WO2024124466A1 - Method for clustering time series data and device - Google Patents

Abstract

Provided is a method for clustering time series data, comprising: pre-clustering sample points in the time series data (S310), wherein the pre-clustering comprises traversing all sample points in the sample points, and on the basis of a distance between a current sample point and a previous sample point of the current sample point, clustering the sample points into corresponding clusters (S311), and calculating a mean value for all sample points in each cluster in all the generated clusters, and determining, on the basis of a mean value difference between a current cluster and adjacent clusters thereof, whether to merge the current cluster and the clusters adjacent thereto (S312); and on the basis of the mean value, clustering all the pre-clustered clusters by using the DBSCAN algorithm (S320).

Description

Method and device for clustering time series data Technical Field

The present disclosure relates to clustering technology, and more particularly, to a method and device for clustering time series data.

Background technique

With the development of Internet computer technology, real-time data streams have become an important form of data information and have been widely used in network traffic control, data monitoring systems, Internet finance and other fields. How to quickly and effectively extract information from high-speed, large-scale real-time data streams has become a major challenge in the field of data stream mining. Cluster analysis is an important technology in the data mining process. The core goal is to classify data based on similarity. It is an unsupervised machine learning task, and density-based clustering algorithms can best reflect efficiency. Machine learning is a data-driven method that can study, research and build a special algorithm to allow computers to learn from data and make predictions, thereby quickly and effectively solving this problem.

However, the existing technology cannot accurately cluster the actually generated time series signals, has poor robustness to noise, and is inefficient.

Therefore, a technique is needed that can accurately cluster time series signals.

Summary of the invention

The purpose of the embodiments of the present disclosure is to provide an effective solution for accurately clustering time series signals. Specifically, the embodiments of the present disclosure provide a method and device for clustering time series data.

According to a first aspect of the present disclosure, a method for clustering time series data is proposed, comprising: pre-clustering sample points in the time series data, wherein the pre-clustering includes traversing all sample points in the sample points, clustering the sample points into corresponding clusters based on the distance between the current sample point and the previous sample point of the current sample point, and calculating the mean of all sample points in each of all the generated clusters, determining whether to merge the current cluster and its adjacent clusters based on the mean difference between the current cluster and its adjacent clusters; and clustering all the clusters after the pre-clustering based on the mean.

In some embodiments, the time series data includes nanopore sequence data and is stored in a memory in floating point format, wherein the nanopore sequence data includes a sequencing signal and an open pore current signal.

In some embodiments, the time series data stored in the memory is converted into an array.

In some embodiments, the distance is obtained by calculating the L1 norm value of the current sample point and the previous sample point of the current sample point.

In some embodiments, clustering the sample points into corresponding clusters based on the distance between the current sample point and the previous sample point of the current sample point includes: when the L1 norm of the current sample point and the previous sample point of the current sample point is less than the initial minimum distance ε, marking the current sample point and the previous sample point as the same cluster; when the L1 norm of the current sample point and the previous sample point of the current sample point is greater than or equal to the ε, if the total number of sample points in the current cluster is less than the minimum number of sample points MinPts, marking the current sample point and the previous sample point as the same cluster, otherwise setting the current sample point to a new cluster.

In some embodiments, based on the mean difference between the current cluster and its adjacent clusters, determining whether to merge the current cluster and its adjacent clusters includes: if the mean difference between the current cluster and its adjacent clusters is less than a threshold eps_c, merging the current cluster and its adjacent clusters; otherwise keeping the current cluster unchanged.

In some embodiments, the initial minimum distance ε, the minimum number of sample points MinPts and the threshold eps_c are determined using nearest neighbor search.

In some embodiments, the initial minimum distance ε, the minimum number of sample points MinPts and the threshold eps_c are adjustable parameters.

In some embodiments, the nearest neighbor search is implemented by building a KD tree or a ball tree.

In some embodiments, clustering all the pre-clustered clusters using the DBSCAN algorithm is based on the mean and also based on the standard deviation.

According to the second aspect of the present disclosure, a device for clustering time series data is also provided, comprising: one or more processors; and one or more memories, wherein the one or more memories store computer-executable instructions, and when the computer-executable instructions are executed by the one or more processors, the one or more processors execute any of the above methods.

