TWI407365B - Method for data clustering - Google Patents

Abstract

A method for data clustering comprises: Summing up value of each dimension of each data point to obtain several reference numbers; sorting the reference numbers; obtaining a scanning range defined as several times of a expending radius with taking a reference number of a central point as center; calculating the distance between the central point and the data point corresponding to the reference number in the scanning range and regarding data points with distance smaller than the expending radius as neighbors. Consequently, this invention can lower the time cost of searching the neighbors and improve the efficiency of clustering.

Description

Data grouping method

The present invention relates to a data grouping method, and more particularly to a density grouping algorithm.

The conventional density data grouping method mainly uses data point density as the basis for grouping. For example, given a parameter R (expansion radius) and MinPts (minimum inclusion point), if the data point density of a certain area satisfies the set condition, the expansion search is performed in the area, and the other similar density is gradually merged to satisfy the set condition. The region, and finally the final clustering results, representative algorithms include DBSCAN or IDBSCAN. Although the conventional grouping method can effectively detect irregular patterns and filter out noise points, the time required for grouping is relatively increased.

The following is a description of several representative custom density data grouping techniques:

1. DBSCAN data grouping method: Step 1 selects one of the data points in advance as one of the initial seed points by a plurality of data points in the data set; and the second step determines whether the current initial seed point radius R is within the minimum inclusion. Point data points, if the threshold value is reached, the data points in the current range are classified into the same cluster and used as seed points, and are expanded one by one from other seed points in the range; Step 3 continues the foregoing step two until All data points in the data set are classified. The conventional DBSCAN data grouping method is grouped in a more logical density judgment manner, so it can be used to filter out noise and data points suitable for irregular patterns, etc., but because of the complicated density of each data point. Judging, it is more cumbersome to group. Moreover, when searching for neighboring points, the distance between all the data points and the core points needs to be calculated, so that it takes a lot of time, resulting in an increase in the operation time cost.

2. IDBSCAN data grouping method: This method is a density data grouping technique proposed by B. Borah and other scholars in 2004. It mainly focuses on the above-mentioned conventional DBSCAN data grouping method, which is based on the sequential judgment of data points for time-consuming behavior. Improvements were made to adopt a strategy of increasing the speed of grouping by reducing the number of queries. The conventional IDBSCAN data grouping method is to equidistantly set 8 mark boundary points on the scan range boundary of the extended seed point radius R, and the data points in the scan range of the expanded seed point radius R are only selected closest to the 8 mark boundaries. The data point of the point is used as the seed point. By reducing the number of seed points, the repeated expansion action can be reduced to overcome the shortcomings of the excessive number of seed points in the DBSCAN data grouping method, but the reduced grouping time is still quite limited. .

In general, the IDBSCAN data grouping method can reduce the number of seed points in an expanded seed point scanning range to no more than 8. However, since the data points close to the expanded seed point cover a large area, if The inclusion of these data points as seed points will increase the time cost of the search. Moreover, even if the number of seed points in the scanning range of the expanded seed is not more than 8, the adjacent seed points have a higher overlapping ratio of scanning ranges, and the proportion of repeated expansion is also relatively high, thereby increasing the time cost. For the above reasons, it is necessary to further improve the above-described conventional data grouping method.

It is an object of the present invention to improve the above disadvantages to provide a data grouping method that reduces the time cost of a density algorithm to search for neighbors.

The second object of the present invention is to provide a data grouping method, which can reduce the number of data points that need to perform distance calculation when searching for neighboring points.

