CN109492428A - A kind of difference method for secret protection towards principal component analysis - Google Patents
A kind of difference method for secret protection towards principal component analysis Download PDFInfo
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- CN109492428A CN109492428A CN201811265579.9A CN201811265579A CN109492428A CN 109492428 A CN109492428 A CN 109492428A CN 201811265579 A CN201811265579 A CN 201811265579A CN 109492428 A CN109492428 A CN 109492428A
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F21/00—Security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
- G06F21/60—Protecting data
- G06F21/62—Protecting access to data via a platform, e.g. using keys or access control rules
- G06F21/6218—Protecting access to data via a platform, e.g. using keys or access control rules to a system of files or objects, e.g. local or distributed file system or database
- G06F21/6245—Protecting personal data, e.g. for financial or medical purposes
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2221/00—Indexing scheme relating to security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
- G06F2221/21—Indexing scheme relating to G06F21/00 and subgroups addressing additional information or applications relating to security arrangements for protecting computers, components thereof, programs or data against unauthorised activity
- G06F2221/2107—File encryption
Abstract
The invention discloses a kind of difference method for secret protection towards principal component analysis, comprising the following steps: data matrix centralization, i.e., each dimension data subtract the mean value of this dimension；Covariance matrix is calculated to data matrixCalculate the eigenvalue λ and feature vector V of covariance matrix A；Calculate the principal component number k retained；Initial data is mapped to principal component space and obtains projection matrix Z；To the projection matrix Z each column Elemental partition privacy budget εj, calculate the random noise of addition；Noise is added to the projection matrix Z, the projection matrix Z ' after obtaining plus making an uproar；Calculate the error between initial data and low-rank approximate data.The present invention both can realize the simplification of data, and can add noise to avoid the data to " inessential " effectively to data set dimensionality reduction; reduce the waste of privacy budget; to improve the availability of data, the data of publication are made to reflect truthful data as far as possible, while protecting the privacy of data.
Description
Technical field
The present invention relates to a kind of difference method for secret protection towards principal component analysis, belongs to field of information security technology.
Background technique
With the continuous development of big data technology, the data of various information system storages are more and more abundant, increase data
Analyze the complexity of processing.As one of the important method of data analysis, principal component analysis can be converted to multivariable several
Primary variables, these primary variables can indicate most information of initial data, disclose data essence.Principal component analysis is real
Showed the simplification of data so that data be easier to using while reduce the computing cost of algorithm.It is generally comprised in data set
Many privacy informations, if directly analyzing data using machine learning or data mining algorithm, it will bring privacy leakage problem.
Difference method for secret protection is a kind of current secret protection technology of hot topic, is realized by noise mechanism, i.e., into output result
Random noise is added to protect data safety, the noise of addition is bigger, and data are safer, however, the availability of data is lower, instead
?.
For multiattribute data, privacy budget of traditional Laplce's mechanism to all properties distribution same size, this
Scheme is simple to operation, but the noise that will lead to addition is too big, and availability of data drastically reduces, while giving the number of " inessential "
According to distribution privacy budget, a part of privacy budget is wasted, therefore the effect is unsatisfactory.
Summary of the invention
Problem to be solved by this invention provides one kind towards principal component analysis aiming at the defects of background technique
Difference method for secret protection, the present invention both can realize the simplification of data, and can be to avoid right effectively to data set dimensionality reduction
The data of " inessential " add noise, reduce the waste of privacy budget, to improve the availability of data, keep the data of publication most
It may reflect truthful data, while protect the privacy of data.
