CN113987578B - Space point set privacy protection matching method based on vector mapping and sliding window scanning - Google Patents

Space point set privacy protection matching method based on vector mapping and sliding window scanning Download PDF

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CN113987578B
CN113987578B CN202111260998.5A CN202111260998A CN113987578B CN 113987578 B CN113987578 B CN 113987578B CN 202111260998 A CN202111260998 A CN 202111260998A CN 113987578 B CN113987578 B CN 113987578B
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CN113987578A (en
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张海涛
宋锐
高兆亚
何向东
庄炜
刘晋源
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Nanjing Chaoda Information Technology Co ltd
Nanjing University of Posts and Telecommunications
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Nanjing University of Posts and Telecommunications
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Abstract

A space point set privacy protection matching method based on vector mapping and sliding window scanning comprises the following steps: under a unified spatial point set reference set, vector embedding is carried out on spatial points to multiple dimensions to obtain a multi-dimensional vector of each spatial point in an embedding space, and finally the vectors are mapped into corresponding complex numbers; and expressing the space point sets expressed in a complex form by both data exchange sides in a unified complex coordinate system, and obtaining a matched space point pair set by using a sliding window scanning method. In the method, the embedding space keeps the spatial topological proximity, and the accuracy of spatial matching calculation is ensured; the mapping conversion from the original space to the embedded space is irreversible, so that the safety of space matching calculation is ensured; the matching method based on sliding window scanning ensures the high efficiency of space matching calculation.

Description

Space point set privacy protection matching method based on vector mapping and sliding window scanning
Technical Field
The invention relates to the technical field of space data privacy protection, in particular to a space point set privacy protection matching method based on vector mapping and sliding window scanning.
Background
The traditional map and the GIS have the problem that multi-level and multi-dimensional abstraction and expression of the real world are difficult to perform comprehensively and effectively, Zhou-cheng-Hu academicians put forward the concept of a 'full-space information system', and from the perspective of spatial thinking, the ubiquitous GIS world is expected to be constructed. Professors in the plunging country, further from an information content perspective, define the abstract description of the real world as seven elements: time, place, person, thing, event, phenomenon, scene, etc. Currently, with the rapid development of internet technology, mobile communication technology and positioning technology, APP applications based on mobile intelligent terminals are widely popularized, and thus a large amount of spatial data is generated. The spatial data collected by APP systems oriented to different applications is usually an abstract description of geographic things from different perspectives. Spatial data collected by multisource APP are integrated to become a key technology for realizing holographic expression of geographic object objects.
Direct data exchange is the most direct method for realizing multi-source spatial data integration. However, this method requires both parties to exchange and share all information, and unmatched space data also needs to be exposed, so that there is a great risk of privacy disclosure. Therefore, a spatial data matching method based on an encryption technology needs to be researched to realize matching calculation between spatial data on the premise of not revealing spatial information. Existing privacy preserving matching methods are divided into two types based on whether they depend on third parties. Typical methods that rely on third parties include: the location privacy protection k-anonymity method based on the trusted chain proposed by Wang Hui et al uses the edge node of the vehicle-mounted network as a third party and combines with a privacy protection model designed by a virtual track proposed by YuHaili et al. Although the method depending on the third party can achieve a good calculation effect, the method is difficult to deal with the problem of the collusion attack. Typical methods that are independent of third parties include: xu, ZQ et al, a privacy protection framework based on multi-policy configurable, Gao, S et al, a privacy protection framework based on user participatory perception, and Hwang, RH et al, a privacy protection framework based on environmental perception. Although the method which does not depend on a third party can effectively avoid the collusion attack, the method generally has the defects of low matching precision and high algorithm complexity.
