CN107491828A - A kind of distributed new based on the optimal multi-kernel function of multi-source time-variable data goes out force prediction method - Google Patents

A kind of distributed new based on the optimal multi-kernel function of multi-source time-variable data goes out force prediction method Download PDF

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CN107491828A
CN107491828A CN201610420301.9A CN201610420301A CN107491828A CN 107491828 A CN107491828 A CN 107491828A CN 201610420301 A CN201610420301 A CN 201610420301A CN 107491828 A CN107491828 A CN 107491828A
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吴倩红
韩蓓
李国杰
郭雅娟
邹云峰
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Shanghai Jiaotong University
Electric Power Research Institute of State Grid Jiangsu Electric Power Co Ltd
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Electric Power Research Institute of State Grid Jiangsu Electric Power Co Ltd
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Abstract

The invention discloses a kind of distributed new based on the optimal multi-kernel function of multi-source time-variable data to go out force prediction method, by using multi-source time-variable data distribution characteristics method, single source data SVM prediction or classification, the nuclear matrix rank space method of difference, structure reflection influences the optimal multi-kernel function for the multi-source time-variable data characteristic distributions that distributed new is contributed, this optimal multi-kernel function is used when distributed new is contributed and predicted, multi-source time-variable data can be merged, it is energy output precision of prediction to improve distribution.

Description

A kind of distributed new based on the optimal multi-kernel function of multi-source time-variable data is contributed pre- Survey method
Technical field
The present invention relates to the distributed new for sending out a kind of based on the optimal multi-kernel function of multi-source time-variable data output prediction side Method, belong to Data Mining.
Background technology
In recent years, with the fast development and popularization and application of computer and information technology, the scale of sector application system Rapid to expand, data caused by sector application are in explosive increase.The data volume of this explosive increase to multi-source, isomery, Higher-dimension, distribution, the data of uncertainty propose challenge, and big data thinking is exactly the product in this environment, big data it is notable One of feature is exactly multi-source heterogeneous characteristic.
The data for influenceing distributed new prediction have a lot, such as distributed new access and operation information, power network Production management information, geographical weather information etc., these data are exactly multi-source data, if effectively utilizing point of multi-source time-variable data Boot point carries out distributed new output prediction, then can improve precision of prediction.
Multi-kernel function is to realize the effective ways of multi-source heterogeneous data fusion, and its base nuclear energy in forming is enough as a series of biographies Sensor equally perceives to respective information, using the teaching of the invention it is possible to provide more flexible and effective information tissue and data mining duty.At present The method that selection is formed on multi-kernel function, mainly there is two methods：
1st, a global kernel function and a local kernel function are directly chosen, mixed kernel function is formed after simple weighted, this The shortcomings that kind of method is：1. the composition of limitation multi-kernel function only has two monokaryon functions；2. do not account for data with existing to concentrate respectively The feature of individual multi-source heterogeneous data；3. conventional global kernel function has Polynomial kernel function Polynomial and Sigmoid core letter Number, this method select global kernel function when be typically optional one, there is blindness.
2nd, it is predicted or classifies first with monokaryon SVM, then chooses precision two kinds of kernel functions of highest and be combined Form multinuclear letter.This method have ignored the variety classes feature from different data sources, not make full use of multi-kernel function pair Multi-source heterogeneous data are effectively treated.
The content of the invention
The purpose of the present invention is to overcome above-mentioned the deficiencies in the prior art, there is provided one kind is based on the optimal multinuclear of multi-source time-variable data The distributed new of function goes out force prediction method, and this method is built by multi-kernel function, function composition compares, function performance ratio Parameter when can effectively handle distributed new related multi-source compared with three steps come optimal multi-kernel function when determining SVM predictions According to there is blindness sex chromosome mosaicism, raising precision of prediction to solve the selection of current support vector machine method Kernel Function.
