JP7096145B2 - Clustering device, clustering method and clustering program - Google Patents

Description

The present invention relates to devices, methods and programs for clustering encrypted datasets.

Conventionally, as a data anonymization method, many k-anonymization algorithms have been proposed, for example, as shown in Non-Patent Documents 1 to 3. Since these methods assume that the user himself anonymizes the data set owned by the user, all operations are processed in plain text.

L. Sweeney, "Achieving k-anonymity privacy promotion using generalization and support," in J. et al. Uncertainty, Fusionss, and Knowledge-Base Systems, vol. 10 (5), 2002, pp. 571-588. K. LeFavre, D.I. J. DeWitt, and R. Ramakrishanan, “Incognito: Effective full-domin k-anonymity,” in Proc. of SIGMOD 2005, 2005, pp. 49-60. K. LeFavre et al. , “Mondrian multimetrical k-anonymity,” in Proc. of the 22nd International Convention on Data Engineering (ICDE '06), IEEE, 2006, pp. 25-35. Kohlmayar F, Presser F, Eckert C, Khun KA. “A flexible applied data anonymization,” J Biomed Information 2013 Dec 12.

When outsourcing anonymization, or when anonymizing data held by multiple institutions together, the data needs to be encrypted. For example, in the method of Non-Patent Document 4, it is assumed that anonymization is performed by a plurality of institutions, but the data holder needs to participate in the protocol, and it is necessary to use deterministic encryption, which reduces anonymity. There were issues such as.

Further, although the above-mentioned k-anonymization algorithm can be executed at high speed in plain text, when the same algorithm is applied to encrypted data as it is, there are the following problems.
In secret calculation, addition and multiplication can be performed while the data is concealed, so theoretically any calculation can be realized in a concealed state. However, even if any calculation method such as Garbled Circuit, secret sharing, homomorphic encryption, etc. is used, the processing is slow and it is difficult to achieve the desired function in a realistic time for large-scale data. It has been known.

An object of the present invention is to provide a clustering device, a clustering method, and a clustering program capable of clustering encrypted data at high speed.

The clustering apparatus according to the present invention has an initial processing unit that allocates at least one initial record to each cluster when dividing a record of an encrypted data set into a predetermined number of clusters, and a record to which each of the clusters belongs. A center of gravity calculation unit that calculates the entire center of gravity, and a division processing unit that executes division processing in parallel for each cluster so that the records that are closest to the center of gravity of the data set belong to the cluster in order. Be prepared.

The center of gravity calculation unit may calculate the center of gravity of the cluster after executing the division process a plurality of times for each cluster.

The initial processing unit may randomly select the initial record.

When the clustering apparatus has records that belong to a plurality of clusters in duplicate as a result of processing by the division processing unit, the first adjustment process for each record belongs only to the cluster closest to the center of gravity. May be provided with a first adjusting unit that executes the above in parallel.

If there is a record that does not belong to any of the clusters as a result of processing by the division processing unit, the clustering apparatus performs a second adjustment process for each record to belong to the cluster closest to the center of gravity. A second adjustment unit that is executed in parallel may be provided.

When there are clusters smaller than a predetermined size as a result of processing by the division processing unit, the clustering apparatus belongs to the cluster having the shortest distance between the centers of gravity of the records belonging to the cluster for each cluster. A third adjustment unit may be provided to execute the third adjustment process to be performed in parallel.

The clustering method according to the present invention includes an initial processing step of allocating at least one initial record to each cluster when dividing a record of an encrypted data set into a predetermined number of clusters, and a record to which each of the clusters belongs. A center of gravity calculation step for calculating the entire center of gravity and a split processing step of parallelly executing a division process of assigning the data set to the cluster in order from the record having the closest distance to the center of the data set for each cluster. The computer runs.

The clustering program according to the present invention has an initial processing step of allocating at least one initial record to each cluster when dividing a record of an encrypted data set into a predetermined number of clusters, and a record belonging to each of the clusters. A center of gravity calculation step for calculating the entire center of gravity and a splitting process for each cluster in which the splitting process of assigning the data set to the cluster in order from the record closest to the center of gravity is executed in parallel. It's meant to be run by a computer.

According to the present invention, encrypted data can be clustered at high speed.

It is a block diagram which shows the functional structure of the clustering apparatus which concerns on embodiment. It is a figure which illustrates the algorithm of the division processing in the clustering method which concerns on embodiment. It is a figure which illustrates the algorithm which includes the 1st adjustment process and the 2nd adjustment process which concerns on embodiment. It is a figure which illustrates the algorithm which includes the 3rd adjustment process and the anonymization process which concerns on embodiment.

