CN110648183A - Grey correlation and QGNN-based resident consumption price index prediction method - Google Patents
Grey correlation and QGNN-based resident consumption price index prediction method Download PDFInfo
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Abstract
The invention relates to a residential consumption price index prediction method based on grey correlation and QGNN, which comprises the steps of firstly, calculating the correlation degree of a residential consumption price index sequence and time sequences such as various influence factor sequences and the like through grey correlation analysis, sequencing according to the correlation degree, deleting an original sequence corresponding to an influence factor smaller than a threshold value of the correlation degree, and updating the time sequences so as to reduce the data volume to be processed; and then, the updated time sequence is used as input, a quantum gate node neural network based on a gradient descent method is adopted, the change rule of the time sequence is learned, and the prediction result and the prediction error of the resident consumption index are calculated. The method is beneficial to reducing the prediction time and improving the prediction precision.
Description
Technical Field
The invention relates to the technical field of resident consumption price index prediction, in particular to a resident consumption price index prediction method based on grey correlation analysis and quantum gate node neural network (QGNN).
Background
Since the resident Consumption Price Index (CPI) is affected by many factors, the CPI reflects the trend of the resident's price level for purchasing the consumption goods and services over a certain period of time. The CPI is used as an important macroscopic economic index for measuring the price level change, so that the CPI is particularly important for predicting the consumption price index, provides theoretical parameters for governments, enterprises and the public to take measures for the future price level change, and has important significance for the stable and rapid development of economy.
In recent years, several time-series prediction methods regarding residential consumption price indices have appeared. A prediction modeling method based on BP neural network, this kind of method is single model prediction, is limited by oneself, has influenced the prediction result, has reduced the prediction precision, the prediction based on RBF neural network is similar to BP neural network at the same time; a quantum neural network-based prediction modeling method introduces a quantum neural network into prediction, and also adopts single model prediction, so that the self-adaptive capacity is improved after quantum is introduced, the corresponding prediction precision is also improved, but the method has the defects of long convergence time, easy falling into local optimal solution and the like; a grey correlation-based BP neural network prediction modeling method combines grey correlation with a BP neural network, prediction accuracy is obviously higher than that of single model prediction, calculation capability and self-adaption capability are enhanced, and the method has good network convergence effect and prediction capability.
Disclosure of Invention
The invention aims to provide a residential consumption price index prediction method based on grey correlation and QGNN, which is beneficial to reducing prediction time and improving prediction precision.
In order to achieve the purpose, the invention adopts the technical scheme that: a resident consumption price index prediction method based on grey correlation and QGNN comprises the steps of firstly, calculating correlation degrees of time sequences such as a resident consumption price index sequence and each influence factor sequence through grey correlation analysis, sequencing according to the correlation degrees, deleting an original sequence corresponding to an influence factor smaller than a correlation degree threshold value, and updating the time sequences to reduce the data volume to be processed; and then, the updated time sequence is used as input, a quantum gate node neural network based on a gradient descent method is adopted, the change rule of the time sequence is learned, and the prediction result and the prediction error of the resident consumption index are calculated.
Further, the method specifically comprises the following steps:
step 1, integrating a resident consumption price index sequence X1 and time sequences of influence factor sequences X2, X3, an influence factor sequence, and the like to form a behavior sample, wherein an original Data matrix to be processed of the behavior sample is Data 0;
step 2, carrying out grey correlation analysis on the Data0, calculating the correlation degree of each influence factor sequence and the time sequence to be researched, and sequencing the correlation degree values to obtain a grey correlation sequence;
step 3, deleting the original Data columns corresponding to the influence factors smaller than the correlation threshold according to the grey correlation sequence, and updating the Data0 into Data 1;
and step 4, importing a quantum gate node neural network based on a gradient descent method for learning and training by taking Data1 as an effective information resource, calculating to obtain a prediction result Y1 and a prediction error alpha 1, and recording the operation time T1.
Further, in step 2, the method for calculating the association degree between each influence factor sequence and the time sequence to be studied includes:
subtracting the initial value image matrix to obtain a difference sequence as follows:
Δ0i(k)=|x′0(k)-x′i(k)|
wherein, Delta0i(k) Denotes the absolute values of the two sequences at time k, x'0(k) Denotes the parent sequence, x'i(k) Expressing the ith subsequence, and calculating the variables by the following formulas respectively:
xi=(xi(1),xi(2),···,xi(k),···)
x′i=(xi(1)/xi(1),xi(2)/xi(1),···,xi(k)/xi(1),···)
=(x′i(1),x′i(2),···,x′i(k),···)(i=0,1,2,···,m)
Δ0i(k)=(Δ0i(1),Δ0i(2),···,Δ0i(k),···)
(i=1,2,···,m)
wherein x isiMatrix representing raw data, xi(k) Kth original data, x 'representing factor i'iAn image matrix representing the raw data;
calculating the relevance of the two sequences as follows:
wherein the correlation coefficientMaximum difference between two polesMinimum difference between two polesPhi is the discrimination coefficient.