Disclosure of Invention
In order to solve the technical problems in the background technology, the invention adopts the following technical scheme:
the space point set privacy protection matching method based on vector mapping and sliding window scanning comprises three stages:
the first stage, vector embedding and complex mapping of spatial point set, includes: under a unified spatial point set reference set, vector embedding is carried out on spatial points to multiple dimensions to obtain a multi-dimensional vector of each spatial point in an embedding space, and finally the vectors are mapped into corresponding complex numbers; the method specifically comprises the following steps:
step 1-1, a data owner defines a uniform reference set according to a space point set range;
step 1-2, the data owner appoints a uniform dimension factor set;
step 1-3, embedding the space point set of a data owner into a dimensional factor set to form a dimensional space according to a reference set and the dimensional factor set, and completing vector embedding of the space point set;
in the second stage, the mapping of the complex representation of the embedded vector to the complex coordinate system includes: mapping the multi-dimensional vector embedded in the first stage into a corresponding complex number; the method specifically comprises the following steps:
step 2-1, the data owner calculates the complex expression of each embedded vector;
step 2-2, the data owners exchange complex sets with each other and express in complex coordinate systems;
and in the third stage, the sliding window scanning matching under a complex coordinate system comprises the following steps: expressing space point sets expressed in a complex form by both data exchange sides in a unified complex coordinate system, and obtaining matched space point pair sets by using a sliding window scanning method; the method specifically comprises the following steps:
step 3-1, the data owner constructs a sliding window with infinite length and theta width in a complex coordinate system of the complex set according to the appointed sliding window width theta, and places the right boundary of the window on the point with the minimum real part in the complex set; wherein the length of the sliding window is the length on the virtual axis and the width is the length on the real axis;
step 3-2, sliding the sliding window from left to right, scanning coordinate points of a complex set of the data owner, and performing matching calculation;
and 3-3, exchanging original spatial data point data among data owners according to the result based on the complex matching calculation, namely, completing the matching and exchanging of data under the condition of not acquiring original information of other unmatched data, and completing the privacy protection matching.
Further, in step 1-1, the spatial point set of one data owner is defined as Pts ═ Pt1，Pt2，…，PtnN is more than or equal to 1, wherein, Pti(x, y),1 ≦ i ≦ n, denoting the ith spatial location point in Pts, Pti·x、PtiY represents the spatial position point PtiThe abscissa and ordinate values of (a).
Further, in step 1-1, from one spatial point set Pts, a range defined as PtsE ═ ((minx, miny), (maxx, maxy)), 1 ≦ i ≦ n, that is:
PtsE＝((min(Pti·x)，min(Pti·y))，(max(Pti·x)，max(Pti·y)))
wherein minx is min (Pt)i·x)，mint＝min(Pti·y)，maxx＝max(Pti·x)，maxy＝max(PtiY) respectively representing the minimum value of the abscissa value, the minimum value of the ordinate value, the maximum value of the abscissa value and the maximum value of the ordinate value of all the spatial position points in the spatial point set Pts.
Further, in step 1-1, a reference set RefS ═ RefPt is obtained according to the spatial point set Pts and the corresponding range PtsE thereof1，RefPt2，…，RefPtnDefine a reference to Pts, where RefPt is any reference point to RefSiWhere (x, y),1 ≦ i ≦ n is included in PtsE, i.e. RefPtiBelongs to PtsE; further, PtsE. minx. ltoreq. RefPtiX is not more than PtsE. maxx, and PtsE. miny is not more than RefPti·y≤PtsE·maxy。
Further, in step 1-2, n-1 reference points are sequentially selected from the reference set RefS to form a combination, which is called a dimension factor of RefS and defined as Dim-DimPt1，DimPt2，…，DimPtn-1}；
Wherein for any two elements DimPT of Dimi、DimPti+1And i is more than or equal to 1 and less than or equal to n-2, which all meet the condition: the presence of one in RefS and DimPTiSame reference point RefPtjThere is one and DimPTi+1Same reference point RefPtkAnd j is not less than 1<k≤n-2；
RefS ═ RefPt for reference set1，RefPt2，…，RefPtnCan generate
Figure BDA0003325515780000041
Dimension factors, forming a dimension factor set Dims ═ { Dim1，Dim2，…，Dimn}。
Further, in step 1-3, according to the spatial point set Pts, the reference set RefS corresponding thereto, and the dimension factor set Dims, the spatial point set Pts is embedded into the dimension factor set Dims to form an m-1 dimensional space defined as:
EebPts＝{EebPt1，EebPt2，…，EebPtn}，
wherein, EebPt is inserted into the pointiContains m-1 embedded values, defined as: EebPti＝{emb1，emb2，…，emb m-11 ≦ i ≦ n, where, for the embedding value embjAccording to its dimensional factor Dimj＝{DimPt1，SimPt2，…，DimPtm-1The calculation formula is as follows:
Figure BDA0003325515780000051
among them, Distance (RefPt)j，Pti) Represents a space point PtiAnd reference point RefPtjThe calculation formula of the Euclidean distance between the two is as follows:
Figure BDA0003325515780000052
in summary, the matrix of the embedding space based on the embedding values is expressed as:
Figure BDA0003325515780000053
wherein, a column of elements in the embedding space matrix is defined as an embedding vector, and
Figure BDA0003325515780000054
defining the ith embedded vector in the embedded space matrix M _ EebPts; the matrix of the embedding space is therefore also expressed as:
M_EebPts＝[V_EebPts1 … V_EebPtsn]。
further, in step 2-1, vector V _ EebPts is embeddediThe process of converting to complex numbers is called a mapping thereof, and the calculation formula is:
Figure BDA0003325515780000055
thus, for the spatial point set Pts ═ Pt1，Pt2，…，PtnObtaining a complex set Cs _ ebpts ═ C _ ebpts correspondingly1，C_EebPts2，…，C_EEbPtsn}。
Further, in step 2-1, a complex coordinate system is defined, and for complex C ═ a + bi, a is referred to as the real part of complex C, denoted re (C); b is called the imaginary part of the complex number C and is marked as im (C); i is called an imaginary unit which is the square root of-1, i.e.