In order to achieve the foregoing object, the technical means and the functions that can be achieved by the technical method include: a data grouping method, comprising: a parameter setting step of setting an expansion radius parameter and a minimum inclusion point parameter; a sorting step is to sum the sum values of the respective dimensions of each data point in an initial array as a reference data, and sort the reference data by size and store in a sorting array; A data point is used as a core point. In the sorting array, the reference data of the core point is taken as a center point, and the number of times of the expansion radius parameter is used as a scanning range, and the multiple is not smaller than And calculating a distance between the data point corresponding to the reference data located in the scan range and the core point, and defining a data point whose distance is smaller than the expansion radius parameter R as a neighboring point; a determining step is determining the number of the neighboring points Whether the parameter is greater than the minimum inclusion point parameter; a group judgment step determines whether the neighbor point is grouped, and if the determination is yes, the search step is performed, and if the determination is no, the neighbor point is added to an expansion array, and After the neighboring point and the core point are divided into the same group, an expansion step is performed; the expanding step is performed by taking the neighboring point as the core point in the expanding array, and the searching step is performed until the neighboring points in the expanding array complete the searching After the step, a termination determining step is performed; and the termination determining step determines whether to terminate according to a termination condition.

The above and other objects, features and advantages of the present invention will become more <RTIgt; The data grouping method of the preferred embodiment of the present invention is to connect at least one database as an execution architecture by using a computer system, wherein the database has an initial array, and the initial array contains a plurality of data points 11 and The data grouping method of the invention performs a parameter setting step S1 for setting an expansion radius (Eps) parameter R and a minimum inclusion point (Minpts) parameter in the computer system.

Referring to FIG. 1 to FIG. 3, the data grouping method according to the preferred embodiment of the present invention performs a sorting step S2, and sums the coordinate values of the respective data points of the data points 11 in the initial array as a reference data. 111, and the reference data 111 corresponding to each of the data points 11 are sorted by size and stored in a sorting array 2. For convenience of description, the present embodiment is described by taking a two-dimensional plane coordinate as an example. The plurality of data points 11 are all scattered in a two-dimensional plane space. Therefore, each data point 11 corresponds to a two-dimensional plane coordinate (a, b), the sorting step S2 is to add the total sum a+b of the coordinate values a and b of the two dimensions (x dimension and y dimension) as the reference data 111, so that each data point 11 corresponds to a reference data 111 respectively. And the coordinate values a and b are not less than 0, that is, each data point is located in the first quadrant of the two-dimensional plane space. For example, please refer to Table 1, which takes the coordinates of data points A, B, C, and D as an example. You only need to add the coordinate values of each dimension of each data point to obtain each data point. Corresponding reference data.

Table 1, coordinates of data points A, B, C, D and reference data

Then, the reference data 111 are sorted by size, and the embodiment is sorted from small to large and stored in a sorting array 2. Taking the data points A, B, C, and D as an example, the sorting in the sorting array 2 is sequentially data points B, A, C, and D. Thus, as shown in FIG. 3, the reference data 111 of the data points 11 are stored in the sorting array 2 in order of size.

For the convenience of the following description, the relationship between the maximum value of the reference data of the data point and the expansion radius parameter R is first introduced. Referring to Fig. 4 and Table 2, when the value of the expansion radius parameter R is 1, the core point O(0, 0) is taken as the center, and the radius of the radius parameter R is used as the radius. A point M(c,d), and its projection point N(c,0) on the X-axis, points O, M, and N together form a right-angled triangle, and two of the right-angled triangles OMN and The relationship with ∠ MON is shown in Table 1.

It can be seen from the results in Table 2 that when ∠ MON is 45. Time, Has a maximum of , that is, relative to the core point O(0, 0), the maximum value of the reference data corresponding to the data point M in the sorting array is the expansion radius parameter R If the coordinate of the core point is (11, 5) and the reference data is 16, the maximum value of the reference data corresponding to the data point M is .

Referring to Figures 1 and 5 to 8, the data grouping method according to the preferred embodiment of the present invention performs a search step S3, in which a data point 11 is used as the core point 12, and in the sorting array 2, The reference data 121 corresponding to the core point 12 is a center point, and the number of times of the expansion radius parameter R is used as a scanning range, and the multiple of the multiple is not less than And calculating the distance between the data point 11' corresponding to the reference data 111' located in the scanning range and the core point 12, and defining the data point whose distance is smaller than the expansion radius parameter R as the neighboring point 11".