According to a third aspect of the present disclosure, a computer storage medium is further provided, on which computer executable instructions are stored. When the computer executable instructions are executed by a processor, the processor is caused to execute any of the above methods.

The present disclosure creatively pre-clusters one-dimensional time series signals, optimizes the search process, and can be fully applied in time series data clustering. Specifically:

1) Regarding the robustness issues of existing technologies

The method based on pre-clustering design can effectively and accurately classify noise points. In theory, it can solve the clustering of noise points of various forms and can be effectively applied to applications that do not need to cluster noise points into other categories.

2) Addressing the low efficiency of existing technologies

The present invention is based on pre-clustering DBSCAN, and the nearest neighbor search process can be optimized by establishing a KD tree or a ball tree for scale restriction. Compared with the DBSCAN algorithm, the time complexity of the improved algorithm is significantly reduced, and when the sample set is large, the clustering convergence time is greatly reduced, which effectively improves the accuracy and efficiency of time series data classification, and has good adaptability to scenes with constantly changing features.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the present disclosure and its advantages, reference will now be made to the following description taken in conjunction with the accompanying drawings, in which:

FIG1 is a schematic diagram showing nanopore sequence data as an example of time series data;

FIG2 is a schematic diagram showing a DBSCAN algorithm;

FIG3 is a schematic flow chart showing a method for clustering time series data according to an embodiment of the present disclosure;

FIG4 is a flowchart showing a specific implementation of a method for clustering time series data according to an embodiment of the present disclosure;

5-7 are diagrams showing pre-clustering results of a method for clustering time series data according to an embodiment of the present disclosure;

FIG8 is a diagram showing a clustering result of a method for clustering time series data according to an embodiment of the present disclosure;

FIG9 is a diagram showing the clustering results of simulated data using the DBSCAN algorithm;

FIG10 is a diagram showing clustering results of simulation data according to a method for clustering time series data according to an embodiment of the present disclosure;

FIG11 is a diagram showing the clustering results of the experimental data using the DBSCAN algorithm;

FIG12 is a diagram showing clustering results of experimental data by a method for clustering time series data according to an embodiment of the present disclosure;

13 is a table showing a comparison of processing time using the DBSCAN algorithm and a method for clustering time series data according to an embodiment of the present disclosure;

FIG. 14 schematically shows a block diagram of a device 1400 for a method of clustering time series data according to an embodiment of the present disclosure.

In the drawings, the same or similar structures are marked with the same or similar reference numerals.

Detailed ways

Other aspects, advantages and salient features of the disclosure will become apparent to those skilled in the art from the following detailed description of exemplary embodiments of the disclosure taken in conjunction with the accompanying drawings.

In this disclosure, the terms "include" and "including" and their derivatives mean inclusion rather than limitation; the term "or" is inclusive, meaning and/or.

In this specification, the various embodiments described below for describing the principles of the present disclosure are merely illustrative and should not be interpreted in any way as limiting the scope of the disclosure. The following description with reference to the accompanying drawings is used to help fully understand the exemplary embodiments of the present disclosure as defined by the claims and their equivalents. The following description includes a variety of specific details to aid understanding, but these details should be considered merely exemplary. Therefore, it should be recognized by those of ordinary skill in the art that various changes and modifications may be made to the embodiments described herein without departing from the scope and spirit of the present disclosure. In addition, for the sake of clarity and brevity, descriptions of well-known functions and structures are omitted. In addition, throughout the accompanying drawings, the same figure numerals are used for similar functions and operations.

FIG. 1 is a schematic diagram showing nanopore sequence data as an example of time-series data.