To solve the above-mentioned problems, it adopts the following technical scheme that
A kind of difference method for secret protection towards principal component analysis of the invention is based on preset sample data set X, sample
This number n, sample space dimension d；Principal component analytical method the following steps are included:
Step 1: data matrix centralization, i.e., each dimension data subtract the mean value of this dimension；
Step 2: calculating covariance matrix with the data matrix that step 1 obtainsWherein, XTIt is data matrix X
Transposition；
Step 3: calculating the eigenvalue λ and feature vector V of covariance matrix A described in step 2, meet AV=λ V；It will be special
Value indicative descending is arranged with: λ1>λ2…>λd, corresponding feature vector is v1,v2…vd；
Step 4: calculating the principal component number k of reservation；
Step 5: initial data being mapped to principal component space and obtains projection matrix Z；
Step 6: giving the projection matrix Z each column Elemental partition privacy budget εj, calculate the random noise of addition；
Step 7: adding noise to the projection matrix Z, the projection matrix Z ' after obtaining plus making an uproar；
Step 8: calculating the error between initial data and low-rank approximate data.
In step 1, for convenience of covariance matrix is solved, each dimension mean value is 0 after centralization, goes mean value to each attribute,
As shown in formula (1):
xjIt is the data of j-th of attribute of all samples, x 'jIt is the data of j-th of attribute of all samples after centralization, xijIt is
The data of i-th of sample, j-th of attribute in data set X,It is the mean value of j-th of attribute.
In step 4, to an eigenvalue contribution value α of setting, wherein 0≤α≤1 calculates the principal component number to be retained
K makes it meet the principal component eigenvalue contribution value per >=α actually retained, in which:
In step 5, the projection matrix Z=XVkIt is mapping of the initial data on principal component space, wherein Vk=v1,
v2…vkIt is the corresponding feature vector of k principal component retained.
In step 6, the random noise is Laplace noise, i.e. noise obeys Laplace distribution Lap (b), and b is scale
Parameter, b=Δ f/ ε, Δ f are global susceptibility, and ε is privacy budget；
It is as follows to obey the Laplace distribution probability density function that scale parameter is b:
Wherein, x indicates all possible value, and p (x) is the probability of all values
Projection matrix Z=XVkJth column indicate mapping of the initial data in j-th of principal component, each column indicate difference
Meaning, equal or unequal privacy budget ε can be distributedj, wherein 1≤j≤k.
Distribute equal privacy budget εj: divide equally:Each column distribute equal privacy budget；
The privacy budget ε that distribution does not waitj: press weight distribution:It is distributed according to principal component characteristic value accounting
Privacy budget.
In step 7, adding the projection matrix after making an uproar is Z '=(z '1,z′2…z′j…z′k), wherein z 'j' expression formula such as
Under:
zjIt is the jth column of projection matrix,It is the global susceptibility of projection matrix.
In step 8, low-rank approximate matrix It is eigenvectors matrix VkTransposition, It is the mean value of attribute, wherein
Approximate data error is calculated using formula (5)；
MSE-F=| | Y-X | |F (5)
||·||FIt is the F norm of matrix；The F norm of matrix refers to the quadratic sum of matrix element evolution again；
The matrix of a m × n is let c be, then the F norm of C are as follows:
The present invention by adopting the above technical scheme, compared with prior art, has following technical effect that
The present invention is directed to the too big defect of traditional Laplce's mechanism addition noise, proposes that one kind more preferably adds the side of making an uproar
Formula achievees the purpose that secret protection, while ensure that number so that the low-rank approximate data that reduction obtains is distorted to a certain extent
According to availability.The method of the present invention is simple, easy to operate and do not limit data set size and attribute, and feature is as follows:
(1) safety for guarantee Principal Component Analysis Algorithm is devised by adding noise appropriate in projection matrix
Principal Component Analysis Algorithm towards difference secret protection, and prove that algorithm meets difference privacy conditions；
(2) compared with traditional Laplce's mechanism, the program, which only adds the data of " important ", makes an uproar, and avoids privacy budget
Waste.It is smaller to data addition noise under identical secret protection degree, to improve the availability of data, make the number of publication
According to reflection truthful data as far as possible, while protecting the privacy of data.
Detailed description of the invention
Fig. 1 is used in experiment provided by the invention for testing the data of difference privacy Principal Component Analysis Algorithm performance
Schematic diagram；
Fig. 2 is the work flow diagram of the difference method for secret protection provided by the invention towards principal component analysis.
