'(t) is the time series after zero-average processing, is the mean value of the time series z(t),

(4) Do discrete wavelet transform on z'(t) to obtain low-frequency subsequence c(n) and high-frequency subsequence d(n);

First-order wavelet decomposition is performed on the preprocessed user network traffic data sequence z'(t), t=1, 2,...,L, and subsequences c(n) and d(n) are obtained:

in and ψ(t) are the scale function and the wavelet function respectively, which are determined by the wavelet basis; c(n) is the low-frequency subsequence, which contains the low-frequency information of the sequence, which is called the approximate coefficient; d(n) is the high-frequency subsequence, which contains the signal The high-frequency information of , is called the detail coefficient; the length of the high-frequency subsequence and the low-frequency subsequence obtained after the first-order wavelet decomposition is L/2, that is, n=1,2,...,L/2.

Further, in a method for predicting user network traffic based on wavelet transform based on Prophet and Gaussian process, step 2 performs Gaussian process regression and prediction on the high-frequency subsequence d(n), and applies the Gaussian process regression model to construct it. modulo to get the prediction result of the high frequency subsequence Including the following processes:

(1) Construction of regression model sample data: For any i=1,2,...,L/2, the input sample of the regression model is x _i ={d(im),d(i-m+1),. ..,d(i-1)} ^T , the ith output sample of the regression model is d(i); the value of m depends on the specific data; thus, construct the sample data set D=(X,d) , where X is the input sample set, and d is the output sample set;

where T represents the transpose operation;

(2) Divide the training sample set and the test sample set: take the first 80% of the data of D=(X,d) as the training sample set D _train =(X _train ,d _train ), and the last 20% as the test sample set D _test = (X _test ,d _test );

(3) Determination of Gaussian regression model parameters: Select the square exponential covariance function SE as the Gaussian process covariance function, as shown below:

Where θ is a hyperparameter, and the optimal hyperparameter θ ^ML can be obtained by the maximum likelihood method:

θ ^ML = argmin(-logp(d _train |X _train ,θ)) (8)

(4) Establish a Gaussian process regression model: it can be considered that d _train obeys a Gaussian process, which is expressed as:

where GP stands for a Gaussian process, is the noise variance, δ _ij is the Kronecker function, when i=j, δ _ij =1; the posterior distribution of the test set output sample d _test obeys the Gaussian distribution:

d _test |X _train ,d _train ,X _test ～N(μtest,Σ _test )(10)

Among them μ _test is the mean value of the output samples of the test set, which is selected as the estimated value of the output samples of the test set; Σ _test is the variance of the output samples of the test set, respectively:

In the formula, K(X _train , X _test )=K(X _test , X _train ) ^T is the covariance matrix between the input samples of the test set and the input samples of the training set, and K(X _test , X _test ) is the value of X _test itself Covariance, In _is the identity matrix; A ^-1 represents the inverse matrix of matrix A;

(5) The predicted values of the training set and the test set output samples are:

Therefore, the predicted value of the high frequency subsequence is obtained

Further, in a method for predicting user network traffic based on Prophet and Gaussian process based on wavelet transform proposed by the present invention, in step 2, for the low-frequency subsequence c(n) obtained after wavelet decomposition, the Prophet model is used to model and predict, and the low-frequency sub-sequence c(n) is obtained. Subsequence prediction results

Decompose the low-frequency subsequence c(n) into the sum of g(n), s(n), and h(n), namely:

c(n)=g(n)+s(n)+h( _n )+εn (15)

Among them, c(n) represents the original low-frequency subsequence, g(n) is the trend item in the user network traffic time series, which represents the aperiodic change of the user network traffic time series, and the periodic term s(n) describes the user network traffic time The sequence changes periodically, h(n) represents the impact of special holidays on the time series value of user network traffic, and the error term _εn represents the special changes that cannot be captured by the model, and it is assumed that it obeys a normal distribution;

The trend term g(n) is shown in the following formula:

Among them, C is the carrying capacity, which refers to the maximum asymptotic value of the time series curve, which is determined by the market scale data or professional domain knowledge; k is the growth rate of the curve, and p is the offset parameter;

The periodic term s(n) is given by:

Among them, P represents the period of the target sequence, c _l is the parameter to be estimated by the model, and 2N is the number of approximate items set to control the degree of filtering;

The holiday item h(n) can be expressed as:

Among them, for the ith holiday, D _i represents the time period during which the holiday has an impact, and an indicative function 1 is defined to indicate whether time n is within the impact period of holiday i; If n∈D _i , otherwise it is 0; and set a parameter κ _i for each holiday to represent the influence range of the holiday, κ _i ∈ N(0,υ _i ² ); assuming there are M holidays,

Use the Prophet algorithm to fit the parameters in the trend item, the period item and the holiday item respectively, and then fit the fitting results. Summation to get the predicted value of the low-frequency subsequence of user network traffic which is:

Respectively. Since the fitting process of the Prophet model is an existing mature technology, it will not be repeated here.