The present disclosure relates to a clustering method for nanopore sequencing signals (i.e., nanopore sequence data). Nanopore sequencing is to immerse a synthetic polymer membrane in an ionic solution. The polymer membrane is covered with modified transmembrane channel proteins (nanopores). Different voltages are applied on both sides of the membrane to generate a voltage difference. The DNA chain is unwound through the nanopore protein under the traction of the motor protein, and different bases will form characteristic ion current change signals. Nanopore electrical signals are one-dimensional time series signals. Nanopore sequencing signals refer to the changes in perforation current recorded when DNA molecules pass through nanopores. This change is mainly caused by different currents of different bases in nanopores. The clustering method provided in the present disclosure is mainly to solve the clustering of time series data such as nanopore sequencing signals. As shown in Figure 1, nanopore sequence data may include sequencing signals and pore current signals. Nanopore sequence data of any form can be collected and stored in a memory in floating point type as sample points for clustering methods.

FIG2 is a schematic diagram showing the DBSCAN algorithm.

In the prior art of clustering time series data, in order to detect real-time time series data (for example, nanopore electrical signals) and cluster them, the density-based clustering analysis algorithm examines the continuity between samples from the perspective of sample density, and continuously expands clustering clusters based on continuous samples to obtain the final clustering results. The DBSCAN algorithm is a clustering algorithm based on density space, which is widely used in the fields of machine learning and data mining. Its clustering principle is generally that the density of each cluster is higher than the density around the cluster, and the density of noise is less than the density of any cluster. As shown in Figure 2, the basic idea of the DBSCAN algorithm is: set a minimum distance ε, and for each point in the data set, draw a circle with the minimum distance ε as the radius. The points in the circle are called neighbors. If the number of neighboring points is less than the threshold MinPts, the current point is set as a boundary molecule; if the number of neighboring points is greater than or equal to MinPts, the point is called a core molecule, and the point and its neighboring points are marked as a cluster; points that are neither core points nor boundary points (i.e., points with zero neighboring points) are called outliers. At the same time, loop all neighboring points, set the neighboring points of each neighboring point to the same cluster, and when all points that meet the conditions are traversed, cluster+1, and start the next loop.

Although the existing DBSCAN algorithm can cluster time series data, it cannot accurately cluster the time series signals generated by actual nanopores, has poor robustness to noise, and has low clustering efficiency when the sample set is large.

Therefore, in order to solve the above problems, the present disclosure proposes an improved method for clustering time series data. The method is a pre-clustering-based clustering method improved according to the above existing DBSCAN algorithm.

FIG. 3 is a schematic flowchart showing a method 300 for clustering time series data according to an embodiment of the present disclosure.

As shown in FIG. 3 , a method 300 for clustering time series data according to an embodiment of the present disclosure may include:

Step S310: pre-clustering sample points in the time series data; and

Step S320: clustering all pre-clustered clusters using the DBSCAN algorithm based on the mean of all sample points in the cluster.

According to an embodiment, the pre-clustering in step S310 may include:

Step S311: traverse all sample points, and cluster the sample points into corresponding clusters based on the distance between the current sample point and the previous sample point of the current sample point; and

Step S312: Calculate the mean of all sample points in each of all generated clusters, and determine whether to merge the current cluster with its adjacent clusters based on the mean difference between the current cluster and its adjacent clusters.

4 , a specific example of performing pre-clustering is shown.

An initial minimum distance eps_p (S410) can be set, and for the input one-dimensional time series data, each sample point pt is traversed from the beginning to the end (S420). If the L1 norm of the current sample point pt and the previous sample point is less than eps_p (S430: yes), the current sample point pt can be marked as the same cluster as the previous sample point (S431), otherwise (S430: no), it is set as a new cluster and continues to the next sample point. Among them, for numerical values, the L1 norm is the absolute value of the difference between the current sample point and the previous sample point. Here, the L1 norm is used as the distance, and those skilled in the art can also conceive of other forms of distance. The result of the above distance-based pre-clustering operation is shown in Figure 5.

During the traversal process, even if the L1 norm of the current sample point pt and the previous sample point is greater than eps_p (S430: No), if the total number of sample points in the current cluster is less than the minimum number of sample points MinPts (S432: Yes), the current sample point pt can also be marked as the same cluster as the previous sample point (S431), otherwise (S432: No) it is set as a new cluster (S433) and continues to the next sample point. The result of the above pre-clustering operation based on the total number of sample points is shown in FIG6.

The clustering result of the above operation may be stored in a database (S440), and the clustering result may include a cluster start index, a cluster end index, a cluster, a mean of all sample points in the cluster, and a standard deviation of all points in the cluster.