The present invention is as follows to solve the technical solution of above-mentioned technical problem：
A kind of distributed new of pin based on the optimal multi-kernel function of multi-source time-variable data goes out force prediction method, specific steps It is as follows：
Step 1, determine to influence the time-variable data source of distributed new output prediction：Source of meteorological data, geodata source, New energy operation information data source；
Step 2, the A kind meteorological datas from the weather station of distributed new plant stand collection source of meteorological data, from generalized information system The B kind geodatas of geographical data source are gathered, from the C kinds new energy fortune of SCADA system collection new energy operation information data source Row data, Q=A+B+C kinds time-variable data, composition collection are combined into altogetherD represents any one time-variable data, daily collection For Xd=[x1,x2,…,xT]∈R1×T, T represents the data for gathering T moment altogether daily, in new energy service data, is distributed It is Y that formula new energy, which is contributed,i=[y1,y2,…,yT]∈R1×T, gather N days altogether；
Step 3, utilize multi-source time-variable data distribution characteristics method, single source data SVM prediction or classification, nuclear moment The battle array rank space method of difference, optimal multi-kernel function K of the structure for distributed new time-variable data source distribution featureopt(xi,xj), I, j represent every kind of time-variable data any two moment；
Step 4, step 4, output prediction is carried out to distributed new using support vector machines, kernel function is using step The optimal multi-kernel function K obtained in rapid 3opt(xi,xj)。
Structure is for the optimal multi-kernel function of distributed new time-variable data source distribution feature, specific steps in step 3 It is as follows：
(1) multi-kernel function is built：
1A. is for d kind time-variable datas, the time-variable data X of common N daysdCharacteristic distributions in corresponding coordinate system following table Show, according to the distribution of data in figure, judge the distribution character of d-th of data source time-variable data, according to distribution character, select its right Answer optimal monokaryon function Kd1(xi,xj), all Q time-variable datas are carried out with the operation, structure distribution characteristics multinuclear kernel function K1 (xi,xj)：
Wherein：Kd1(xi,xj) it is in linear kernel function, Polynomial kernel function, Radial basis kernel function and Sigmoid kernel functions One kind；
1B. is for d kind time-variable datas, using it as linear kernel function, Polynomial kernel function, Radial basis kernel function With the input feature vector amount of Sigmoid kernel function support vector machines, comparison prediction or nicety of grading, precision of prediction highest core is selected Kernel function K of the function as d-th of data source time-variable datad2(xi,xj), the operation is carried out to all Q time-variable datas, built SVM multinuclear kernel functions K2(xi,xj)：
Wherein：Kd2(xi,xj) it is in linear kernel function, Polynomial kernel function, Radial basis kernel function and Sigmoid kernel functions One kind；
(2) multi-kernel function is formed and compared：If K1(xi,xj) and K2(xi,xj) kernel function form identical, then this multi-kernel function For optimal multi-kernel function corresponding to multi-source time-variable data：Kopt(xi,xj)=K1(xi,xj)=K2(xi,xj), if K1(xi,xj) and K2 (xi,xj) composition it is different, then turn (3)；
(3) multi-kernel function performance comparision：
3A. calculates optimal weighting coefficientses λ：
3B. is to multi-kernel function K1(xi,xj) and K2(xi,xj) be weighted, form weighting multinuclear kernel function K3(xi,xj)：
Wherein：Wherein：Kd3(xi,xj) it is linear kernel function, Polynomial kernel function, Radial basis kernel function and Sigmoid cores One kind in function, λ are the optimal weighting coefficientses that calculate in 3A, 0<λ<1；
3C. is calculated in K for the time-variable data of d kind data sourcesd1(xi,xj)、Kd2(xi,xj)、Kd3(xi,xj) kernel function Nuclear matrix under mapping：
Wherein：D=1,2 ..., Q, s=1,2,3, s represent K1(xi,xj)、K2(xi,xj)、K3(xi,xj) three seed nucleus function pairs The subscript answered；
3D. utilizes nuclear matrix rank space method of difference method, calculates the A obtained by 3B1,s,A2,s,…,AQ,s, s=1,2,3 order Spatial Difference is measured：
Wherein：D=1,2 ..., Q, s=1,2,3, rank (A) are the order for seeking matrix A；
3E. compares RSD1、RSD2With RSD3The size of value, function corresponding to selection maximum melt as multi-source time-variable data The optimal multi-kernel function K closedopt(xi,xj)。
Compared with prior art, the beneficial effects of the invention are as follows：
The Selection of kernel function of traditional support vector machine is always an open question, for that can realize multi-source heterogeneous data The multi-kernel function selection of fusion more has blindness so that distributed new output precision of prediction is relatively low, and of the invention adopts With multi-source time-variable data distribution characteristics method, single source data SVM prediction or classification, the nuclear matrix rank space method of difference, energy Enough judge the characteristic distributions of all distributed new correlation multi-source time-variable datas, local kernel function is selected still for every kind of data Global kernel function provides foundation, constructs optimal multi-kernel function, realizes the fusion of multi-source time-variable data, and it is energy to improve distribution Source output precision of prediction.