Hereinafter, an example of the embodiment of the present invention will be described.
FIG. 1 is a block diagram showing a functional configuration of the clustering apparatus 1 according to the present embodiment.
The clustering device 1 is an information processing device (computer) such as a server device or a personal computer, and includes a control unit 10 and a storage unit 20, as well as various data input / output devices and communication devices.

The control unit 10 is a part that controls the entire clustering device 1, and realizes each function in the present embodiment by appropriately reading and executing various programs stored in the storage unit 20. The control unit 10 may be a CPU.

The storage unit 20 is a storage area for various programs and various data for making the hardware group function as the clustering device 1, and may be a ROM, RAM, flash memory, hard disk (HDD), or the like. Specifically, the storage unit 20 stores a program (clustering program) for causing the control unit 10 to execute each function of the present embodiment, a data set to be processed by this program, various variables, flags, and the like. do.

The control unit 10 includes an initial processing unit 11, a center of gravity calculation unit 12, a division processing unit 13, a first adjustment unit 14, a second adjustment unit 15, and a third adjustment unit 16. The control unit 10 divides the data set to be processed into a plurality of clusters while being encrypted by these functional units.
The clustering device 1 realizes k-anonymization by using each record of the data set as a data point and changing the point belonging to each divided cluster to a representative point such as the center of gravity.

The initial processing unit 11 allocates at least one initial record to each cluster when dividing a plurality of records of the encrypted data set into a predetermined number of clusters.
The method of allocating the initial record is not limited, but in the present embodiment, the processing speed is prioritized, and the initial processing unit 11 randomly selects the initial record.

The center of gravity calculation unit 12 calculates the center of gravity of the entire record to which the cluster belongs.
The records belonging to the cluster increase every time the division processing unit 13 performs division processing. Therefore, the center of gravity may be updated every time the division process is performed, but in the present embodiment, the processing speed is prioritized, and the center of gravity calculation unit 12 calculates the center of gravity of the cluster after executing the division process a plurality of times for each cluster. And update. For example, the center of gravity calculation unit 12 omits each update during the iterative process, and updates the center of gravity once after the completion of the predetermined number of division processes or several times until the predetermined number of division processes are completed. You may.

The division processing unit 13 executes the division processing for each cluster in parallel a predetermined number of times in order from the record having the closest distance to the center of gravity of the data set. The number of executions may be, for example, k + α times, which is obtained by adding an appropriately set adjustment number α to the minimum number k of clusters in k-anonymization.
As a result, the division processing unit 13 executes the process of searching for records that are close to the center of gravity in parallel by the number of clusters, and improves the processing speed.

If there are duplicate records belonging to a plurality of clusters as a result of processing by the division processing unit 13, the first adjusting unit 14 assigns each corresponding record to only the cluster closest to the center of gravity, and the other. The first adjustment process for canceling the affiliation with the cluster is executed in parallel.

If there is a record that does not belong to any of the clusters as a result of processing by the division processing unit 13, the second adjustment unit 15 makes the corresponding record belong to the cluster closest to the center of gravity. Execute processing in parallel.

If there is a cluster of a predetermined size, that is, less than the minimum number k in k-anonymization as a result of processing by the division processing unit 13, the third adjustment unit 16 belongs to this cluster for each corresponding cluster. The third adjustment process of making the existing records belong to another cluster having the shortest distance between the centers of gravity is executed in parallel.

FIG. 2 is a diagram illustrating the algorithm A of the division processing in the clustering method according to the present embodiment.
In the algorithm A, the encrypted data set E (D), the parameter k in k-anonymization, and the adjustment parameter α are input.

First, let r _i [0] be the value (data point) of the i-th record of the data set E (D). Further, r _i [j] is set as a flag indicating whether or not the record r _i belongs to the jth cluster (= E (1)) (= E (0)) (step 2).
When the number of records in the data set is n and the number of clusters is K, ri [j] is initialized to E (0) in 1 ≦ _i ≦ n and 1 ≦ j ≦ K (step 3).

Further, let _di [j] be the distance between r _i [0] and the center of gravity g (c _j ) of the cluster c _j (step 4).
In 1 ≦ _i ≦ n and 1 ≦ j ≦ K, di [j] is initialized to E (∞) (step 5).