The mean value of all sample points in each cluster obtained by the above operation can be calculated. If the mean difference between the cluster and the adjacent cluster is less than the threshold value eps_c (S450: yes), the two clusters can be merged (S451), otherwise (S450: no) the cluster remains unchanged (S452). The result of the above pre-clustering operation based on mean difference is shown in FIG7.

The clustering result of the above pre-clustering operation may be updated according to the result of the cluster merging operation.

For the result of the pre-clustering operation, all clusters can be clustered using the DBSCAN algorithm based on the mean of all sample points in each cluster (S460). According to an embodiment, clustering can be further performed based on the standard deviation of all sample points in each cluster. The clustering result of the above clustering operation can be updated. The result of the above clustering operation is shown in FIG8.

In the above example, eps_p controls the difference between adjacent sample points, MinPts is the minimum number of points in a cluster, and eps_c controls the difference between adjacent cluster averages in pre-clustering. eps_p, MinPts, and eps_c are adjustable parameters. For example, the floating-point data stored in the memory can be converted into an array, and the optimal parameters can be determined using the nearest neighbor search. The nearest neighbor search is an optimization problem of finding the point closest to (or most similar to) a given point in a given set. The nearest neighbor search can be implemented by establishing a KD tree or a ball tree, etc. The present disclosure applies the above method to cluster the real-time time series data based on the determined optimal parameters and obtains the clustering results.

FIG. 9 is a diagram showing the clustering results of the simulation data using the DBSCAN algorithm.

FIG. 10 is a diagram showing clustering results of simulation data according to a method for clustering time series data according to an embodiment of the present disclosure.

By comparing FIG. 9 and FIG. 10 , it can be seen that the clustering method of the present invention has a better clustering effect on the sample points in the simulated data sample set than the clustering effect using the DBSCAN algorithm, and has good robustness to the noise in the simulated data sample set.

FIG. 11 is a diagram showing the clustering results of the experimental data using the DBSCAN algorithm.

FIG. 12 is a diagram showing clustering results of experimental data by a method for clustering time series data according to an embodiment of the present disclosure.

Similarly, by comparing FIG. 11 and FIG. 12 , it can be seen that the clustering effect of the clustering method disclosed in the present invention on the sample points in the experimental data sample set is better than the clustering effect using the DBSCAN algorithm, and has good robustness to the noise in the experimental data sample set.

Figure 13 is a table showing a comparison of the processing time of the method for clustering time series data using the DBSCAN algorithm and according to an embodiment of the present disclosure.

As can be seen from the table in Figure 13, when the number of sample points in the sample set is 1000, 30000 and 50000, the clustering time using the DBSCAN algorithm is 0.01s, 6.238s and 29.395s respectively, while the clustering time using the clustering method disclosed in the present invention is 0.0038s, 0.0409s and 0.0719s respectively. The clustering speed using the clustering method disclosed in the present invention is 2.63 times, 152.53 times and 408.80 times higher than the clustering speed using the DBSCAN algorithm. Therefore, the clustering time using the clustering method disclosed in the present invention is significantly lower than the clustering time using the DBSCAN algorithm, and the efficiency is significantly improved.

In summary, the present invention creatively pre-clusters one-dimensional time series data, which is beneficial to improving the accuracy and efficiency of subsequent DBSCAN-based clustering and can solve the problem that current time series data clustering is sensitive to noise and inefficient.

The present invention can be implemented based on the development environment shown in Table 1. Although the present invention can run stably on a machine with a general CPU configuration, the algorithm module involves the reading, writing and storage of a large amount of data as well as the training and testing of the model, which requires a large amount of data calculation and operation. Running in a high-performance CPU or a hardware and software environment with a GPU configuration can significantly improve efficiency and stability. A single-channel nanopore sequencing device and a PC are used to collect data. The target library data is collected using the nanopore sequencing device, and the collected signal data and other information are saved as a dat file structure and stored in real time in the PC hard disk.

Table 1. Development environment

FIG14 schematically shows a block diagram of a device 1400 for clustering time series data according to an embodiment of the present disclosure. The device shown in FIG14 can be any device with processing capabilities. It should be noted that the device shown in FIG14 is only an example and should not bring any limitation to the functions and scope of use of the embodiments of the present application.