Brief description of the drawings
Fig. 1 is that the distributed new based on the optimal multi-kernel function of multi-source time-variable data goes out force prediction method
Fig. 2 is using the flow chart of multi-source time-variable data distribution characteristics method construction multi-kernel function in step 3
Fig. 3 is the flow chart that optimal multi-kernel function is selected after two multi-kernel function linear weighted functions of step 3
Embodiment
To become apparent the present invention, hereby to be preferable to carry out example, and accompanying drawing is coordinated to be described in detail below.Fig. 1 is more The distributed new of the optimal multi-kernel function of source time-variable data goes out force prediction method overall flow figure, i.e. following step 1 to step 4。
Step 1, determine to influence the time-variable data source of distributed new output prediction：Source of meteorological data, geodata source, New energy operation information data source；
Step 2, the A kind meteorological datas from the weather station of distributed new plant stand collection source of meteorological data, from generalized information system The B kind geodatas of geographical data source are gathered, from the C kinds new energy fortune of SCADA system collection new energy operation information data source Row data, Q=A+B+C kinds time-variable data, composition collection are combined into altogetherD represents any one time-variable data, daily collection For Xd=[x1,x2,…,xT]∈R1×T, T represents the data for gathering T moment altogether daily, gathered N days altogether, to be predicted distributed new It is Y that the energy, which is contributed,i=[y1,y2,…,yT]∈R1×T；
Step 3, utilize multi-source time-variable data distribution characteristics method, single source data SVM prediction or classification, nuclear moment The battle array rank space method of difference, optimal multi-kernel function K of the structure for distributed new time-variable data source distribution featureopt(xi,xj), I, j represent every kind of time-variable data any two moment, comprise the following steps that：
(1) multi-kernel function is built：
1A. is for d kind time-variable datas, the time-variable data X of common N daysdCharacteristic distributions in corresponding coordinate system following table Show, according to the distribution of data in figure, judge the distribution character of d-th of data source time-variable data, according to distribution character, select its right Answer optimal monokaryon function Kd1(xi,xj), all Q time-variable datas are carried out with the operation, structure distribution characteristics multinuclear kernel function K1 (xi,xj)：
Wherein：Kd1(xi,xj) it is in linear kernel function, Polynomial kernel function, Radial basis kernel function and Sigmoid kernel functions One kind；
1B. is for d kind time-variable datas, using it as linear kernel function, Polynomial kernel function, Radial basis kernel function With the input feature vector amount of Sigmoid kernel function support vector machines, comparison prediction or nicety of grading, precision of prediction highest core is selected Kernel function K of the function as d-th of data source time-variable datad2(xi,xj), the operation is carried out to all Q time-variable datas, built SVM multinuclear kernel functions K2(xi,xj)：
Wherein：Kd2(xi,xj) it is in linear kernel function, Polynomial kernel function, Radial basis kernel function and Sigmoid kernel functions One kind；
(2) multi-kernel function is formed and compared：If K1(xi,xj) and K2(xi,xj) kernel function form identical, then this multi-kernel function For optimal multi-kernel function corresponding to multi-source time-variable data：Kopt(xi,xj)=K1(xi,xj)=K2(xi,xj), if K1(xi,xj) and K2 (xi,xj) composition it is different, then turn (3)；
(3) multi-kernel function performance comparision：
3A. calculates optimal weighting coefficientses λ：
1. in multi-kernel function, the function after mapping is：
In formula：φ3、φ1、φ2Respectively weight multi-kernel function K3(xi,xj), multi-source time-variable data distribution characteristics method multinuclear Function K1(xi,xj), single source data SVM prediction or classification multi-kernel function K2(xi,xj) corresponding to Function Mapping；
2. distance is：
3. seek the One- place 2-th Order multinomial on λ：
4. maximizing L (λ), that is, the polynomial max problem of One- place 2-th Order is sought, then λ is tried to achieve by following formula：