Figure BDA0003325515780000061
A two-dimensional plane coordinate system established by taking a plurality of C real components Re (C) as a horizontal axis and an imaginary component im (C) as a vertical axis is defined as a complex coordinate system.
Further, in step 3-2, given a set of spatial points Pts and its corresponding complex set Cs _ EebPts, for any two spatial points Pti、PtjI is more than or equal to 1, j is more than or equal to n and corresponding complex number C _ EebPtsi，C_EebPtsjI is more than or equal to 1, j is less than or equal to n, if C _ EebPtsi，C_EebPtsjIn the same complex coordinate system, andthe following two conditions are satisfied:
in complex coordinate system, there is a self-defined width theta as sliding window, C _ EebPtsi，C_EebPtsjOccurring simultaneously in the window, i.e., 0. ltoreq. Re (C _ EebPts)i)-Re(C_EebPtsj)|≤θ；
C_EebPtsi，C_EebPtsjThe difference value of the imaginary parts of the two-dimensional image is also within a threshold value theta x i, namely, the condition 0 ≦ Im (C _ EebPts) is satisfiedi)-Im(C_EebPtsj)|≤θ×i；
Then call C _ EebPtsiAnd C _ EebPtsjMatching, further called two space points PtiWith PtjAnd (6) matching.
The invention has the beneficial effects that: the embedding space keeps the spatial topological proximity, and the accuracy of spatial matching calculation is ensured; the mapping conversion from the original space to the embedded space is irreversible, so that the safety of space matching calculation is ensured; the matching method based on sliding window scanning ensures the high efficiency of space matching calculation, and is embodied in that:
(1) the accuracy is high: in the vector mapping and complex expression process of the space point set, original position point data can be well kept in the property of spatial proximity although being processed into complex data, namely the original data matching inevitably has complex data matching, the original data is not matched, and corresponding complex numbers are not matched, so that the matching calculation has high accuracy.
(2) The safety is strong: the two parties agree with a specific reference set and a specific dimensionality set, use a uniform embedding rule to carry out vector mapping and complex expression on the space point set, and then use complex data to carry out matching calculation. Because the conversion from the original space to the embedding space is irreversible, the inverse operation that the matching parties reversely deduce the original information through complex values is effectively avoided, and the strong safety of space matching calculation is ensured.
(3) The matching speed is high: the matching of the space point sets is carried out in a complex coordinate system, and redundant matching operation is effectively avoided by using a sliding window scanning method, so that the calculation efficiency is greatly improved.
Drawings
FIG. 1 is a spatial point set distribution of data owner A in an embodiment of the present invention.
FIG. 2 is a spatial point set distribution of data owner B in an embodiment of the present invention.
Fig. 3 is a spatial distribution of a reference set in an embodiment of the invention.
Fig. 4 shows the distribution of the spatial point sets of both sides of the data owner in the complex number space after the spatial point sets are converted into the complex number set in the embodiment of the present invention.
Fig. 5 is a schematic view of an initial position of a sliding window in an embodiment of the present invention.
FIG. 6 is a diagram of a sliding window scan process in an embodiment of the present invention-A2 now leaving the window.
Fig. 7 is a schematic diagram of a sliding window scan process in an embodiment of the present invention, a3 entry window.
FIG. 8 is a process of sliding window scanning in an embodiment of the present invention-A4 is an off-window schematic.
Fig. 9 is a spatial distribution of the resulting set of matching point pairs in an embodiment of the present invention.
Detailed Description
The technical scheme of the invention is further explained in detail by combining the drawings in the specification.