For example, referring to FIGS. 5 and 6, the present embodiment is described by the core point 12 of the two-dimensional plane coordinate (3, 5), and the reference data 121 of the core point 12 is 8. Next, referring to FIGS. 7 and 8, in the sorting array 2, the reference data 121 corresponding to the core point 12 is taken as a center point, and the number of times of the expansion radius parameter R is used as the scanning range. For example, the expansion radius parameter R of the embodiment is selected to be 2, and the multiple is selected as As described above, if the reference point 121 of the core point 12 is taken as the center point, the left and right sides are respectively taken. The scanning range of R, the reference data 111 in the scanning range, and the corresponding data point 11 must contain all the neighboring points 11" located within the expansion range of the core point 12. Therefore, the scanning range is continued by the above example. for As shown in FIG. 8, in the sorting array 2, the reference data 121 of the core point 12 is taken as a center point, and the left and right sides are respectively taken. For the scanning range, the data point 11' corresponding to the reference data 111' located in the scanning range must contain all the neighboring points 11" in the circle 3. The multiplier is preferably not less than Because the multiple is less than For example, if the multiple is 1.3, the scanning range cannot cover all adjacent points 11", and may cause partial neighboring points 11" to be missed.

In addition, since the data points corresponding to the adjacent reference data in the sorting array 2 are not necessarily adjacent in the two-dimensional plane, for example, refer to FIG. 9 and point E (13, 3) The reference data 111 of the point F (15, 3) and the point G (3, 14) are 16, 18, and 17, respectively, which are judged to be adjacent in the sorting array 2, and in the two-dimensional plane, the point G (3, 14) The distance from E (13, 3) and point F (15, 3) is quite different. Therefore, in this embodiment, as shown in FIG. 10, the distances between the data points 11' and the core points 12 are respectively calculated. In this embodiment, the distance calculation is performed by using the Euclidean formula, and if the distance is smaller than the expansion radius R The data point 11", that is, the data point 11" located in the expansion range (circle 3) of the core point 12, defines the data point 11" as the neighboring point 11". Thus, only the data points 11' that are not adjacent points 11" can be screened out by the distance operation to obtain the adjacent points 11". Therefore, when searching for the neighboring point, only the data point 11' corresponding to the reference data 111' in the scanning range needs to be distance-operated, without having to perform distance calculation on all the data points as in the conventional density data grouping method. Therefore, the time cost of searching for neighbors can be greatly reduced, thereby improving the efficiency of grouping.

Referring to Figures 1 and 10, the data grouping method of the preferred embodiment of the present invention then performs a determining step S4 to determine whether the number of neighboring points 11" is greater than the minimum containing point parameter. If the determination is "Yes" Then, a group judgment step S5 is performed, and if the determination is "NO", the search step S3 is performed. More specifically, if the number of the neighboring points 11" is greater than the minimum inclusion point parameter, the grouping determining step S5 is performed; if the determination is "No", another data point 11 is taken out of the initial array to perform the searching step. S3.

Referring to FIGS. 1 and 10, the grouping determining step S5 of the data grouping method according to the preferred embodiment of the present invention determines whether the neighboring point 11" is grouped. If the determination is YES, the searching step is performed; If the determination is "No", the neighboring point 11" is added to an expanded array, and the clustering number of the neighboring point 11" is updated. More specifically, if the neighboring point 11 ′′ has been grouped, the searching step S3 is performed again; if the neighboring point 11 ′′ has not been grouped, the grouping number of the neighboring point 11 ′′ is updated, that is, the neighboring point 11 is also "The core point 12 is divided into the same group, and then the adjacent point 11" is added to the expanded array, and an expansion step S6 is performed.

Referring to FIGS. 1 and 10, the expanding step S6 of the data grouping method according to the preferred embodiment of the present invention performs the searching step S3 by taking the neighboring point 11" from the expanded array as the core point 12 until the expanding array. After the neighboring point 11" completes the searching step S3, a termination determining step S7 is performed. More specifically, the searching step S3 is performed by using each adjacent point 11" in the expanded array as the core point 12, until the neighboring point 11" in the expanded array completes the searching step S3, and the termination determining step is performed. S7.