3B. is to multi-kernel function K1(xi,xj) and K2(xi,xj) be weighted, form weighting multinuclear kernel function K3(xi,xj)：
Wherein：Wherein：Kd3(xi,xj) it is linear kernel function, Polynomial kernel function, Radial basis kernel function and Sigmoid cores One kind in function, λ are the optimal weighting coefficientses that calculate in 3A, 0<λ<1；
3C. is calculated in K for the time-variable data of d kind data sourcesd1(xi,xj)、Kd2(xi,xj)、Kd3(xi,xj) kernel function Nuclear matrix under mapping：
Wherein：D=1,2 ..., Q, s=1,2,3, s represent K1(xi,xj)、K2(xi,xj)、K3(xi,xj) three seed nucleus function pairs The subscript answered；
3D. utilizes nuclear matrix rank space method of difference method, calculates the A obtained by 3B1,s,A2,s,…,AQ,s, s=1,2,3 order Spatial Difference is measured：
Wherein：D=1,2 ..., Q, s=1,2,3, rank (A) are the order for seeking matrix A；
3E. compares RSD1、RSD2With RSD3The size of value, function corresponding to selection maximum melt as multi-source time-variable data The optimal multi-kernel function K closedopt(xi,xj)。
Step 4, output prediction is carried out to distributed new using support vector machines, kernel function is used in step 3 and obtained The optimal multi-kernel function K arrivedopt(xi,xj)。
The present invention is by using using multi-source time-variable data distribution characteristics method, single source data SVM prediction or classification Method, the nuclear matrix rank space method of difference, construct optimal multi-kernel function, realize the fusion of multi-source time-variable data, improve distributed New energy output precision of prediction, is suitable for the analysis of multi-source data.

Claims (2)

1. a kind of distributed new based on the optimal multi-kernel function of multi-source time-variable data goes out force prediction method, it is characterised in that This method comprises the following steps：
Step 1, determine to influence the time-variable data source of distributed new output prediction, including source of meteorological data, geodata source With new energy service data source；
Step 2, the A kind meteorological datas from the weather station of distributed new plant stand collection source of meteorological data, are gathered from generalized information system The B kind geodatas in geodata source, number is run from the C kinds new energy of SCADA system collection new energy operation information data source According to Q=A+B+C kinds time-variable data, composition collection are combined into altogetherD represents any one time-variable data, and collection is X dailyd =[x1,x2,…,xT]∈R1×T, the daily data for gathering T moment altogether of T representatives, gather N days altogether, distributed new to be predicted Contribute as Yi=[y1,y2,…,yT]∈R1×T；
Step 3, utilize multi-source time-variable data distribution characteristics method, single source data SVM prediction or classification, nuclear matrix order Spatial diversity method, optimal multi-kernel function K of the structure for distributed new time-variable data source distribution featureopt(xi,xj), i, j Represent every kind of time-variable data any two moment；
Step 4, output prediction is carried out to distributed new using support vector machines, kernel function uses what is obtained in step 3 Optimal multi-kernel function Kopt(xi,xj)。
2. optimal multinuclear letter of step 3 structure for distributed new time-variable data source distribution feature in the claim 1 Number, it is characterised in that the step 3 is specific as follows：
(1) multi-kernel function is built：
1A. is for d kind time-variable datas, the time-variable data X of common N daysdCharacteristic distributions represented under corresponding coordinate system, root According to the distribution of data in coordinate system, judge the distribution character of d-th of data source time-variable data, select corresponding optimal monokaryon function Kd1 (xi,xj), all Q time-variable datas are carried out with the operation, structure distribution characteristics multinuclear kernel function K1(xi,xj)：
<mrow> <msub> <mi>K</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>d</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>Q</mi> </munderover> <msub> <mi>K</mi> <mrow> <mi>d</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> </mrow>
Wherein：Kd1(xi,xj) be linear kernel function, Polynomial kernel function, Radial basis kernel function and Sigmoid kernel functions in one Kind；