@3.60GHz)，其可以根据存储在只读存储器(ROM)1402中的程序或者从存储部分1408加载到随机访问存储器(RAM)1403中的程序而执行各种适当的动作和处理。在RAM 1403中，还存储有设备1400操作所需的各种程序和数据。CPU或GPU 1401、ROM 1402以及RAM 1403通过总线1404彼此相连。输入/输出(I/O)接口1405也连接至总线1404。 As shown in FIG. 14 , the device 1400 according to this embodiment includes a central processing unit (CPU) 1401 (e.g., the CPU in Table 1:

@3.60GHz), which can perform various appropriate actions and processes according to the program stored in the read-only memory (ROM) 1402 or the program loaded from the storage part 1408 to the random access memory (RAM) 1403. In the RAM 1403, various programs and data required for the operation of the device 1400 are also stored. The CPU or GPU 1401, the ROM 1402, and the RAM 1403 are connected to each other through the bus 1404. An input/output (I/O) interface 1405 is also connected to the bus 1404.

The device 1400 may also include one or more of the following components connected to the I/O interface 1405: an input section 1406 including a keyboard or a mouse, etc.; an output section 1407 including a cathode ray tube (CRT) or a liquid crystal display (LCD), etc. and a speaker, etc.; a storage section 1408 including a hard disk, etc.; and a communication section 1409 including a network interface card such as a LAN card or a modem. The communication section 1409 performs communication processing via a network such as the Internet. A drive 1410 is also connected to the I/O interface 1405 as needed. A removable medium 1411, such as a magnetic disk, an optical disk, a magneto-optical disk, or a semiconductor memory, etc., is installed on the drive 1410 as needed, so that a computer program read therefrom is installed into the storage section 1408 as needed.

In particular, according to an embodiment of the present disclosure, the process described above with reference to the flowchart can be implemented as a computer software program. For example, an embodiment of the present disclosure includes a computer program product, which includes a computer program carried on a computer-readable medium, and the computer program includes a program code for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from a network through a communication part 1409, and/or installed from a removable medium 1411. When the computer program is executed by a central processing unit (CPU) 1401, the above-mentioned functions defined in the device of the embodiment of the present application are executed.

It should be noted that the computer-readable medium shown in the present disclosure may be a computer-readable signal medium or a computer-readable storage medium or any combination of the above two. The computer-readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared or semiconductor system, device or device, or any combination of the above. More specific examples of computer-readable storage media may include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present disclosure, a computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in combination with an instruction execution system, device or device. In the present disclosure, a computer-readable signal medium may include a data signal propagated in a baseband or as part of a carrier wave, in which a computer-readable program code is carried. This propagated data signal may take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. Computer-readable signal media may also be any computer-readable medium other than computer-readable storage media, which may send, propagate or transmit a program for use by or in conjunction with an instruction execution system, apparatus or device. The program code contained on the computer-readable medium may be transmitted using any appropriate medium, including but not limited to: wireless, wire, optical cable or RF, etc., or any suitable combination of the above.

The method of the present invention and the devices involved have been described above in conjunction with the embodiments. It will be appreciated by those skilled in the art that the method shown above is exemplary only. The method of the present invention is not limited to the steps and sequence shown above. The device shown above may include more modules, for example, it may also include modules that can be developed or developed in the future and can be used for the device, etc. The various identifiers shown above are exemplary rather than restrictive, and the present invention is not limited to the specific cells that serve as examples of these identifiers. Those skilled in the art may make many improvements, modifications and substitutions based on the teachings of the illustrated embodiments, and may extend to other fields where time series need to be clustered.

The program running on the device according to the present disclosure may be a program that enables a computer to implement the functions of the embodiments of the present disclosure by controlling a central processing unit (CPU). The program or information processed by the program may be temporarily stored in a volatile memory (such as a random access memory RAM), a hard disk drive (HDD), a non-volatile memory (such as a flash memory), or other memory systems.

