TWI474139B - Data clustering method and computer product thereof - Google Patents

Description

Data grouping method and its computer program software

The invention relates to a data grouping method and a computer program software thereof, in particular to a data clustering method based on a fuzzy clustering method and a computer program software thereof.

With the rapid development of the economy and the rapid advancement of information technology, people can easily obtain a large amount of information or materials through various channels. To process this data, various data clustering algorithms were developed to help people conduct data mining and data classification.

Clustering is a multivariate data analysis in mathematical statistics. Data grouping can classify the original data into groups and find the center points (representative points) of each data group to reduce the complexity of data analysis. The operation principle of data grouping calculus is based on the characteristic distribution of the data (ellipse or circle), and the data with higher similarity is divided into a cluster, and then the whole data is divided into a plurality of data groups. .

The data grouping algorithm can be divided into two types: Hierarchical clustering and Partitioning clustering. The hierarchical grouping method splits or aggregates the data layers, and then represents the entire data in a tree structure. The split-type grouping rule is to first specify the number of groups and then use the iterative operation to perform data grouping.

Common segmentation grouping methods include Fuzzy C-means clustering algorithm and GK group calculus (Gustafson). -Kessel clustering algorithm), GG grouping algorithm (Gath and Geva clustering algorithm), and the like.

The distance calculation of the fuzzy average grouping algorithm is calculated by the number of Euclidean distanc to identify the data structure as a spherical group. The GK grouping algorithm and the GG grouping algorithm are used to classify the non-spherical structure data. However, the GK grouping algorithm is combined with the fuzzy covariate matrix, and its objective function is limited by the Mahalanobis distance calculated by this fuzzy covariate matrix. The GG grouping algorithm is suitable for the data distribution to multivariate normal Gaussian. distributed.

Since the current data grouping algorithms are mostly limited by the distribution of the data itself, in the case where the distribution state of the data itself is unknown, it is easy to produce a phenomenon in which the grouping effect is poor and the grouping operation time is too long.

Therefore, a new data grouping method is needed to improve the correctness of data grouping and reduce the time required for grouping operations.

One aspect of the present invention is to provide a data grouping method and a computer program software thereof to improve the correctness and time efficiency of data grouping.

According to an embodiment of the present invention, in the data grouping method, a plurality of pieces of data, a preset common variability threshold, and a preset convergence value are first provided. Next, the original maturity matrix (membership matix) of the data is calculated. Then, the original center matrix of the data is calculated from the original attribution matrix. Next, the original covariance matrix of the data is calculated from the original central matrix. Then, the original covariation The number matrix performs a common variance determination step, wherein the covariance determination step comprises: determining whether an absolute value of the original covariance matrix is greater than a preset covariance threshold to provide a first determination result; and determining an original covariance matrix Whether the absolute value is less than the reciprocal of the preset common variability threshold provides a second determination result. When the first judgment result and the second judgment result are no, the first data update step is performed to update the original attribution matrix and the original center matrix.

According to another embodiment of the present invention, in the data grouping method, a plurality of pieces of data, a preset common variability threshold, and a preset convergence value are first provided. Next, the original attribution matrix of the data is calculated, wherein the original attribution matrix contains the above information. Then, the original center matrix of the above data is calculated according to the original attribution matrix. Next, the original covariance matrix of the above data is calculated from the original central matrix. Then, a first data update step is performed to update the original attribution matrix and the original center matrix. In the first data updating step, a pivoting operation is first performed to update the determinant value of the original covariance matrix to obtain an updated covariance matrix. Then, it is determined whether the absolute value of the updated common variance matrix is greater than a preset common variance threshold to provide a first determination result. Next, it is determined whether the absolute value of the updated covariance matrix is less than a reciprocal of the preset covariance threshold to provide a second determination result. When the first judgment result and the second judgment result are no, the original attribution matrix and the original center matrix are updated by using the updated covariance matrix. Next, it is determined whether the difference between the updated central matrix and the original central matrix is less than a preset convergence value to provide a third determination result. When the third determination result is YES, the above-mentioned data is grouped according to the updated attribution degree matrix.

It can be seen from the above description that the data grouping method of the embodiment of the present invention is advantageous. The co-variation threshold and the adjustable covariance matrix are used to converge the grouping iterations, thus improving the correctness and time efficiency of data grouping.