First, the following definitions are given:
definition 1: and (3) space point set: pts ═ Pt1，Pt2，…，PtnN is more than or equal to 1 and represents a space point set, wherein Pt i1 ≦ i ≦ n, representing the ith spatial location point in Pts, Pti·x、PtiY represents the spatial position point PtiThe abscissa and ordinate values of (a).
Definition 2: spatial point set range: given a spatial point set Pts ═ Pt1，Pt2，…，Ptn}, the range of which is defined as: PtsE ═(minx, miny), (maxx, maxy)) 1. ltoreq. i.ltoreq.n, where minx ≦ min (Pt)i·x)，miny＝min(Pti·y)，maxx＝max(Pti·x)，maxy＝max(PtiY) minimum value of abscissa values, ordinate, respectively representing all points of spatial positionThe minimum value of the standard value, the maximum value of the horizontal coordinate value and the maximum value of the vertical coordinate value.
PtsE＝((min(Pti·x)，min(Pti·y))，(max(Pti·x)，max(Pti·y)))
Definition 3: reference set: given a set of spatial points Pts and its corresponding range PtsE, RefS ═ RefPt1，RefPt2，…，RefPtnDefine a reference set of Pts, in which RefPt is any reference point for RefSiWhere (x, y),1 ≦ i ≦ n is included in PtsE, i.e. RefPtiBelongs to PtsE, and further PtsE. minx. ltoreq. RefPtiX is not more than PtsE. maxx, and PtsE. miny is not more than RefPti·y≤RtsE·maxy。
Definition 4: dimension factor: given a reference set RefS ═ RefPt1，RefPt2，…，RefPtnSelecting n-1 reference points from the RefS in sequence to form a combination, which is called a dimension factor of the RefS and defined as: dim ═ { DimPt1，DimPt2，…，DimPtn-1}。
Wherein for any two elements DimPT of Dimi、DimPti+1And i is more than or equal to 1 and less than or equal to n-2, which all meet the condition: the presence of one in RefS and DimPTiSame reference point RefPtjIn the presence of one and DimPTi+1Same reference point RefPtkAnd j is not less than 1<k≤n-2。
RefS ═ RefPt for reference set1，RefPt2，…，RefPtnCan generate
Figure BDA0003325515780000092
Forming a dimension factor set Dims ═ Dim1，Dim2，…，Dimn}。
Definition 5: embedding space: given a spatial point set Pts ═ Pt1，Pt2，…，PtnAnd its corresponding reference set RefS ═ RefPt1，RefPt2，…，RefPtmD, dimension factor set Dims ═ Dim1，Dim2，…，Dimm-1And embedding the space point set Pts into a dimension factor set Dims to form an m-1-dimensional space defined as:
EebPts＝{EebPts1，EebPt2，…，EebPtn}，
wherein, EebPt is inserted into the pointiContains m-1 embedded values, defined as: EebPti＝{emb1，emb2，…，emb m-11 ≦ i ≦ n, where, for the embedding value embjAccording to its dimensional factor Dimj＝{DimPt1，DimPt2，…，DimPtm-1Can be calculated by the following formula:
Figure BDA0003325515780000091
among them, Distance (RefPt)j，Pti) Represents a space point PtiAnd reference point RefPtjThe calculation formula of the Euclidean distance between the two is as follows:
Figure BDA0003325515780000101
further, the matrix expression of the embedding space based on the embedding values is:
Figure BDA0003325515780000102
wherein a column of elements in the embedding space matrix is defined as an embedding vector,
Figure BDA0003325515780000103
defined as the i-th embedded vector in the embedded spatial matrix M _ ebpts. Thus, the matrix of the embedding space can also be expressed as:
M_EebPts＝[V_EebPts1 … V_EebPtsn]
will vector V _ EebPtsiThe process of converting to complex numbers is called a mapping thereof, and the calculation formula is:
Figure BDA0003325515780000104
thus, for spatial point set Pts ═ Pt1，Pt2，…，PtnObtaining a complex set Cs _ ebpts ═ C _ ebpts, correspondingly1，C_EebPts2，…，C_EebPtsn}。
Definition 6: a plurality of coordinate systems: for complex C ═ a + bi, a refers to the real part of complex C and is noted: re (C); b is called the imaginary part of the complex number C, noted: im (C); i is called an imaginary unit which is the square root of-1, i.e.
Figure BDA0003325515780000105
When the imaginary part b is 0, then C is a real number; when the imaginary part b is not equal to 0 and the real part a is 0, C is called a pure imaginary number. A two-dimensional plane coordinate system established by taking a plurality of C real components Re (C) as a horizontal axis and an imaginary component im (C) as a vertical axis is defined as a complex coordinate system.