Next, K = floor (n / k) records are randomly selected from the data set E (D) (step 6).
Assuming that the i-th record is selected for the i-th cluster, ri [ _i ] is updated to E (1) and g ( _ci ) is updated to E ( _ri [0]) (step 7). ).

In steps 9 to 15, the division process is repeated k + α times for each of K clusters. This division process is parallelized to the same number as the number of clusters, and steps 12 and 13 are executed in parallel in units of clusters.

The division processing unit 13 selects the record i'that has the minimum distance from the center of gravity g (c _j ) with respect to the cluster c _j from the records that do not belong to any of the clusters (step 12). .. Then, the division processing unit 13 updates r _i' [j] and di _' [j] (step 13).

When the iterative processing of k + α times is completed, the record r _i in which the flag r _i [j] is E (1) belongs to the cluster c _j .
The center of gravity calculation unit 12 updates the center of gravity g (c _j ) for all the clusters c _j (step 17).

The number of repetitions is adjusted by the parameter α, but as the number of repetitions increases, the number of records that belong to multiple clusters increases, and as the number of times decreases, the number of records that do not belong to any cluster increases. do.
The parameter α is appropriately set according to the situation, but the records that are not clustered correctly are adjusted by the following processing.

FIG. 3 is a diagram illustrating an algorithm B including a first adjustment process and a second adjustment process according to the present embodiment.

In the first adjustment process of steps 23 to 27, the records belonging to a plurality of clusters, that is, the records r _i in which the sum (1 ≦ j ≦ K) of r _i [j] is neither E (0) nor E (1). Is adjusted. The first adjusting unit 14 processes these records in parallel.

The first adjusting unit 14 selects the cluster _c'j having the smallest distance di [ _j ] from the center of gravity for each record r _i (step 25), and sets the flag r _i [j'] to E (1). , Other flags _∀ri [j ≠ j'] are updated to E (0) (step 26).

In the second adjustment process of steps 29 to 33, a record that does not belong to any of the clusters, that is, a record r _i whose sum (1 ≦ j ≦ K) of r _i [j] is E (0) is adjusted. The second adjustment unit 15 processes these records in parallel.

The second adjusting unit 15 selects the cluster _c'j having the smallest distance from the center of gravity for each record r _i (step 31), and updates the flag r _i [j'] to E (1) (step 32). ).

When the first adjustment process and the second adjustment process are completed, the center of gravity g (c _j ) is updated for all the clusters c _j (step 34).

FIG. 4 is a diagram illustrating an algorithm C including a third adjustment process and an anonymization process according to the present embodiment.

In the third adjustment process of steps 43 to 47, the cluster c _j in which the number of records belonging to the cluster is smaller than k, that is, the sum of r _i [j] (1 ≦ i ≦ n) is smaller than E (k) is adjusted. Will be done. The third coordinating unit 16 processes these clusters in parallel.

The third adjustment unit 16 selects another cluster _c'h with the minimum distance between the centers of gravity for the cluster c _j to be adjusted (step 45), and makes all the records of the cluster c _j belong to the cluster _c'h . Therefore, the flag r _i [h'] is updated to E (1), and the flag r _i [j] is updated to E (0) (step 46).

Subsequently, the control unit 10 updates the value r _i [0] of all the records to the center of gravity g (c _j ) of the cluster c _j to which the control unit 10 belongs for k-anonymization (steps 48 to 50).
Then, the control unit 10 outputs the set of ri [ ₀ ] as a clustered data set E (D') (step 51).

According to the present embodiment, when the clustering apparatus 1 divides the records of the encrypted data set into clusters, the number of clusters to be divided is determined from the beginning, and at least one initial record is assigned to each cluster. After that, for each cluster, the division processing to belong to this cluster is executed in parallel in order from the record closest to the center of gravity.

In the conventional clustering method, it is necessary to determine (Argmin) which cluster belongs to all the records. For example, the process of calculating the distance between each record and the cluster, determining the cluster to which it belongs, and updating the cluster is performed for all records, but this algorithm is difficult to process in parallel, and at least Argmin or Argmax processing was required for the number of records.
On the other hand, since the clustering apparatus 1 calculates the distance from each cluster to the record and then updates the center of gravity of the cluster, the same number of parallel processing as the number of clusters can be performed. Therefore, by parallelizing the heavy process of searching for records that are close to the center of gravity, data set clustering (for example, k-anonymization) can be executed at high speed even on the ciphertext.