Suppose that the data set to be grouped X={x ₁ , x ₂ ,..., x _n } has p characteristic attributes, where x _k is any sample of the data set X, x _k =[x _k1 ,x _k2 ,...,x _kp ] R ^p , k = 1, 2, ... n. The data set X can be expressed in the form of a matrix as follows: If the goal of grouping is to divide the data set X into c groups G _i , i=1, 2...c. The attribution information of each of the (membership) u _ik can be expressed by the following formula: In addition, u _ik needs to meet the following three conditions:

Equations (3) and (4) represent that any data sample x _k in the data set X belongs to only one group, and equation (5) represents that a group contains at least one data sample, and at most n-1 data. sample.

For the GK algorithm, its objective function is defined as follows:

Where X is a data set, which is a matrix of n×p; U is a matrix of c×n, U=[u _ik ], 1≦i≦c, 1≦k≦n; V is a vector, V=[ v ₁ ,v ₂ ,...,v _c ],v _i R ^p ,1≦i≦c; v _i is the center of the group G _i , i=1,2,...,c;u _ik is the attribution of the data sample x _k belonging to the cluster G _i , u _ik [0, 1], i = 1, 2, ..., c, k = 1, 2, ..., n. m is the weighted index, m [1, ∞].

d ² ( x _k , v _i ) represents the square of the distance from the data sample x _k to the cluster center v _i , which can be expressed by:

Where Ai is a matrix, which can be expressed by the following formula

Where ρ _i is a constant and F _i is a covariance matrix of the i-th group, which can be expressed by the following formula:

In the operation flow of the GK algorithm, first, the ambiguity parameter m, the number of groups to be divided c, the stop condition ε (ie, the preset convergence value), and the initial setting U ^{(0) are provided} , where U ⁽⁰⁾ represents the first The degree of attribution matrix of 0 iterations.

Next, the group center matrix v _{i is} calculated. The calculation of the group center matrix v _i is done using the following formula:

Where l is the number of iterations.

Then, the distance d ² ( x _k , v _i ) is calculated using the above formula (7). Next, the attribution degree matrix U ⁽ l ⁾ is updated to U ⁽ l ⁺¹⁾ .

Here, if , the attribution degree u _ik can be expressed as follows

If , then u _ik ^{( l )} is 0.

Next, it is judged whether | U ^{( l )} - U ^{( l +1)} | is smaller than the preset convergence value ε. If the judgment result is yes, the data is classified according to the attribution degree matrix; if the judgment result is no, then ( l )=( l +1) is set, and the calculation step of the group center is returned to start the algorithm.

The GK algorithm is suitable for detecting elliptical distribution data. However, for non-measured elliptical distribution data, the GK algorithm cannot be effectively classified. Therefore, embodiments of the present invention provide a data grouping method to solve this problem and improve the effect of data grouping. In the following description, a data grouping method according to an embodiment of the present invention will be described in detail.

Please refer to FIG. 1 , which is a schematic flowchart diagram of a data grouping method 100 according to an embodiment of the present invention. In the data grouping method 100, a data providing step 110 is first performed to provide data to be grouped. As described above, the data to be grouped can be represented by a matrix X. Next, an initial setting providing step 120 is performed to provide preset values such as a preset number of clusters, an initial condition U ⁽⁰⁾ , a convergence value, and the like. In addition, although the initial condition U ⁽⁰⁾ of the present embodiment is determined by the user, in other embodiments of the present invention, the initial condition U ⁽⁰⁾ may also be calculated based on the data X to be grouped. In addition, the initial setting providing step 120 also provides a user-preset total variability threshold D. In this embodiment, the value of the covariation threshold D is 290, and the equation is calculated as follows: Where x _j =( x _{j 1} , x _{j 2} ,..., x _{j 3} ) represents the jth sample vector, and a _i =( a _{i 1} , a _{i 2} ,..., a _ip ) represents the first i group center vector.

It should be noted that the common variability threshold D of the embodiment of the present invention is not limited to 290. In other embodiments of the invention, the covariation threshold D may vary depending on the desired grouping of data. The common variability threshold D is used to improve the efficiency of the clustering algorithm. How to apply this common variability threshold D will be described later.

Then, a calculation step 130 is performed to calculate a attribution matrix, a center matrix, and a covariance matrix. In this embodiment, the calculation of the attribution matrix and the central matrix may be calculated according to the calculation formula of the foregoing GK algorithm, but the embodiment of the present invention is not limited thereto. The calculation step 130 is different from the GK algorithm in calculating the covariance matrix. The GK algorithm calculates a covariance matrix for each group. The calculation step 130 of the embodiment calculates a covariance matrix 针对 for all groups, and the covariance matrix is calculated as follows:

Where Σ ⁽⁰⁾ represents a matrix of common variograms with an iteration number of 0; λ si represents an eigen-value; Γ si represents a eigen-value.