1B. for d kind time-variable datas, using its as linear kernel function, Polynomial kernel function, Radial basis kernel function with The input feature vector amount of Sigmoid kernel function support vector machines, comparison prediction or nicety of grading, select precision of prediction highest core letter Kernel function K of the number as d-th of data source time-variable datad2(xi,xj), the operation is carried out to all Q time-variable datas, built SVM multinuclear kernel functions K2(xi,xj)：
<mrow> <msub> <mi>K</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>d</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>Q</mi> </munderover> <msub> <mi>K</mi> <mrow> <mi>d</mi> <mn>2</mn> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> </mrow>
Wherein：Kd2(xi,xj) be linear kernel function, Polynomial kernel function, Radial basis kernel function and Sigmoid kernel functions in one Kind；
(2) multi-kernel function is formed and compared：If K1(xi,xj) and K2(xi,xj) kernel function form it is identical, then this multi-kernel function is more Optimal multi-kernel function corresponding to the time-variable data of source：Kopt(xi,xj)=K1(xi,xj)=K2(xi,xj), if K1(xi,xj) and K2(xi, xj) composition it is different, then turn (3)；
(3) multi-kernel function performance comparision：
3A. calculates optimal weighting coefficientses λ：
<mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>D</mi> <mo>=</mo> <msub> <mi>K</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> </mrow> <mo>)</mo> </mrow> <mo>-</mo> <mn>2</mn> <msub> <mi>K</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>K</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>E</mi> <mo>=</mo> <msub> <mi>K</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> </mrow> <mo>)</mo> </mrow> <mo>-</mo> <mn>2</mn> <msub> <mi>K</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>K</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>j</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>A</mi> <mo>=</mo> <mi>D</mi> <mo>+</mo> <mi>E</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>B</mi> <mo>=</mo> <mo>-</mo> <mn>2</mn> <mi>E</mi> </mrow> </mtd> </mtr> </mtable> </mfenced>
<mrow> <mi>&amp;lambda;</mi> <mo>=</mo> <mo>-</mo> <mfrac> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>T</mi> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>By</mi> <mi>i</mi> </msub> <msub> <mi>y</mi> <mi>j</mi> </msub> </mrow> <mrow> <mn>2</mn> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>T</mi> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>Ay</mi> <mi>i</mi> </msub> <msub> <mi>y</mi> <mi>j</mi> </msub> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>T</mi> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>Ey</mi> <mi>i</mi> </msub> <msub> <mi>y</mi> <mi>j</mi> </msub> </mrow> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>T</mi> </munderover> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>i</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mrow> <mo>(</mo> <mrow> <mi>D</mi> <mo>+</mo> <mi>E</mi> </mrow> <mo>)</mo> </mrow> <msub> <mi>y</mi> <mi>i</mi> </msub> <msub> <mi>y</mi> <mi>j</mi> </msub> </mrow> </mfrac> </mrow>
3B. is to multi-kernel function K1(xi,xj) and K2(xi,xj) be weighted, form weighting multinuclear kernel function K3(xi,xj)：
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>K</mi> <mn>3</mn> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>&amp;lambda;K</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>-</mo> <mi>&amp;lambda;</mi> </mrow> <mo>)</mo> </mrow> <msub> <mi>K</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mi>&amp;lambda;</mi> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>d</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>Q</mi> </munderover> <msub> <mi>K</mi> <mrow> <mi>d</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>-</mo> <mi>&amp;lambda;</mi> </mrow> <mo>)</mo> </mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>d</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>Q</mi> </munderover> <msub> <mi>K</mi> <mrow> <mi>d</mi> <mn>2</mn> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>d</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>Q</mi> </munderover> <mrow> <mo>&amp;lsqb;</mo> <mrow> <msub> <mi>&amp;lambda;K</mi> <mrow> <mi>d</mi> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>-</mo> <mi>&amp;lambda;</mi> </mrow> <mo>)</mo> </mrow> <msub> <mi>K</mi> <mrow> <mi>d</mi> <mn>2</mn> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> <mo>&amp;rsqb;</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>d</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>Q</mi> </munderover> <msub> <mi>K</mi> <mrow> <mi>d</mi> <mn>3</mn> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mi>j</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced>