The clustering device 1 can speed up the processing by reducing the frequency of recalculating the center of gravity of the cluster less than the frequency of updating the cluster. The frequency of recalculation may be appropriately set depending on the trade-off with the accuracy of clustering.
Further, the clustering apparatus 1 can speed up the processing by randomly selecting the initial record of each cluster.

When the clustering apparatus 1 has duplicate records belonging to a plurality of clusters as a result of the division processing, the clustering apparatus 1 executes the first adjustment processing in parallel for each of these records so that the records belong only to the cluster closest to the center of gravity. do.
Further, if there are records that do not belong to any of the clusters as a result of the division processing, the clustering apparatus 1 performs a second adjustment process in parallel for each of these records so that the records belong to the cluster closest to the center of gravity. Run.
Further, when the clustering apparatus 1 has clusters smaller than a predetermined size as a result of the division processing, the clustering apparatus 1 makes the records to which the clusters belong belong to the other cluster having the shortest distance between the centers of gravity. 3 The adjustment process is executed in parallel.
Therefore, the clustering apparatus 1 can adjust the portion where the clustering cannot be sufficiently performed by the division processing, and can execute the various adjustment processes at high speed by parallelizing them.

Although the embodiments of the present invention have been described above, the present invention is not limited to the above-described embodiments. Moreover, the effects described in the above-described embodiments are merely a list of the most suitable effects resulting from the present invention, and the effects according to the present invention are not limited to those described in the embodiments.

The clustering method by the clustering device 1 is realized by software. When realized by software, the programs that make up this software are installed in the information processing device (computer). Further, these programs may be recorded on a removable medium such as a CD-ROM and distributed to the user, or may be distributed by being downloaded to the user's computer via a network. Further, these programs may be provided to the user's computer as a Web service via a network without being downloaded.

1 Clustering device 10 Control unit 11 Initial processing unit 12 Center of gravity calculation unit 13 Division processing unit 14 1st adjustment unit 15 2nd adjustment unit 16 3rd adjustment unit 20 Storage unit

Claims (8)

An initial processing unit that allocates at least one initial record to each cluster when dividing the records of the encrypted data set into a predetermined number of clusters.
For each of the clusters, a center of gravity calculation unit that calculates the center of gravity of the entire record to which it belongs on the ciphertext ,
For each cluster, the division process of assigning the data set to the cluster in order from the record calculated on the ciphertext and having the closest distance to the center of gravity is executed in parallel with the same number of clusters. A clustering device that includes a unit. The clustering apparatus according to claim 1, wherein the center of gravity calculation unit calculates the center of gravity of the cluster after executing the division process a plurality of times for each cluster. The clustering apparatus according to claim 1 or 2, wherein the initial processing unit randomly selects the initial record. If there are duplicate records belonging to a plurality of clusters as a processing result by the division processing unit, the first adjustment process of making each record belong only to the cluster closest to the center of gravity is executed in parallel. The clustering apparatus according to any one of claims 1 to 3, further comprising a first adjusting unit. If there is a record that does not belong to any cluster as a processing result by the division processing unit, the second adjustment process of making the record belong to the cluster closest to the center of gravity is executed in parallel for each record. 2. The clustering apparatus according to any one of claims 1 to 4, further comprising an adjusting unit. If there are clusters smaller than a predetermined size as a result of processing by the division processing unit, the third adjustment process of making the records belonging to the cluster belong to the cluster having the shortest distance between the centers of gravity for each cluster. The clustering apparatus according to any one of claims 1 to 5, further comprising a third adjusting unit for executing the above in parallel. An initial processing step that allocates at least one initial record to each cluster when dividing records in an encrypted dataset into a predetermined number of clusters.
For each of the clusters, a center of gravity calculation step for calculating the center of gravity of the entire record to which the record belongs on the ciphertext , and
For each cluster, the division process of assigning the data set to the cluster in order from the record calculated on the ciphertext and having the closest distance to the center of gravity is executed in parallel with the same number of clusters. Steps and how the computer performs the clustering method. An initial processing step that allocates at least one initial record to each cluster when dividing records in an encrypted dataset into a predetermined number of clusters.
For each of the clusters, a center of gravity calculation step for calculating the center of gravity of the entire record to which the record belongs on the ciphertext , and
For each cluster, the division process of assigning the data set to the cluster in order from the record calculated on the cryptographic text and having the closest distance to the center of gravity is executed in parallel with the same number of clusters. A clustering program that lets your computer perform steps and.

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