Next, a common variance determination step 140 is performed. The common variance determination step 140 determines whether the absolute value of the common variance matrix is greater than the common variance threshold D, and whether the absolute value of the common variance matrix is less than 1/D, and provides two determination results accordingly. If one of the two determination results is yes, the common variance adjustment step 150 is performed; if both determinations are negative, the update step 160 is performed. In the following description, the update step 160 will be described first.

The updating step 160 uses the covariance matrix to update the attribution matrix and the central matrix. The update calculation of the attribution degree matrix and the central matrix in this embodiment is calculated according to the calculation formula of the GK algorithm described above, and the calculation manner of the update step 160 is not described here. However, it is worth noting that this Embodiments of the invention are not limited thereto. When the attribution matrix is updated, the central matrix can also be updated according to the updated attribution matrix.

After the updating step 160, a determining step 170 is next performed to determine whether the absolute value of the difference between the updated central matrix and the original central matrix is less than a preset convergence value. If the result of the determination is yes, it indicates that the updated attribution matrix satisfies the classification requirement of the user, so the grouping step 190 is performed to classify the data according to the updated attribution matrix. If the result of the determination is no, indicating the updated attribution matrix and satisfying the classification requirement of the user, an iterative operation is required to calculate a new attribution matrix.

In the present embodiment, when the determination result of the determination step 170 is NO, the covariance matrix update step 180 is performed to update the covariance matrix. In this embodiment, the covariance matrix update step 180 performs a pivoting operation on the covariance matrix, such that the determinant value of the covariance matrix is changed, and the updated covariance matrix is obtained.

After the common variance matrix update step 180, the method then returns to the aforementioned common variance determination step 140 to determine whether the absolute value of the updated covariance matrix is greater than the common variance threshold D, and to determine the updated covariance matrix. Whether the absolute value is less than 1/D, and provides two judgment results accordingly. If one of the two determination results is yes, the common variance adjustment step 150 is performed; if both determinations are negative, the update step 160 is performed.

By continuously updating the covariance matrix by successive iterative operations, multiple updated attribution matrices and central matrices can be obtained. The absolute difference (|v _i ⁽ⁿ⁾ -v _i ⁽ⁿ ) between the central matrix (v _i ⁽ⁿ⁾ ) and the n-1th updated central matrix (v _i ^(n-1) ) after the nth update ^-1) |) is less than the preset convergence value, the iterative operation is stopped, and the data classification is performed according to the nth updated attribution degree matrix.

Next, in the following description, the covariation adjustment step 150 will be described.

As described above, when one of the two determination results of the co-variation number determination step 140 is YES, the data grouping method 100 of the present embodiment performs the co-variation number adjustment step 150. The covariance adjustment step 150 sets the original covariance matrix (or the n-1th updated covariance matrix) as an identity matrix. Then, an updating step 160 is performed to update the original attribution matrix and the original central matrix by using the identity matrix to obtain the updated attribution matrix and the central matrix (or the n-th updated attribution matrix and the central matrix). ). The calculated equations are expressed as follows:

As can be seen from the above description, the data grouping method 100 according to the embodiment of the present invention uses the common variability threshold to determine whether the attribution matrix is updated by the Euclidean distance or the Mahalanobis distance. The original attribution matrix (or the n-1th updated attribution matrix), the original central matrix (or the n-1th) are continuously updated by the iteration operation by adjusting the value -ln|Σ _i ^-1 | The updated central matrix) and the original covariance matrix (or the n-1th updated covariance matrix) to obtain the updated attribution matrix (or the nth time) corresponding to the Euclidean distance or the Mahalanobis distance The updated attribution matrix), the updated central matrix (or the central matrix after the nth update), and the updated covariance matrix (or the covariance matrix after the nth update).

Therefore, the data grouping method 100 of the embodiment of the present invention is not limited to the distribution pattern of the data to be grouped. In addition, the data grouping method 100 of the embodiment of the present invention performs a pivoting operation on the covariance matrix in the covariance matrix updating step 180, which can also improve the classification efficiency of the data grouping method 100.