Definition 7: matching: given a spatial point set Pts ═ Pt1，Pt2，…，PtnH and its corresponding complex set Cs _ ebpts ═ C _ ebpts1，C_EebPts2，…，C_EebPtsnFor any two spatial points Pti、PtjI is more than or equal to 1, j is more than or equal to n and corresponding complex number C _ EebPtsi，C_EebPtsjI is more than or equal to 1, j is less than or equal to n, if C _ EebPtsi，C_EebPtsjIn the same complex coordinate system, the following two conditions are satisfied:
(1) in complex coordinate system, there is a self-defined width theta as sliding window, C _ EebPtsi，C_EebPtsjAppear in the window at the same time, i.e., 0. ltoreq. Re (C _ EebPts)i)-Re(C_EebPtsj)|≤θ；
(2)C_EebPtsi，C_EebPtsjIs/are as followsThe difference value of the imaginary parts is also within the threshold value theta multiplied by i, namely the condition 0 ≦ Im (C _ EebPts) is meti)-Im(C_EebPtsj)|≤θ×i；
Then call C _ EebPtsiAnd C _ EebPtsjMatching, further called PtiWith PtjAnd (6) matching.
A specific embodiment of the present invention, in conjunction with fig. 1-9, includes the following steps:
the first stage is as follows: vector embedding of the set of spatial points.
Step 1) both parties of the data owner A, B define a unified reference set according to the spatial point set range.
In this example, the set of spatial points for the data owner A, B are:
PtsA＝{PtA1，PtA2，…，PtA8}
＝{(18,86),(52,90),(80,80),(40,76),(20,46),(48,32),(76,38),(10,18)}
PtsB＝{PtB1，PtB2，…，PtB8}＝
＝{(50,12),(86,24),(46,30)，(38,76)，(4，74),(32，98),(82，82),(74,66)}
the distribution of the spatial point set data of the data owner a is shown in fig. 1, and the distribution of the spatial point set data of the data owner B is shown in fig. 2.
According to definition 2, A, B, two parties can obtain the range of each spatial point set, and the two parties interact to finally obtain the union PtsE ═ of the range ((Pt (min))i·x)，min(Pti·y))，(max(Pti·x)，max(Pti·y)))＝((4，12)，(86，98))。
Further, RefS is obtained as a reference set of both spatial point sets A, B according to definition 3, n is 4 in this example, and RefS is obtained as a reference set { RefPt ═ RefS ═ c1，RefPt2，…，RefPt4{ (10,30), (50,50), (44,88), (82,24) }. The spatial distribution of the reference set RefS is shown in fig. 3.
Step 2) data owner A, B both agree on a unified set of dimensional factors.
In this example, A, B the agreed reference set RefS { (10,30), (50,50), (44,88), (82,24) }, according to definition 4, the dimension factor set Dims ═ { Dim }1，Dim2，…，Dim4}, wherein:
Dim1＝{DimPt1，DimPt2，DimPt3}
＝{(10,30)，(50,50)，(44,88)}
Dim2＝{DimPt1，DimPt2，DimPt4}
＝{(10,30)，(50,50)，(82,24)}
Dim3＝{DimPt1，DimPt3，DimPt4}
＝{(10,30)，(44,88)，(82,24)}
Dim4＝{DimPt2，DimPt3，DimPt4}
＝{(50,50)，(44，88)，(82,24)}
namely: dims { [ (10,30), (50,50), (44,88) ], [ (10,30), (50,50), (82,24) ], [ (10,30), (44,88), (82,24) ], [ (50,50), (44,88), (82,24) ] }.
Step 3) both parties of the data owner A, B each perform vector embedding on their spatial point sets.
According to definition 5, both data owners A, B embed their spatial point sets into the dimensional factor sets to form the dimensional space, based on the reference set and the dimensional factor sets.
In this example, first, taking the spatial data of the data owner a as an example, a specific embedding process is given.