Further, in the step 4, the calculation of the quantum gate node neural network is realized by adopting a gradient descent method, a network model is established, and the hidden layer argument offset matrix theta and the network output layer argument offset matrix theta of the quantum gate node neural network are positioned and calculatedThe global optimal solution specifically comprises the following steps:
(1) input sample normalization and network parameter initialization;
first, there is T0The quantum argument matrix of each input sample is:
wherein,respectively representing the normalized sample matrix and the corresponding quantum argument matrix; t is0Representing the number of input samples; a isi、biIs a normalization constant;
secondly, the parameters of the quantum gate node neural network are initialized as follows:
hidden layer output matrixHidden layer argument offset matrixNetwork output matrixAmplitude and angle bias matrix of network output layerWherein, θ andto be initialized at [0,2 π]A matrix of inner uniform values; n, p and m are respectively the number of input layers, the number of hidden layers and the number of network outputs;
(2) calculating the output of the quantum gate node neural network;
for r 1 → T0The method comprises the following steps:
wherein,representing the multiplication of each column of the matrix to obtain a rowVector quantity;
(3) and (3) calculating the error of the neural network, and expressing the error by using a Frobenius norm as:
(4) calculating the back propagation of errors;
wherein Ω is p × T0The intermediate variable matrix of (2):
second, for r 1 → p, the partial derivative of E for the r column of θ is:
wherein ω is 1 XT0The intermediate variable matrix of (2):
(5) updating theta and
wherein α represents a learning step;
judging whether an iteration end condition is reached, if so, exiting the loop; otherwise, the step (2) is switched to, and the circulation is continued.
Compared with the prior art, the invention has the following beneficial effects: compared with the traditional neural network method, the method has the advantages that the prediction time is shortened, the method is more stable, the prediction precision is higher, the local optimization is not easy to happen, the resident consumption price index can be accurately predicted, theoretical parameters are provided for measures taken by governments, enterprises and the public for future price level changes, and the method has important significance for stable and rapid development of economy.
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FIG. 1 is a flow chart of an implementation of an embodiment of the present invention.
FIG. 2 is a schematic diagram of a quantum gate node neural network in an embodiment of the invention.
FIG. 3 is a flowchart of a method for implementing quantum gate node neural network computation by using a gradient descent method according to an embodiment of the present invention.
Detailed Description
The invention is further described with reference to the following figures and specific embodiments.
The invention provides a residential consumption price index prediction method based on grey correlation and QGNN, which comprises the steps of firstly, calculating the correlation degree of a residential consumption price index sequence and time sequences such as various influence factor sequences and the like through grey correlation analysis, sequencing according to the correlation degree, deleting an original sequence corresponding to an influence factor smaller than a threshold value of the correlation degree, and updating the time sequences so as to reduce the data volume to be processed; and then, the updated time sequence is used as input, a quantum gate node neural network based on a gradient descent method is adopted, the change rule of the time sequence is learned, and the prediction result and the prediction error of the resident consumption index are calculated. As shown in fig. 1, the method specifically includes the following steps:
step 1, integrating a resident consumption price index sequence X1 and time sequences of influencing factor sequences X2, X3, Xn and the like to form a behavior sample, wherein an original Data matrix to be processed of the behavior sample is Data 0.
And 2, performing gray correlation analysis on the Data0, calculating the correlation degree of each influence factor sequence and the time sequence to be researched, and sequencing the correlation degree values to obtain a gray correlation sequence. In order to observe the relationship between the time series to be researched and various influencing factors more intuitively, graphs of the change rate of X1 and X2, X3, and Xn are made according to Data 0.
And 3, deleting the original Data columns corresponding to the influence factors smaller than the correlation threshold according to the grey correlation sequence, and updating the Data0 into the Data 1. In this embodiment, the relevance threshold is 0.8, and generally, when the relevance is greater than or equal to 0.8, the relevance between the time series to be studied and each influencing factor is good.
And step 4, importing a quantum gate node neural network based on a gradient descent method for learning and training by taking Data1 as an effective information resource, calculating to obtain a prediction result Y1 and a prediction error alpha 1, and recording the operation time T1.