Please refer to FIG. 2, which is a schematic flowchart diagram of a data grouping method 200 according to an embodiment of the present invention. The data grouping method 200 is similar to the data grouping method 100, but differs in that the data grouping method 200 further includes a step step 210. The counting step 210 determines whether the number of times performed by the co-variation number determining step 140 is greater than a preset number of updates. If the number of times performed by the common variance determination step 140 is greater than the preset number of updates, the common variance adjustment step 150 is performed to force the common variance matrix to be an identity matrix, and then an update step 160 is performed to utilize the identity matrix. Update the attribution matrix and the central matrix. The preset update number may be provided by the initial setting providing step 120 or by the counting step 210. In this embodiment, the preset update number is 100, but the embodiment of the present invention is not limited thereto.

For the data grouping method 100, the total mutated matrix has not been able to make the judgment result of the common variability determination step 140 YES, and the central matrix after multiple updates cannot satisfy the user's preset convergence value. At this time, the data grouping method 100 may fall into the infinite loop of the iteration, and the appropriate attribution matrix cannot be calculated. Therefore, the data grouping method 200 of the present embodiment uses the counting step 210 to forcibly jump out of the infinite loop of the iteration, so as to improve the chance that the data grouping method 200 finds the appropriate attribution matrix, thereby improving the efficiency of data grouping.

In the following description, the effect of the data grouping method of the embodiment of the present invention will be described by way of an embodiment.

Please refer to FIG. 3, which illustrates the format of the data to be grouped according to an embodiment of the present invention. In this embodiment, the format of the data to be grouped is a Comma Separated Values (CSV) format, which separates all values by a comma (","). The data used in Figure 3 is the iris data set, which contains four characteristics, namely the length of the flower bud, the width of the flower bud, the length of the petals, and the width of the petals.

After obtaining the data to be grouped, the data grouping tool program is used to perform the data grouping method of the embodiment of the present invention. When performing the data grouping method of the embodiment of the present invention, it is necessary to set parameters such as the number of clusters and the number of fuzzy numbers. In the present embodiment, the number of clusters is set to 3, and the number of fuzzy numbers is set to 2.

After the setting is completed, the data grouping method of the embodiment of the present invention is used to group the data shown in FIG. 3 to obtain the clustering result as shown in FIG. Since the settings are divided into three groups, there are three center coordinates, each center containing four dimensions (variables). The first group center is [5.0036, 3.430, 1.4850, 0.2515]; the second group center is [6.7751, 3.0524, 5.6469, 2.0536]; the third group center is [5.8892, 2.7612, 4.3642, 1.3974].

It has been proved by experiments that the correct rate of the data grouping method of the embodiment of the present invention is as high as 89.33%. The data grouping method of the embodiment of the present invention really helps to mention High efficiency of data grouping.

In addition, the above embodiments may be implemented by a computer program product, which may include a machine readable medium storing a plurality of instructions, which can program a computer to perform the steps in the above embodiments. The machine readable medium can be, but is not limited to, a floppy disk, a compact disc, a CD-ROM, a magneto-optical disc, a read-only memory, a random access memory, an erasable programmable read only memory (EPROM), an electronically erasable device. Except for programmable read only memory (EEPROM), optical card or magnetic card, flash memory, or any machine readable medium suitable for storing electronic instructions. Furthermore, embodiments of the present invention can also be downloaded as a computer program product that can be transferred from a remote computer to a requesting computer by using a data signal of a communication connection (such as a connection such as a network connection).

While the invention has been described above in terms of several embodiments, it is not intended to limit the scope of the invention, and the invention may be practiced in various embodiments without departing from the spirit and scope of the invention. The scope of protection of the present invention is defined by the scope of the appended claims.

100‧‧‧ data grouping method

110‧‧‧Information provision steps

120‧‧‧Initial setting steps

130‧‧‧ Calculation steps

140‧‧‧Common variation judgment step

150‧‧‧Common variation adjustment steps

160‧‧‧Update steps

170‧‧‧ Judgment steps

180‧‧‧Common variation matrix update step

190‧‧‧ grouping steps

200‧‧‧ data grouping method

210‧‧‧ steps

The above and other objects, features, and advantages of the present invention will become more apparent and understood.

FIG. 1 is a schematic flow chart showing a data grouping method according to an embodiment of the present invention.

2 is a diagram showing a data grouping method according to another embodiment of the present invention. Schematic diagram of the process.

Figure 3 is a diagram showing the format of a data to be grouped according to an embodiment of the present invention.

Fig. 4 is a diagram showing the grouping result of the data grouping method according to an embodiment of the present invention.