Reference set RefS { (10,30), (50,50), (44,88), (82,24) }, dimension factor set Dims { (Dim) of data owner a1，Dim2，…，Dim4}。
First spatial data point Pt for AA1(18,86) its corresponding dimensional factor Dim1＝{DimPt1，DimPt2，DimPt3{ (10,30), (50,50), (44,88) }, then according to definition 5, the embedding point emb is calculated1The process of (2) is as follows:
Figure BDA0003325515780000131
similarly, the following can be calculated: emb (element b)2≈193.8416，emb3≈171.7520，emb4≈163.3499。
Further obtaining PtA1Embedded vector of
Figure BDA0003325515780000141
Figure BDA0003325515780000142
Further, an embedding space matrix corresponding to the space point set in the data owner a can be obtained:
Figure BDA0003325515780000143
then, the data owner B adopts the same steps to finally obtain the embedded spatial matrix corresponding to the spatial point set:
Figure BDA0003325515780000144
and a second stage: mapping of complex representation of embedded vector to complex coordinate system
Step 1) according to definition 6, both parties of the data owner A, B calculate the complex representation of their respective embedded vectors.
In this example, first, taking the spatial data of the data owner a as an example, a complex representation of a specific embedded vector is given.
First spatial data point Pt for AA1(18,86), wherein m is 8, n is 4,
Figure BDA0003325515780000151
then its corresponding plural expression
Figure BDA0003325515780000152
The calculation process of (2) is as follows:
Figure BDA0003325515780000153
in the same way, can obtain
Figure BDA0003325515780000154
Figure BDA0003325515780000155
Figure BDA0003325515780000156
Figure BDA0003325515780000157
Figure BDA0003325515780000158
Figure BDA0003325515780000159
Figure BDA00033255157800001510
Figure BDA00033255157800001511
Figure BDA00033255157800001512
Figure BDA00033255157800001513
Then the complex set of data owner a
Figure BDA00033255157800001514
Figure BDA00033255157800001515
Namely:
Figure BDA00033255157800001516
then, the data owner B adopts the same steps to finally obtain the space of the data owner BComplex number set corresponding to point set
Figure BDA00033255157800001517
Figure BDA00033255157800001518
And step 2) the data owner and the data owner exchange own complex sets and represent the complex sets of the data owner and the data owner in a complex coordinate system.
In this example, the complex set of data owner A, B is represented in a complex coordinate system as shown in FIG. 4.
And a third stage: data matching based on sliding window scanning.
Step 1) initialization of a sliding window.
According to the width theta of the appointed sliding window, the data owner and the data owner construct a sliding window with infinite length (length on an imaginary axis) and theta width (length on a real axis) in a complex coordinate system where the complex set is located, and the right boundary of the window is placed on a point where the real part of the complex set is minimum.
In this example, θ is 5, and the sliding window is constructed and its position in the complex coordinate system of both data owners A, B is shown in fig. 5.
And step 2) sliding the sliding window from left to right for scanning and performing matching calculation.
The sliding window slides and scans coordinate points of the plural data sets of both data owners from left to right, and performs matching calculation according to definition 7.
In this example, the first data owner a entering the window has a spatial location point a2, as shown in fig. 5, and when a2 is within the window, no point on party B enters, as shown in fig. 6, and no point on party B matches a 2.
Continuing sliding the window to the right; when A3 enters the window, as shown in fig. 7, there is a point B7 on the B side in the window, and it is calculated whether the two points A3 and B7 match.
The complex value of a3 is expressed as: c _ EebPtsA3-49.1451-13.6093i, i.e. Re (C _ EebPts)A3)＝-49.1451,Im(C_EebPtsA3)＝-13.6093i。
The complex value of B7 is expressed as: c _ EebPtsB7-50.3436-12.7452i, i.e. Re (C _ EebPts)B7)＝-50.3436,Im(C_EebPtsB7)＝-12.7452i。
Since both A3 and B7 are within the sliding window, the difference between the real parts of points A3 and B7 satisfies condition 1 in definition 7, that is, the difference between the real parts of points A3 and B7 satisfies condition 1
Figure BDA0003325515780000171
Figure BDA0003325515780000172
At the same time, the difference of the imaginary parts of a3 and B7 is calculated:
Figure BDA0003325515780000173
Figure BDA0003325515780000174
condition 2 in definition 7 is satisfied. Therefore, a3 and B7 are determined to match.
Next, the window continues to slide to the right, A3 leaves the window, and the matching calculation for point A3 ends.
Further, the window continues to slide to the right, and the third data owner, point a, entering the window is point a4, as shown in fig. 8, when B4 also calculates the difference between the imaginary components of two points in the window, i.e., satisfying condition 1 of definition 7:
Figure BDA0003325515780000175
Figure BDA0003325515780000176
condition 2 of definition 7 is satisfied, and therefore, a4 and B4 match.
Further, sliding window scanning matching is performed in the same way, and finally a set of matching point pairs is obtained as follows: { (A3, B7), (A4, B4), (A6, B3) }, a graphic representation of which is shown in FIG. 9.