Wherein：Wherein：Kd3(xi,xj) it is in linear kernel function, Polynomial kernel function, Radial basis kernel function and Sigmoid kernel functions One kind, a is the optimal weighting coefficientses that calculate in 3A, 0<λ<1；
3C. is calculated in K for the time-variable data of d kind data sourcesd1(xi,xj)、Kd2(xi,xj)、Kd3(xi,xj) kernel function mapping Under nuclear matrix：
<mrow> <msub> <mi>A</mi> <mrow> <mi>d</mi> <mo>,</mo> <mi>s</mi> </mrow> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>K</mi> <mrow> <mi>d</mi> <mi>s</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mi>L</mi> </mtd> <mtd> <mrow> <msub> <mi>K</mi> <mrow> <mi>d</mi> <mi>s</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mi>T</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>M</mi> </mtd> <mtd> <mi>O</mi> </mtd> <mtd> <mi>M</mi> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>K</mi> <mrow> <mi>d</mi> <mi>s</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>T</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mi>L</mi> </mtd> <mtd> <mrow> <msub> <mi>K</mi> <mrow> <mi>d</mi> <mi>s</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>T</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mi>T</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
Wherein：D=1,2 ..., Q, s=1,2,3, s represent K1(xi,xj)、K2(xi,xj)、K3(xi,xj) corresponding to three seed nucleus functions Subscript；
3D. utilizes nuclear matrix rank space method of difference method, calculates the A obtained by 3B1,s,A2,s,…,AQ,s, s=1,2,3 rank space Diversity measure：
<mrow> <msub> <mi>RSD</mi> <mi>s</mi> </msub> <mrow> <mo>(</mo> <mrow> <msub> <mi>A</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>s</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>A</mi> <mrow> <mn>2</mn> <mo>,</mo> <mi>s</mi> </mrow> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>A</mi> <mrow> <mi>Q</mi> <mo>,</mo> <mi>s</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mi>Q</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>d</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>Q</mi> </munderover> <mfenced open = "{" close = "}"> <mtable> <mtr> <mtd> <mrow> <mn>2</mn> <mo>&amp;times;</mo> <mi>r</mi> <mi>a</mi> <mi>n</mi> <mi>k</mi> <mrow> <mo>(</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>A</mi> <mrow> <mi>d</mi> <mo>,</mo> <mi>s</mi> </mrow> <mi>T</mi> </msubsup> </mtd> <mtd> <mrow> <msubsup> <mi>A</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>s</mi> </mrow> <mi>T</mi> </msubsup> <mo>...</mo> <msubsup> <mi>A</mi> <mrow> <mi>d</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>s</mi> </mrow> <mi>T</mi> </msubsup> <msubsup> <mi>A</mi> <mrow> <mi>d</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>s</mi> </mrow> <mi>T</mi> </msubsup> <mo>...</mo> <msubsup> <mi>A</mi> <mrow> <mi>Q</mi> <mo>,</mo> <mi>s</mi> </mrow> <mi>T</mi> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mi>T</mi> </msup> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>-</mo> <mi>r</mi> <mi>a</mi> <mi>n</mi> <mi>k</mi> <mrow> <mo>(</mo> <msub> <mi>A</mi> <mrow> <mi>d</mi> <mo>,</mo> <mi>s</mi> </mrow> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mi>r</mi> <mi>a</mi> <mi>n</mi> <mi>k</mi> <mrow> <mo>(</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <mrow> <msubsup> <mi>A</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>s</mi> </mrow> <mi>T</mi> </msubsup> <mo>...</mo> <msubsup> <mi>A</mi> <mrow> <mi>d</mi> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mi>s</mi> </mrow> <mi>T</mi> </msubsup> <msubsup> <mi>A</mi> <mrow> <mi>d</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>s</mi> </mrow> <mi>T</mi> </msubsup> <mo>...</mo> <msubsup> <mi>A</mi> <mrow> <mi>Q</mi> <mo>,</mo> <mi>s</mi> </mrow> <mi>T</mi> </msubsup> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mi>T</mi> </msup> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
Wherein：D=1,2 ..., Q, s=1,2,3, rank (A) are the order of matrix A；
3E. compares RSD1、RSD2With RSD3The size of value, what function corresponding to selection maximum merged as multi-source time-variable data Optimal multi-kernel function Kopt(xi,xj)。
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