100‧‧‧ data grouping method

110‧‧‧Information provision steps

120‧‧‧Initial setting steps

130‧‧‧ Calculation steps

140‧‧‧Common variation judgment step

150‧‧‧Common variation adjustment steps

160‧‧‧Update steps

170‧‧‧ Judgment steps

180‧‧‧Common variation matrix update step

190‧‧‧ grouping steps

Claims (10)

A data grouping method includes: providing a plurality of data, a preset common variance threshold, and a preset convergence value; calculating a membership matix of the data; calculating according to the original attribution matrix One of the data is a center matrix; the original covariance matrix is calculated according to the original central matrix; and the common covariance matrix is subjected to a common variance determination step, wherein The covariance determination step includes: determining whether an absolute value of the original covariance matrix is greater than the preset covariance threshold to provide a first determination result; and determining whether an absolute value of the original covariance matrix is less than And a reciprocal of the preset common variance threshold to provide a second determination result; when the first determination result and the second determination result are negative, performing a first data update step to update the original attribution matrix And the original central matrix, wherein the first data updating step comprises: updating the original attribution matrix by using the original covariance matrix And obtaining a first updated attribution matrix; and calculating a first updated central matrix according to the first updated attribution matrix; determining whether the difference between the first updated central matrix and the original central matrix is Less than the preset convergence value to provide a third determination result; and when the third determination result is yes, according to the first updated attribution degree The matrix is used to group the data. For example, the data grouping method described in claim 1 wherein the total variation threshold is 290. For example, the data grouping method described in claim 1 further includes: when the third determination result is no, performing a pivoting operation to update the determinant value of the original covariance matrix to obtain An updated common variance number matrix; the common variance number determining step is performed on the updated common variance number matrix to determine whether the absolute value of the updated common variance number matrix is greater than the preset common variance number threshold to provide a first Determining a result, and determining whether the absolute value of the updated covariance matrix is less than a reciprocal of the preset covariance threshold to provide a fifth determination result; and when the fourth determination result or the fifth determination result is If yes, a second data update step is performed to update the first updated attribution matrix and the first updated central matrix by using the updated covariance matrix. The data grouping method of claim 3, further comprising: when the first judgment result or the second judgment result is YES, performing a third data update step to update the original attribution matrix and the An original center matrix, wherein the third data updating step comprises: setting the original covariance matrix to an identity matrix; and updating the original attribution matrix and the original by using the identity matrix Determining a central matrix to obtain a second updated attribution matrix and a second updated central matrix; determining whether a difference between the second updated central matrix and the original central matrix is less than the preset convergence value to provide a a sixth determination result; and when the sixth determination result is YES, grouping the data according to the second updated attribution degree matrix. The method for grouping data according to item 3 of the patent application scope further includes: providing a preset update number; determining whether the number of times the common variance determination step is performed is greater than the preset update number; and determining the total variation number The third data update step is performed when the number of times the step is performed is greater than the preset number of updates. A data grouping method includes: providing a plurality of data, a preset common variance threshold, and a preset convergence value; calculating a primary attribution matrix of the data; and calculating the data according to the original attribution matrix An original central matrix; calculating an original covariance matrix of the data according to the original central matrix; performing a first data updating step to update the original attribution matrix and the original central matrix, wherein the first data update The step includes: performing a pivoting operation to update the original covariation Determining the determinant value of the matrix, and obtaining an updated covariance matrix; determining whether the absolute value of the updated covariance matrix is greater than the preset covariance threshold to provide a first determination result; determining the update Whether the absolute value of the post-covariance matrix is less than the reciprocal of the preset co-variation threshold to provide a second determination result; and when the first determination result and the second determination result are negative, using the update a common variance matrix to update the original attribution matrix and the original central matrix; determining whether a difference between the updated central matrix and the original central matrix is less than the preset convergence value to provide a third determination result; When the third determination result is YES, the pieces of data are grouped according to the updated attribution degree matrix. For example, the data grouping method described in claim 6 wherein the total variation threshold is 290. The method for grouping data according to claim 6 further includes: when the first judgment result or the second judgment result is YES, performing a second data update step to update the original attribution matrix and the The original center matrix, wherein the second data updating step comprises: setting the original covariance matrix to an identity matrix; and updating the original attribution matrix and the central matrix by using the identity matrix. For example, the data grouping method described in claim 6 further includes: determining whether an absolute value of the original covariance matrix is greater than the preset covariance threshold to provide a fourth determination result; determining the original total Whether the absolute value of the variance matrix is less than the reciprocal of the preset co-variation threshold to provide a fifth determination result; and when the fourth determination result and the fifth determination result are negative, performing the first data update step. A computer program software that, after being loaded by a computer, can perform the data grouping method as described in claim 6 of the patent application.