And 3) exchanging original spatial data points by the two parties based on the matching point pairs.
Based on the result based on the complex matching result, the data owner double-exchanges the original spatial data point data.
In this example, data owner a exchanges its spatial data points A3, a4, and a6 to data owner B, which exchanges its spatial data points B3, B4, and B7 to data owner a. Finally, the two parties finish the matching and exchange of data under the condition that other unmatched data original information is not obtained, and the aim of privacy protection matching is achieved.
The above description is only a preferred embodiment of the present invention, and the scope of the present invention is not limited to the above embodiment, but equivalent modifications or changes made by those skilled in the art according to the present disclosure should be included in the scope of the present invention as set forth in the appended claims.

Claims (9)

1. A space point set privacy protection matching method based on vector mapping and sliding window scanning is characterized by comprising the following steps: the method comprises three stages:
the first stage, vector embedding and complex mapping of spatial point set, includes: under a unified spatial point set reference set, vector embedding is carried out on spatial points to multiple dimensions to obtain a multi-dimensional vector of each spatial point in an embedding space, and finally the vectors are mapped into corresponding complex numbers; the method specifically comprises the following steps:
step 1-1, a data owner defines a uniform reference set according to a space point set range;
step 1-2, the data owner appoints a uniform dimension factor set;
step 1-3, embedding the space point set of a data owner into a dimensional factor set to form a dimensional space according to a reference set and the dimensional factor set, and completing vector embedding of the space point set;
the second stage, the mapping of the complex representation of the embedded vector to the complex coordinate system, comprises: mapping the multi-dimensional vector embedded in the first stage into a corresponding complex number; the method specifically comprises the following steps:
step 2-1, the data owner calculates the complex expression of each embedded vector;
step 2-2, the data owners exchange complex sets with each other and express in complex coordinate systems;
and in the third stage, the sliding window scanning matching under a complex coordinate system comprises the following steps: expressing space point sets expressed in a complex form by both data exchange sides in a unified complex coordinate system, and obtaining matched space point pair sets by using a sliding window scanning method; the method specifically comprises the following steps:
step 3-1, the data owner constructs a sliding window with infinite length and theta width in a complex coordinate system of the complex set according to the appointed sliding window width theta, and places the right boundary of the window on the point with the minimum real part in the complex set; wherein the length of the sliding window is the length on the virtual axis and the width is the length on the real axis;
step 3-2, sliding the sliding window from left to right, scanning coordinate points of a complex set of the data owner, and performing matching calculation;
and 3-3, exchanging original spatial data point data among data owners according to the result based on the complex matching calculation, namely, completing the matching and exchanging of data under the condition of not acquiring original information of other unmatched data, and completing the privacy protection matching.
2. The vector mapping and sliding window scanning-based spatial point set privacy protection matching method according to claim 1, wherein: in step 1-1, the spatial point set of one data owner is defined as Pts ═ Pt1，Pt2，...，PtnN is more than or equal to 1, wherein, Pti1 ≦ i ≦ n, representing the ith spatial location point in Pts, Pti·x、PtiY represents the spatial position point PtiThe abscissa and ordinate values of (a).
3. The method for matching spatial point set privacy protection based on vector mapping and sliding window scanning according to claim 2, wherein: in step 1-1, from a spatial point set Pts, a range defined as PtsE ═ ((minx, miny), (maxx, maxy)), 1 ≦ i ≦ n is obtained, that is:
PtsE＝((min(Pti·x)，min(Pti·y))，(max(Pti·x)，max(Pti·y)))
wherein minx is min (Pt)i·x)，miny＝min(Pti·y)，maxx＝max(Pti·x)，maxy＝max(PtiY) respectively representing the minimum value of the abscissa value, the minimum value of the ordinate value, the maximum value of the abscissa value and the maximum value of the ordinate value of all the spatial position points in the spatial point set Pts.