Further, a method for predicting user network traffic based on Prophet and Gaussian process based on wavelet transform proposed by the present invention performs discrete wavelet inverse transform on the prediction results of the above-mentioned high-frequency sub-sequences and low-frequency sub-sequences, and reconstructs the result.

in the formula and represent the predicted values of low-frequency subsequences and high-frequency subsequences, respectively; Eliminate the effect of zero averaging and take the index, restore the original scale of network traffic, and obtain the final prediction result of the user network traffic time series

The present invention adopts the above technical scheme, and has the following beneficial effects compared with the prior art:

The present invention proposes a combined prediction model of Prophet and Gaussian process regression based on wavelet transform. The time series of user network traffic data is decomposed into low frequency parts representing long-term trend changes and high frequency parts representing random mutations by using wavelet decomposition. Prophet model and Gaussian process regression model are used for predictive modeling, which have good predictive effects. Compared with the traditional autoregressive moving average model, this method can better capture the mutation characteristics of time series, and is more suitable for user traffic forecasting.

Description of drawings

FIG. 1 is a flow chart of the method of the present invention.

Detailed ways

The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

The present invention provides a method for predicting user traffic based on Prophet and Gaussian process based on wavelet transform. Aiming at the complex characteristics of user network traffic time series such as non-stationarity and time-varying, wavelet transform is used to preprocess and analyze the user network traffic time series. After wavelet transform, high-frequency subsequences and low-frequency subsequences are obtained. The high-frequency subsequences reflect the abruptness and irregular fluctuation characteristics of the user network traffic time series, while the low-frequency subsequences reflect the user network traffic time series. Cyclical and long-term dependencies. According to the characteristics of high frequency subsequence and low frequency subsequence, the present invention uses Prophet model to predict low frequency subsequence, uses Gaussian process regression model to predict high frequency subsequence, and finally performs inverse discrete wavelet transform to reconstruct the final network traffic prediction. result.

As shown in Figure 1, the method of the present invention specifically comprises the following steps:

The first step: data preprocessing, this step includes the following processes:

(1) Obtain the time series of network traffic data of a single user. For example, take one hour or one day as a time slot, count the traffic used in each time slot, and obtain the user network traffic time series u(t), t=1, 2,...,L, where u(t) is the traffic used by the user in time slot t.

(2) Scale the user traffic data, that is, perform the following processing on u(t):

z(t)=log ₁₀ (u(t)+1) (1)

In the formula, z(t) is the time series of user network traffic after scale compression.

(3) Preprocess the time series z(t) to make the mean 0:

In the formula, z'(t) is the time series after zero-average processing, is the mean value of the time series z(t),

Step 2: Do discrete wavelet transform on z'(t) to obtain low-frequency subsequence c(n) and high-frequency subsequence d(n).

First-order wavelet decomposition is performed on the preprocessed user network traffic data sequence z'(t), t=1, 2,...,L, and subsequences c(n) and d(n) are obtained:

in and ψ(t) are the scale function and the wavelet function, respectively, determined by the wavelet basis. Considering the symmetry and regularity, the db4 wavelet is chosen as the wavelet base. c(n) is a low-frequency subsequence, which contains the low-frequency information of the sequence, and is called an approximation coefficient. d(n) is the high frequency subsequence, which contains the high frequency information of the signal, which is called the detail coefficient. The length of the high frequency subsequence and the low frequency subsequence obtained after the first-order wavelet decomposition is L/2, that is, n=1,2,...,L/2.

Step 3: Perform Gaussian process regression and prediction on the high-frequency subsequence d(n). The high-frequency subsequence d(n) can be considered to obey the Gaussian distribution. Therefore, the Gaussian process regression model can be used to model it, and the prediction result of the high-frequency subsequence can be obtained. This step includes the following processes:

(1) Regression model sample data construction. For any i=1,2,...,L/2, the input samples of the regression model are x _i ={d(i-7),d(i-6),...,d(i-1) } ^T , the ith output sample of the regression model is d(i). Thus, the sample data set D=(X, d) is constructed, where X is the input sample set, and d is the output sample set.

where T represents the transpose operation.

(2) Divide the training sample set and the test sample set. The first 80% of the data of D=(X, d) are used as a training sample set D _train = (X _train , d _train ), and the last 20% are used as a test sample set D _test = (X _test , d _test ).

(3) The parameters of the Gaussian regression model are determined. Select the squared exponential covariance function (SE) as the Gaussian process covariance function as follows:

Where θ is a hyperparameter, and the optimal hyperparameter θ ^ML can be obtained by the maximum likelihood method:

θ ^ML = argmin(-logp(d _train |X _train ,θ)) (8)

(4) Establish a Gaussian process regression model. It can be considered that d _train obeys a Gaussian process, expressed as:

where GP stands for a Gaussian process, is the noise variance. δ _ij is a Kronecker function, and when i=j, δ _ij =1.