Specific embodiment
The implementation of technical solution of the present invention is described in further detail with reference to the accompanying drawing, it should be understood that these examples
It is only illustrative of the invention and is not intended to limit the scope of the invention, after the present invention has been read, those skilled in the art couple
The modification of various equivalent forms of the invention falls within the application range as defined in the appended claims.
The present invention, which first calculates, retains principal component number, then initial data is mapped to principal component space and obtains projection matrix,
For projection matrix each column Elemental partition privacy budget, Laplace noise of the addition in data is calculated, it both can effectively logarithm
According to collection dimensionality reduction, the simplification of data is realized, and can add noise to avoid the data to " inessential ", reduce the wave of privacy budget
Take, to improve the availability of data.It difference secret protection technical definition of the present invention one and its stringent attacks
Hit model, and carried out stringent mathematical proof and quantificational expression to privacy risk, at the same difference privacy mechanism also can it is main at
Good balance is obtained in terms of analysis result availability and safety two.
Referring to fig. 2, specific embodiment is as follows:
Step 1: collection obtains sample data set Secom.txt, storage be each attribute in semiconductor process number
According to sample number 1567, attribute number is 591, data set X={ x1,x2…x591, xiIt is the number of all sample ith attributes
According to.With formula (1) to every one-dimensional data centralization.10 attribute datas of data set after centralization are taken, as follows:
x1=[16.47710442,81.32710442, -81.84289558 ... -35.64289558, -
119.53289558-69.53289558]T
x50=[- 7.93969674, -0.99239674,5.01130326 ... -4.19689674,7.65940326,
7.02220326]T
x100=[- 0.0266401, -0.0173401,0.1202599 ... -0.0192401,0.1435599, -
0.0647401]T
x150=[- 2.54326790, -0.529267903, -1.99526790 ... -2.84217094e-14,
1.43873210-2.84217094e-14]T
x200=[- 0.91205637,0.11794363, -1.82205637 ... -7.61205637, -2.47205637, -
2.84205637]T
x250=[110.29433331,83.37773331, -5.24676669 ... 7.68593331, -10.22116669,
12.12073331]T
x300=[- 0.04006684, -0.00416684, -0.00196684 ... -0.02826684,0.02093316, -
0.03726684]T
x350=[2.14776410e-03, -2.25223590e-03, -4.45223590e-03 ... -3.46944695e-
17, -3.46944695e-17, -3.46944695e-17]T
x400=[- 0.9083303, -1.9865303, -0.2702303 ... 0.3510697, -1.0224303,
2.3229697]T
x450=[0.59278442, -0.23961558, -0.46731558 ... 0.38228442,1.83908442,
1.08908442]T
Step 2: calculating covariance matrix A with the data matrix that step 1 obtains.
Step 3: calculating the eigenvalue λ and feature vector V of step 2 covariance matrix A.Characteristic value descending is arranged, first 5
Characteristic value and feature vector are as follows:
λ1=53415197.85687523v1=[- 6.39070760e-04,2.35722934e-05,2.36801459e-
04,…,2.61329351e-08,5.62597732e-09,3.89298443e-04]T
λ2=21746671.90465921v2=[- 1.20314234e-04, -6.60163227e-04,1.58026311e-
04,…,-6.06233975e-09,5.96647587e-09,-2.32070657e-04]T
λ3=8248376.61529074v3=[1.22460363e-04,1.71369126e-03,3.28185512e-
04,…,1.09328336e-09,8.83024927e-09,7.13534990e-04]T
λ4=2073880.85929397v4=[- 2.72221201e-03,2.04941860e-04,4.20363040e-
04,…,2.66843972e-07,5.91392106e-08,-1.42694472e-03]T
λ5=1315404.38775829v5=[- 1.19198101e-05, -3.62618336e-03, -2.27104930e-
04,…,-3.24788891e-07,-9.39871716e-08,-3.98748600e-03]T
Step 4: being determined according to formula (2) and retain principal component number.Take eigenvalue contribution value α=95%, then require per >=
95%, calculate to obtain k=5.