The technical scheme of the invention is detailed as follows:
1. grey correlation analysis model
The grey system theory is a new method for researching the problems of less data, poor information and uncertainty, and becomes a new idea for carrying out system analysis, modeling, prediction, decision and control in many fields. The grey correlation analysis is the most active branch in the grey system theory, and the basic idea is to perform trend analysis according to the closeness degree of curve shapes of a reference sequence and a comparison sequence, wherein the closer the curves are, the higher the correlation degree of the two sequences is, and the smaller the correlation degree is otherwise. The gray correlation analysis has the advantages of small self-calculation amount, strong adaptability, simple principle and the like, so that the development speed of the gray correlation analysis is far higher than that of other branches of a gray system, and the gray correlation analysis is more generally applied to life.
Based on grey correlation analysis, the main steps of calculating the correlation degree of each influence factor sequence and the time sequence to be researched are as follows:
(1) subtracting the initial value image matrix to obtain a difference sequence as follows:
Δ0i(k)=|x′0(k)-x′i(k)| (1)
wherein, Delta0i(k) Denotes the absolute values of the two sequences at time k, x'0(k) Denotes the parent sequence, x'i(k) Expressing the ith subsequence, and calculating the variables by the following formulas respectively:
xi=(xi(1),xi(2),···,xi(k),···) (2)
wherein x isiMatrix representing raw data, xi(k) Kth original data, x 'representing factor i'iAn image matrix representing the raw data;
calculating the relevance of the two sequences as follows:
wherein the correlation coefficientMaximum difference between two polesMinimum difference between two polesThe discrimination coefficient phi is 0.5.
2. Quantum gate node neural network (QGNN) based on gradient descent method
Conventional neural networks have been successfully applied to many fields with their unique advantages. However, with the continuous increase of information processing amount and complexity, the defects of poor training capability, insufficient calculation speed and the like of the artificial neural network cannot meet the requirements, and professor Kak of the university in louisiana state in the 90 th century in the 20 th century proposed a quantum neural network, which combines the advantages of quantum calculation and the neural network, has high convergence speed, and better solves the problems of large information amount, complex data and the like of modern scientific research. After that, many ideas and models are continuously proposed, such as quantum artificial neural network, quantum derived neural network, quantum dot neural network, quantum gate general-based neural network, quantum gate node neural network model, and the like. The invention combines the quantum gate node neural network with a gradient descent learning algorithm to search the optimal value of the parameter to be researched.
2.1 Quantum gate node neural network (QGNN)
The principle of the quantum gate node neural network is shown in fig. 2. In the figure, | x1>,|x2>,...,|xnIs > input, | h1>,|h2>,...,|hpIs output from hidden layer, | y1>,|y2>,...,|ym> is the network output.
(1) Let the quantum state of the input sample be:
wherein T represents the T-th training sample, and T is the total0Sample, T1, 20Let n-dimensional Euclidean space training sample
(2) According to the quantum rotating gate and the multi-position controlled gate, the following steps are obtained:
wherein, j is 1,2, and p, k is 1,2, and m; theta andrespectively representing a hidden layer output argument bias matrix and a network output layer argument bias matrix;respectively representing the probability argument of the input sample, the hidden layer output and the network output, and:
(3) if the state |1> of each layer of qubits is taken as the actual output of the layer, then the actual output of each layer is:
2.2 network model
The invention adopts a gradient descent method to realize the calculation of the quantum gate node neural network, establishes a network model, accurately positions and calculates the argument offset matrix theta of the hidden layer of the quantum gate node neural network and the argument offset matrix of the output layer of the networkThe global optimal solution of (1), the implementation flow thereofAs shown in fig. 3, the method specifically includes the following steps:
(1) input sample normalization and network parameter initialization
First, there is T0The quantum argument matrix of each input sample is:
wherein,respectively representing the normalized sample matrix and the corresponding quantum argument matrix; t is0Representing the number of input samples; a isi、biIs a normalization constant.
Secondly, the parameters of the quantum gate node neural network are initialized as follows:
hidden layer output matrixHidden layer argument offset matrixNetwork output matrixAmplitude and angle bias matrix of network output layerWherein, θ andto be initialized at [0,2 π]A matrix of inner uniform values; n, p and m are the number of input layers, the number of hidden layers and the number of network outputs, respectively.
(2) Computing output of a quantum gate node neural network
For r 1 → T0The method comprises the following steps:
wherein,the expression is to perform the multiplication calculation on each column of the matrix to obtain a row vector.
(3) And (3) calculating the error of the neural network, and expressing the error by using a Frobenius norm as:
(4) Error back propagation calculation
First, for r 1 → m, E pairThe partial derivatives of the r-th column of (1) are:
wherein Ω is p × T0The intermediate variable matrix of (2):
second, for r 1 → p, the partial derivative of E for the r column of θ is:
wherein ω is 1 XT0The intermediate variable matrix of (2):
(5) updating theta andsee equations (22) and (23):
where α represents a learning step.