4. The method for matching spatial point set privacy protection based on vector mapping and sliding window scanning according to claim 3, wherein: in step 1-1, a reference set RefS ═ RefPt is obtained according to the spatial point set Pts and the corresponding range PtsE thereof1，RefPt2，...，RefPtnDefine a reference to Pts, where RefPt is any reference point to RefSiWhere (x, y),1 ≦ i ≦ n is included in PtsE, i.e. RefPtiBelongs to PtsE; further, PtsE. minx. ltoreq. RefPtiX is not more than PtsE. maxx, and PtsE. miny is not more than RefPti·y≤PtsE·maxy。
5. The method for matching spatial point set privacy protection based on vector mapping and sliding window scanning according to claim 4, wherein: in step 1-2, n-1 reference points are sequentially selected from the reference set RefS to form a combination, which is called a dimension factor of RefS and defined as Dim ═ { DimPt ═1，DimPt2，...，DimPtn-1}；
Wherein for any two elements DimPT of Dimi、DimPti+1And i is more than or equal to 1 and less than or equal to n-2, which all meet the condition: the presence of one in RefS and DimPTiSame reference point RefPtjThere is one and DimPTi+1Same reference point RefPtkJ is more than or equal to 1 and less than or equal to k and less than or equal to n-2;
RefS ═ RefPt for reference set1，RefPt2，...，RefPtnCan generate
Figure FDA0003640266310000031
Dimension factors, forming a dimension factor set Dims ═ { Dim1，Dim2，...，Dimn}。
6. The method for matching spatial point set privacy protection based on vector mapping and sliding window scanning according to claim 5, wherein: in step 1-3, according to the spatial point set Pts, the reference set RefS corresponding thereto, and the dimensional factor set Dims, the spatial point set Pts is embedded into the dimensional factor set Dims to form an m-1 dimensional space defined as:
EebPts＝{EebPt1，EebPt2，...，EebPtn}，
wherein, EebPt is inserted into the pointiContains m-1 embedded values, defined as: EebPti＝{emb1，emb2，...，embm-11 ≦ i ≦ n, where, for the embedding value embjAccording to its dimensional factor Dimj＝{DimPt1，DimPt2，...，DimPtm-1The calculation formula is as follows:
Figure FDA0003640266310000041
among them, Distance (RefPt)j，Pti) Represents a space point PtiAnd reference point RefPtjThe calculation formula of the Euclidean distance between the two is as follows:
Figure FDA0003640266310000042
in summary, the matrix of the embedding space based on the embedding values is expressed as:
Figure FDA0003640266310000043
wherein, a column of elements in the embedding space matrix is defined as an embedding vector, and
Figure FDA0003640266310000044
defining the ith embedded vector in the embedded space matrix M _ EebPts; the matrix of the embedding space is therefore also represented as:
M_EebPts＝[V_EebPts1 … V_EebPtsn]。
7. the method for matching spatial point set privacy protection based on vector mapping and sliding window scanning according to claim 1, wherein: in step 2-1, the vector V _ EebPts is embeddediThe process of converting to complex numbers is called a mapping thereof, and the calculation formula is:
Figure FDA0003640266310000045
thus, for the spatial point set Pts ═ Pt1，Pt2，...，PtnGet a complex set Cs _ ebpts ═ C _ ebpts, correspondingly1，C_EebPts2，...，C_EebPtsn}。
8. The method for matching spatial point set privacy protection based on vector mapping and sliding window scanning according to claim 7, wherein: in step 2-1, a complex coordinate system is defined, and for complex C ═ a + bi, a is referred to as the real part of complex C and is denoted as re (C); b is called the imaginary part of the complex number C and is marked as im (C); i is called an imaginary unit which is the square root of-1, i.e.
Figure FDA0003640266310000051
A two-dimensional plane coordinate system established by taking a plurality of C real components Re (C) as a horizontal axis and an imaginary component im (C) as a vertical axis is defined as a complex coordinate system.
9. The method for matching spatial point set privacy protection based on vector mapping and sliding window scanning according to claim 8, wherein: in step 3-2, a set of spatial points Pts and their corresponding are givenComplex set Cs _ EbPts for any two spatial points Pti、PtjI is more than or equal to 1, j is more than or equal to n and corresponding complex number C _ EebPtsi，C_EebPtsjI is more than or equal to 1, j is less than or equal to n, if C _ EebPtsi，C_EebPtsjIn the same complex coordinate system, the following two conditions are satisfied:
in complex coordinate system, there is a self-defined width theta as sliding window, C _ EebPtsi，C_EebPtsjOccurring simultaneously in the window, i.e., 0. ltoreq. Re (C _ EebPts)i)-Re(C_EebPtsj)|≤θ；
C_EebPtsi，C_EebPtsjThe difference value of the imaginary parts of (C) is also within the threshold value theta x i, namely the condition 0 ≦ Im (C _ EebPts) is satisfiedi)-Im(C_EebPtsj)|≤θ×i；
Then call C _ EebPtsiAnd C _ EebPtsjMatching, further called two space points PtiWith PtjAnd (6) matching.
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