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 PDF

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CN110648183A
CN110648183A CN201910943167.4A CN201910943167A CN110648183A CN 110648183 A CN110648183 A CN 110648183A CN 201910943167 A CN201910943167 A CN 201910943167A CN 110648183 A CN110648183 A CN 110648183A
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廖一鹏
张进
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Fuzhou University
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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

Grey correlation and QGNN-based resident consumption price index prediction method
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:
Figure BDA0002223485400000021
wherein the correlation coefficient
Figure BDA0002223485400000022
Maximum difference between two poles
Figure BDA0002223485400000023
Minimum difference between two poles
Figure BDA0002223485400000024
Phi 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 calculated
Figure BDA0002223485400000031
The 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:
Figure BDA0002223485400000032
wherein,
Figure BDA0002223485400000033
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 matrix
Figure BDA0002223485400000035
Network output matrix
Figure BDA0002223485400000036
Amplitude and angle bias matrix of network output layer
Figure BDA0002223485400000037
Wherein, θ and
Figure BDA0002223485400000038
to 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:
Figure BDA0002223485400000039
Figure BDA00022234854000000310
wherein,
Figure BDA00022234854000000311
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:
Figure BDA00022234854000000312
wherein,
Figure BDA0002223485400000041
a desired output matrix for the neural network;
(4) calculating the back propagation of errors;
first, for r 1 → m, E pair
Figure BDA0002223485400000042
The partial derivatives of the r-th column of (1) are:
Figure BDA0002223485400000043
wherein Ω is p × T0The intermediate variable matrix of (2):
Figure BDA0002223485400000044
second, for r 1 → p, the partial derivative of E for the r column of θ is:
Figure BDA0002223485400000045
wherein ω is 1 XT0The intermediate variable matrix of (2):
Figure BDA0002223485400000046
(5) updating theta and
Figure BDA0002223485400000048
Figure BDA0002223485400000049
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.
Drawings
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)
Figure BDA0002223485400000065
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:
Figure BDA0002223485400000061
wherein the correlation coefficient
Figure BDA0002223485400000062
Maximum difference between two poles
Figure BDA0002223485400000063
Minimum difference between two poles
Figure BDA0002223485400000064
The 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:
Figure BDA0002223485400000071
wherein T represents the T-th training sample, and T is the total0Sample, T1, 20Let n-dimensional Euclidean space training sample
Figure BDA0002223485400000072
(2) According to the quantum rotating gate and the multi-position controlled gate, the following steps are obtained:
Figure BDA0002223485400000073
Figure BDA0002223485400000074
wherein, j is 1,2, and p, k is 1,2, and m; theta and
Figure BDA0002223485400000075
respectively representing a hidden layer output argument bias matrix and a network output layer argument bias matrix;
Figure BDA0002223485400000076
respectively representing the probability argument of the input sample, the hidden layer output and the network output, and:
Figure BDA0002223485400000077
Figure BDA0002223485400000078
(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:
Figure BDA00022234854000000710
Figure BDA00022234854000000711
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 network
Figure BDA00022234854000000712
The 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:
Figure BDA0002223485400000081
wherein,
Figure BDA0002223485400000082
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 matrix
Figure BDA0002223485400000083
Hidden layer argument offset matrix
Figure BDA0002223485400000084
Network output matrixAmplitude and angle bias matrix of network output layer
Figure BDA0002223485400000086
Wherein, θ and
Figure BDA0002223485400000087
to 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:
Figure BDA0002223485400000088
Figure BDA0002223485400000089
wherein,
Figure BDA00022234854000000810
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:
Figure BDA00022234854000000811
wherein,
Figure BDA00022234854000000812
is the desired output matrix of the neural network.
(4) Error back propagation calculation
First, for r 1 → m, E pairThe partial derivatives of the r-th column of (1) are:
Figure BDA0002223485400000091
wherein Ω is p × T0The intermediate variable matrix of (2):
Figure BDA0002223485400000092
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):
Figure BDA0002223485400000094
(5) updating theta andsee equations (22) and (23):
Figure BDA0002223485400000096
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:
wherein the correlation coefficient
Figure FDA0002223485390000022
Maximum difference between two poles
Figure FDA0002223485390000023
Minimum difference between two poles
Figure FDA0002223485390000024
Phi is the discrimination coefficient.
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 calculated
Figure FDA0002223485390000025
The 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:
Figure FDA0002223485390000026
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 matrix
Figure FDA0002223485390000028
Hidden layer argument offset matrix
Figure FDA0002223485390000029
Network output matrix
Figure FDA00022234853900000210
Amplitude and angle bias matrix of network output layer
Figure FDA00022234853900000211
Wherein, 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:
Figure FDA00022234853900000213
Figure FDA0002223485390000031
wherein,
Figure FDA0002223485390000032
performing 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:
Figure FDA0002223485390000033
wherein,
Figure FDA0002223485390000034
a desired output matrix for the neural network;
(4) calculating the back propagation of errors;
first, for r 1 → m, E pair
Figure FDA0002223485390000035
The partial derivatives of the r-th column of (1) are:
Figure FDA0002223485390000036
wherein Ω is p × T0The intermediate variable matrix of (2):
Figure FDA0002223485390000037
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):
Figure FDA0002223485390000039
(5) updating theta and
Figure FDA00022234853900000310
Figure FDA00022234853900000311
Figure FDA00022234853900000312
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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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111239715A (en) * 2020-01-13 2020-06-05 哈尔滨工业大学 Fingerprint positioning method combining gray correlation and neural network

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111239715A (en) * 2020-01-13 2020-06-05 哈尔滨工业大学 Fingerprint positioning method combining gray correlation and neural network

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Application publication date: 20200103