Judging whether an iteration end condition is reached, if so, exiting the loop; otherwise, the step (2) is switched to, and the circulation is continued.
The above are preferred embodiments of the present invention, and all changes made according to the technical scheme of the present invention that produce functional effects do not exceed the scope of the technical scheme of the present invention belong to the protection scope of the present invention.
Claims (4)
1. A residential consumption price index prediction method based on gray correlation and QGNN is characterized in that firstly, correlation degrees of a residential consumption price index sequence and time sequences such as various influence factor sequences are calculated through gray correlation analysis, the correlation degrees are sorted according to the correlation degrees, original sequences corresponding to influence factors smaller than a threshold value of the correlation degrees are deleted, and the time sequences are updated to reduce the data volume to be processed; and then, the updated time sequence is used as input, a quantum gate node neural network based on a gradient descent method is adopted, the change rule of the time sequence is learned, and the prediction result and the prediction error of the resident consumption index are calculated.
2. The residential consumption price index prediction method based on gray correlation and QGNN according to claim 1, comprising the following steps:
step 1, integrating a resident consumption price index sequence X1 and time sequences of influence factor sequences X2, X3, an influence factor sequence, and the like to form a behavior sample, wherein an original Data matrix to be processed of the behavior sample is Data 0;
step 2, carrying out grey correlation analysis on the Data0, calculating the correlation degree of each influence factor sequence and the time sequence to be researched, and sequencing the correlation degree values to obtain a grey correlation sequence;
step 3, deleting the original Data columns corresponding to the influence factors smaller than the correlation threshold according to the grey correlation sequence, and updating the Data0 into Data 1;
and step 4, importing a quantum gate node neural network based on a gradient descent method for learning and training by taking Data1 as an effective information resource, calculating to obtain a prediction result Y1 and a prediction error alpha 1, and recording the operation time T1.
3. The method for predicting residential consumption price index based on grey correlation and QGNN according to claim 2, wherein in the step 2, the method for calculating the correlation degree between each influence factor sequence and the time sequence to be researched comprises the following steps:
subtracting the initial value image matrix to obtain a difference sequence as follows:
Δ0i(k)=|x′0(k)-x′i(k)|
wherein, Delta0i(k) Denotes the absolute values of the two sequences at time k, x'0(k) Denotes the parent sequence, x'i(k) Expressing the ith subsequence, and calculating the variables by the following formulas respectively:
xi=(xi(1),xi(2),···,xi(k),···)
x′i=(xi(1)/xi(1),xi(2)/xi(1),···,xi(k)/xi(1),···)
=(x′i(1),x′i(2),···,x′i(k),···)(i=0,1,2,···,m)
Δ0i(k)=(Δ0i(1),Δ0i(2),···,Δ0i(k),···)
(i=1,2,···,m)
wherein x isiMatrix representing raw data, xi(k) Kth original data, x 'representing factor i'iAn image matrix representing the raw data;
calculating the relevance of the two sequences as follows:
4. The residential consumption price index prediction method based on gray correlation and QGNN as claimed in claim 3, wherein in step 4, the calculation of the QGNN is realized by gradient descent method, a network model is established, and the hidden layer argument offset matrix θ and the network output layer argument offset matrix θ of the QGNN are positioned and calculatedThe global optimal solution specifically comprises the following steps:
(1) input sample normalization and network parameter initialization;
first, there is T0The quantum argument matrix of each input sample is:
wherein,respectively representing the normalized sample matrix and the corresponding quantum argument matrix; t is0Representing the number of input samples; a isi、biIs a normalization constant;
secondly, the parameters of the quantum gate node neural network are initialized as follows:
hidden layer output matrixHidden layer argument offset matrixNetwork output matrixAmplitude and angle bias matrix of network output layerWherein, θ andto be initialized at [0,2 π]A matrix of inner uniform values; n, p and m are respectively the number of input layers, the number of hidden layers and the number of network outputs;
(2) calculating the output of the quantum gate node neural network;
for r 1 → T0The method comprises the following steps:
(3) and (3) calculating the error of the neural network, and expressing the error by using a Frobenius norm as:
(4) calculating the back propagation of errors;
wherein Ω is p × T0The intermediate variable matrix of (2):
second, for r 1 → p, the partial derivative of E for the r column of θ is:
wherein ω is 1 XT0The intermediate variable matrix of (2):
wherein α represents a learning step;
judging whether an iteration end condition is reached, if so, exiting the loop; otherwise, the step (2) is switched to, and the circulation is continued.
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