Step 5: calculating projection matrix Z=XV5。V5=(v1,v2…v5) be retain the corresponding feature of 5 principal components to
Amount.Projection matrix Z is as follows:
Step 6: the random noise of addition is set.If privacy budget ε ∈ [0.1,1], projection matrix each column is distributed by dividing equally
The privacy budget got isSusceptibility isRemember zjIt is arranged for the jth of projection matrix Z, then the result after being added to random noise
ForAdd the projection matrix Z ' after making an uproar as follows:
Step 7: exporting low-rank approximate matrix according to formula (5).
Step 8: assessment algorithm performance.Difference privacy principal component analysis effect is assessed using MSE-F, MSE-F is that low-rank is close
Error between likelihood data and initial data, MSE-F is smaller, and algorithm availability is higher.
It is to be compared by the respectively distribution privacy budget of the invention used and by weight distribution privacy budget herein, compares
Under identical privacy budget level, which kind of adds mode bring error of making an uproar smaller.Since Laplace noise is random noise, institute
With each ε value of correspondence, every group of experiment is carried out 100 times, records MSE-F average value, as shown in Fig. 1.
As shown in Figure 1, under identical privacy budget level, what the present invention used divides equally distribution ratio by weight distribution bring
Error is smaller, this illustrates that present invention availability of data under identical secret protection rank is higher, and privacy budget is bigger, error
It is smaller.
In conclusion the invention proposes a kind of difference method for secret protection towards principal component analysis, by being original
Data projection matrix each column Elemental partition privacy budget, is providing the noise for reducing addition while secret protection.The present invention
It is possible to prevente effectively from the data to " inessential " add noise, the waste of privacy budget is reduced, so that the availability of data is improved,
The data of publication are made to reflect truthful data as far as possible, the data publication and privacy for being applicable to different scales and different dimensions are protected
Shield.
The above is only some embodiments of the invention, it is noted that for the ordinary skill people of the art
For member, various improvements and modifications may be made without departing from the principle of the present invention, these improvements and modifications are also answered
It is considered as protection scope of the present invention.
Claims (8)
1. a kind of difference method for secret protection towards principal component analysis, which is characterized in that it is based on preset sample data set X,
Number of samples n, sample space dimension d；Principal component analytical method the following steps are included:
Step 1: data matrix centralization, i.e., each dimension data subtract the mean value of this dimension；
Step 2: calculating covariance matrix with the data matrix that step 1 obtainsWherein, XTIt is turning for data matrix X
It sets；
Step 3: calculating the eigenvalue λ and feature vector V of covariance matrix A described in step 2, meet AV=λ V；By characteristic value
Descending is arranged with: λ1>λ2…>λd, corresponding feature vector is v1,v2…vd；
Step 4: calculating the principal component number k of reservation；
Step 5: initial data being mapped to principal component space and obtains projection matrix Z；
Step 6: giving the projection matrix Z each column Elemental partition privacy budget εj, calculate the random noise of addition；
Step 7: adding noise to the projection matrix Z, the projection matrix Z ' after obtaining plus making an uproar；
Step 8: calculating the error between initial data and low-rank approximate data.
2. the difference method for secret protection according to claim 1 towards principal component analysis, which is characterized in that in step 1,
For convenience of covariance matrix is solved, each dimension mean value is 0 after centralization, goes mean value to each attribute, as shown in formula (1):
xjIt is the data of j-th of attribute of all samples, x 'jIt is the data of j-th of attribute of all samples after centralization, xijIt is data
Collect the data of i-th of sample, j-th of attribute in X,It is the mean value of j-th of attribute.
3. the difference method for secret protection according to claim 1 towards principal component analysis, which is characterized in that in step 4,
To an eigenvalue contribution value α of setting, wherein 0≤α≤1 calculates the principal component number k to be retained, it is made to meet practical protect
The principal component eigenvalue contribution value per >=α stayed, in which:
4. the difference method for secret protection according to claim 1 towards principal component analysis, which is characterized in that in step 5,
The projection matrix Z=XVkIt is mapping of the initial data on principal component space, wherein Vk=v1,v2…vkIt is the k master retained
The corresponding feature vector of ingredient.