Referring to FIGS. 1 and 10, the termination determining step S7 of the data grouping method according to the preferred embodiment of the present invention determines that the termination condition is terminated. More specifically, the termination condition is that all the data points 11 in the initial array have completed the searching step S3. If it is determined that the termination condition is not reached, that is, if the data point 11 is not performing the searching step S3, then the The other data point 11 is taken in the initial array to perform the searching step S3 until all the data points 11 have undergone the searching step S3, and then terminate. So far, the data grouping method of the present invention has been completed.

Referring to Table 3, in order to verify that the data grouping method of the present invention has the advantage of high grouping efficiency, the data sets A to F are grouped and compared with the conventional DBSCAN and IDBSCAN data grouping methods. Among them, data sets A to F have 115,000 data points, and contain 15000 noise points, and the graphic size is 900×650 pixels.

As can be seen from the results, the data grouping method of the present invention can significantly reduce the time cost and improve the grouping efficiency.

The data grouping method of the invention can reduce the time cost of searching for neighboring points by the density algorithm, so as to improve the efficiency of data grouping.

The data grouping method of the invention can reduce the number of data points that need to perform distance calculation when searching for neighboring points, can greatly reduce the time cost of searching for neighboring points, and reduce the computational complexity, and the effect is that the number of data points is larger. more obvious.

While the invention has been described in connection with the preferred embodiments described above, it is not intended to limit the scope of the invention. The technical scope of the invention is protected, and therefore the scope of the invention is defined by the scope of the appended claims.

[this invention]

11. . . Data point

11’. . . Data point

11"...adjacent point

111. . . Reference data

111’. . . Reference data

12. . . Core point

121. . . Reference data

2. . . Sorting array

3. . . circle

Figure 1: Flow chart of the data grouping method of the present invention.

Fig. 2 is a schematic diagram showing the distribution of data points of the data grouping method of the present invention.

Figure 3 is a schematic illustration of the sequencing steps of the data grouping method of the present invention.

Figure 4: Schematic diagram of the data grouping method of the present invention.

Figure 5: Schematic diagram of the core points and data points distribution of the data grouping method of the present invention.

Figure 6 is a schematic diagram of a sorting array of the data grouping method of the present invention.

Figure 7: Schematic diagram of the searching step of the data grouping method of the present invention in a plane space.

Fig. 8 is a view showing the reference data of the searching step of the data grouping method of the present invention.

Figure 9 is a schematic diagram of non-adjacent data points of the data grouping method of the present invention.

Fig. 10 is a view showing the distance judgment of the data grouping method of the present invention.

Claims (3)

A data grouping method includes: a parameter setting step of setting an expansion radius parameter and a minimum inclusion point parameter; and a sorting step of summing the coordinate values of each dimension of each data point in an initial array as a sum Referring to the data, and sorting the reference data by size and storing in a sorting array; in a searching step, using one of the data points as a core point, in the sorting array, taking the reference data of the core point as a center point, The multiple of the expansion radius parameter is used as the scanning range, and the multiple is not less than And calculating a distance between the data point corresponding to the reference data located in the scanning range and the core point, and defining a data point whose distance is smaller than the expansion radius parameter as a neighboring point; and determining a number of the neighboring points in a determining step Whether it is greater than the minimum inclusion point parameter; a group judgment step determines whether the neighbor point is grouped, and if the determination is yes, the search step is performed, and if the determination is no, the neighbor point is added to an expansion array, and After the neighboring point is divided into the same group as the core point, an expansion step is performed. The expansion step is performed by taking the neighboring point as the core point in the expanded array, and the searching step is performed until the neighboring points in the expanded array are completed. After the searching step, a termination determining step is performed; and the termination determining step determines whether to terminate according to a termination condition. According to the data grouping method described in the first aspect of the patent application, in the determining step, if the determination is YES, the grouping determining step is performed, and if the determination is "NO", the searching step is performed. According to the data grouping method described in claim 1, wherein the termination condition in the termination determining step is that all the data points in the initial array have completed the searching step, and if it is determined that the termination condition is not reached, the initial step is Another data point is taken in the array to perform the search step, and if the termination condition is reached, the termination is terminated.