The program for realizing the functions of each embodiment of the present disclosure can be recorded on a computer-readable recording medium. The corresponding functions can be realized by making a computer system read the program recorded on the recording medium and executing these programs. The so-called "computer system" herein can be a computer system embedded in the device, which can include an operating system or hardware (such as a peripheral device). "Computer-readable recording medium" can be a semiconductor recording medium, an optical recording medium, a magnetic recording medium, a recording medium of a short-term dynamic storage program, or any other recording medium readable by a computer.

The various features or functional modules of the devices used in the above embodiments can be implemented or executed by circuits (e.g., monolithic or multi-chip integrated circuits). Circuits designed to perform the functions described in this specification may include general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic, discrete hardware components, or any combination of the above devices. The general-purpose processor may be a microprocessor, or any existing processor, controller, microcontroller, or state machine. The above circuits may be digital circuits or analog circuits. In the case where new integrated circuit technologies have emerged to replace existing integrated circuits due to advances in semiconductor technology, one or more embodiments of the present disclosure may also be implemented using these new integrated circuit technologies.

As described above, the embodiments of the present disclosure have been described in detail with reference to the accompanying drawings. However, the specific structure is not limited to the above embodiments, and the present disclosure also includes any design changes that do not deviate from the main purpose of the present disclosure. In addition, various changes can be made to the present disclosure within the scope of the claims, and the embodiments obtained by appropriately combining the technical means disclosed in different embodiments are also included in the technical scope of the present disclosure. In addition, the components with the same effect described in the above embodiments can be replaced by each other.

Claims (12)

A method for clustering time series data, comprising: Pre-clustering the sample points in the time series data, wherein the pre-clustering includes: Traversing all sample points among the sample points, clustering the sample points into corresponding clusters based on the distance between a current sample point and a previous sample point of the current sample point; and Calculating the mean of all sample points in each of all generated clusters, and determining whether to merge the current cluster with the adjacent clusters based on the mean difference between the current cluster and the adjacent clusters; and All the pre-clustered clusters are clustered based on the mean. The method according to claim 1, wherein the timing data includes nanopore sequence data and is stored in a memory in a floating point format, wherein the nanopore sequence data includes a sequencing signal and an opening current signal. The method according to claim 2 further includes: converting the time series data stored in the memory into an array. The method according to claim 1, wherein the distance is obtained by calculating the value of the L1 norm of the current sample point and the previous sample point of the current sample point. The method according to claim 4, wherein clustering the sample points into corresponding clusters based on the distance between the current sample point and a previous sample point of the current sample point comprises: When the L1 norm of the current sample point and the previous sample point of the current sample point is less than the initial minimum distance ε, the current sample point and the previous sample point are marked as the same cluster; When the L1 norm of the current sample point and the previous sample point of the current sample point is greater than or equal to the ε, if the total number of sample points in the current cluster is less than the minimum number of sample points MinPts, the current sample point and the previous sample point are marked as the same cluster, otherwise the current sample point is set to a new cluster. The method according to claim 5, wherein determining whether to merge the current cluster with the clusters adjacent to it based on the mean difference between the current cluster and the clusters adjacent to it comprises: If the mean difference between the current cluster and its adjacent clusters is less than the threshold eps_c, the current cluster and its adjacent clusters are merged; Otherwise the current cluster is kept unchanged. The method according to claim 6 further comprises: using nearest neighbor search to determine the initial minimum distance ε, the minimum number of sample points MinPts and the threshold eps_c. The method according to claim 7, wherein the initial minimum distance ε, the minimum number of sample points MinPts and the threshold eps_c are adjustable parameters. The method according to claim 8, further comprising: implementing the nearest neighbor search by establishing a KD tree or a ball tree. The method according to claim 1, wherein clustering all the pre-clustered clusters using the DBSCAN algorithm is based on the mean and is also based on the standard deviation. A device for clustering time series data, comprising: one or more processors; and One or more memories storing computer executable instructions which, when executed by the one or more processors, cause the one or more processors to perform the method according to any one of claims 1 to 10. A computer storage medium having computer executable instructions stored thereon, wherein when the computer executable instructions are executed by a processor, the processor is caused to perform the method according to any one of claims 1 to 10.

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