5. the difference method for secret protection according to claim 1 towards principal component analysis, which is characterized in that in step 6,
The random noise is Laplace noise, i.e. noise obeys Laplace distribution Lap (b), and b is scale parameter, b=Δ f/ ε, Δ
F is global susceptibility, and ε is privacy budget；
It is as follows to obey the Laplace distribution probability density function that scale parameter is b:
Wherein, x indicates all possible value, and p (x) is the probability of all values
Projection matrix Z=XVkJth column indicate mapping of the initial data in j-th of principal component, each column expression is different to be contained
Justice can distribute equal or unequal privacy budget εj, wherein 1≤j≤k.
6. the difference method for secret protection according to claim 5 towards principal component analysis, which is characterized in that distribution is equal
Privacy budget εj: divide equally:Each column distribute equal privacy budget；
The privacy budget ε that distribution does not waitj: press weight distribution:Privacy is distributed according to principal component characteristic value accounting
Budget.
7. the difference method for secret protection according to claim 1 towards principal component analysis, which is characterized in that in step 7,
Adding the projection matrix after making an uproar is Z '=(z '1,z′2…z′j…z′k), wherein z 'jExpression formula it is as follows:
zjIt is the jth column of projection matrix,It is the global susceptibility of projection matrix.
8. the difference method for secret protection according to claim 2 towards principal component analysis, which is characterized in that in step 8,
Low-rank approximate matrix It is eigenvectors matrix VkTransposition,It is the mean value of attribute, wherein
Approximate data error is calculated using formula (5)；
MSE-F=| | Y-X | |F (5)
||·||FIt is the F norm of matrix；The F norm of matrix refers to the quadratic sum of matrix element evolution again；
The matrix of a m × n is let c be, then the F norm of C are as follows:
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Cited By (5)
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| CN110334546A (en) * | 2019-07-08 | 2019-10-15 | 辽宁工业大学 | Difference privacy high dimensional data based on principal component analysis optimization issues guard method |
| CN111241582A (en) * | 2020-01-10 | 2020-06-05 | 鹏城实验室 | Data privacy protection method and device and computer readable storage medium |
| CN112560094A (en) * | 2020-12-18 | 2021-03-26 | 湖南大学 | Dual optimization-based high-availability graph data privacy protection method |
| CN114710259A (en) * | 2022-03-22 | 2022-07-05 | 中南大学 | Multi-party combined safety PCA projection method and data correlation analysis method |
| CN116761164A (en) * | 2023-08-11 | 2023-09-15 | 北京科技大学 | Privacy data transmission method and system based on matrix completion |
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Cited By (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110334546A (en) * | 2019-07-08 | 2019-10-15 | 辽宁工业大学 | Difference privacy high dimensional data based on principal component analysis optimization issues guard method |
| CN110334546B (en) * | 2019-07-08 | 2021-11-23 | 辽宁工业大学 | Difference privacy high-dimensional data release protection method based on principal component analysis optimization |
| CN111241582A (en) * | 2020-01-10 | 2020-06-05 | 鹏城实验室 | Data privacy protection method and device and computer readable storage medium |
| CN111241582B (en) * | 2020-01-10 | 2022-06-10 | 鹏城实验室 | Data privacy protection method and device and computer readable storage medium |
| CN112560094A (en) * | 2020-12-18 | 2021-03-26 | 湖南大学 | Dual optimization-based high-availability graph data privacy protection method |
| CN114710259A (en) * | 2022-03-22 | 2022-07-05 | 中南大学 | Multi-party combined safety PCA projection method and data correlation analysis method |
| CN114710259B (en) * | 2022-03-22 | 2024-04-19 | 中南大学 | Multi-party combined safety PCA projection method and data correlation analysis method |
| CN116761164A (en) * | 2023-08-11 | 2023-09-15 | 北京科技大学 | Privacy data transmission method and system based on matrix completion |
| CN116761164B (en) * | 2023-08-11 | 2023-11-14 | 北京科技大学 | Privacy data transmission method and system based on matrix completion |
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