The posterior distribution of the test set output sample d _test follows a Gaussian distribution: ^d _test |X _train ,d _train ,X _test ～N(μ _test ,Σ _test ) (10)

Among them μ _test is the mean value of the output samples of the test set, which is generally selected as the estimated value of the output samples of the test set.

Σ _test is the variance of the output samples of the test set, which are:

In the formula, K(X _train , X _test )=K(X _test , X _train ) ^T is the covariance matrix between the input samples of the test set and the input samples of the training set, and K(X _test , X _test ) is the value of X _test itself covariance, In _is the identity matrix. A ^-1 means to inverse matrix A.

(5) The predicted values of the training set and the test set output samples are:

Therefore, the predicted value of the high frequency subsequence is obtained

Step 4: For the low-frequency subsequence c(n) obtained after wavelet decomposition, use the Prophet model to model and predict, and obtain the prediction result of the low-frequency subsequence

Decompose the low-frequency subsequence c(n) into the sum of g(n), s(n), and h(n), namely:

c(n)=g(n)+s(n)+h( _n )+εn (15)

Among them, c(n) represents the original low-frequency subsequence, g(n) is the trend item in the user network traffic time series, which represents the aperiodic change of the user network traffic time series, and the periodic term s(n) describes the user network traffic time The sequence changes periodically, and h(n) represents the impact of special holidays on the time series value of user network traffic. The error term _εn represents a special variation that cannot be captured by the model and can be assumed to follow a normal distribution.

The trend term g(n) is shown in the following formula:

Among them, C is the carrying capacity, which refers to the maximum asymptotic value of the time series curve, such as the total market size, the total population, etc. Usually this value is determined by market size data or domain expertise. k represents the growth rate of the curve, and p is the offset parameter, which is generally obtained by automatic fitting of the Prophet algorithm. Set the bearer capacity C to 5 times the maximum historical traffic used by the user.

The periodic term s(n) is given by:

Among them, P represents the period of the target sequence, _cl is the parameter to be estimated by the model, and 2N is the number of approximate items set to control the degree of filtering. Set P to 7, and the corresponding N value is usually 3.

The holiday item h(n) can be expressed as:

Among them, for the ith holiday, D _i represents the time period during which the holiday has an impact. Define an indicative function 1, indicating whether time n is within the influence period of holiday i. If n∈D _i , 0 otherwise. And set a parameter κ _i for each holiday to represent the influence range of the holiday, κ _i ∈ N(0,υ _i ² ). Suppose there are M holidays,

Use the Prophet algorithm to fit the parameters in the trend item, the period item and the holiday item respectively, and then fit the fitting results. Summation to get the predicted value of the low-frequency subsequence of user network traffic which is:

Respectively. Since the fitting process of the Prophet model is an existing mature technology, it will not be repeated here.

Step 5: Perform inverse discrete wavelet transform on the prediction results of the above high-frequency subsequences and low-frequency subsequences, and reconstruct to obtain

in the formula and represent the predicted values of the low-frequency subsequence and the high-frequency subsequence, respectively. right Eliminate the effect of zero averaging and take the index, restore the original scale of network traffic, and obtain the final prediction result of the user network traffic time series

The specific embodiments described herein are merely illustrative of the spirit of the invention. Those skilled in the art to which the present invention pertains can make various modifications or additions to the described specific embodiments or substitute in similar manners, but will not deviate from the spirit of the present invention or go beyond the definition of the appended claims range.

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 x_i={ 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 D_train=(X_train,d_train), rear 20% is used as test sample set D_test=(X_test,d_test)；

(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 method^ML:

θ^ML=argmin (- logp (d_train|X_train,θ)) (8)

(4) Gaussian process regression model is established: it is believed that d_trainGaussian process is obeyed, is indicated are as follows:

Wherein, GP indicates Gaussian process,For noise variance, δ_ijFor Kronecker function, as i=j, δ_ij=1；Test set Close output sample d_testPosterior distrbutionp Gaussian distributed:

d_test|X_train,d_train,X_test~N (μ_test,Σ_test) (10)

Wherein μ_testThe mean value for gathering output sample for test selects it to gather the estimated value of output sample as test；Σ_testFor The variance of test set output sample, is respectively as follows:

K (X in formula_train,X_test)=K (X_test,X_train)^TBetween test set input sample and training set input sample Covariance matrix, K (X_test,X_test) it is X_testThe covariance of itself, I_nFor 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)+ε_n (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 term_s(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 represented_nThe 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, c_lFor 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, D_iIt 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 ∈ D_i, it is otherwise 0；It and is each section A parameter κ is arranged in holiday_iTo indicate the coverage of festivals or holidays, κ_i∈N(0,υ_i 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