CN112132217B - A Categorical Data Clustering Method Based on Intra-cluster Dissimilarity - Google Patents

Abstract

The invention discloses a classification type data clustering method based on inter-cluster dissimilarity among clusters, which provides a new dissimilarity calculating method based on inter-cluster similarity among clusters, and completes automatic selection of a cluster center based on the dissimilarity. The dissimilarity degree of the invention reserves the characteristics of data, achieves the standard of dissimilarity between low clusters and high clusters, improves the clustering precision, purity and recall rate, effectively improves the clustering effect of the classified data, can prevent the loss of important characteristic values in the clustering process, strengthens the similarity between the characteristic values in the clusters, and weakens the similarity between the characteristic values in the clusters; by the automatic cluster center selection method, errors caused by randomly selecting the cluster center or manually selecting the cluster center to cluster are greatly reduced.

Description

A Categorical Data Clustering Method Based on Intra-cluster Dissimilarity

technical field

The invention relates to the technical field of data clustering, in particular to a clustering method for classified data based on intra-cluster and inter-cluster dissimilarity.

Background technique

A clustering algorithm is an algorithm in machine learning that involves grouping data. In a given dataset, we can divide it into some different groups by clustering algorithm. In theory, the data of the same group have the same attributes or characteristics, and the attributes or characteristics of different groups of data will differ greatly. Clustering algorithm is a kind of unsupervised learning algorithm, and as a commonly used data analysis algorithm, it has been applied in many fields.

In the field of data science, we use clustering algorithms to implement cluster analysis, and we can obtain data information more clearly by grouping data. As an important part of data mining, the classification data clustering algorithm can help analysts summarize the disease characteristics of each type of patient from the database of the rehabilitation treatment plan recommendation system, allowing analysts to focus on a specific patient groups for further analysis.

The classic k-means algorithm uses the Euclidean distance when calculating the mean value of the cluster and the dissimilarity between data objects, which is only suitable for numerical data sets with continuous features. For categorical data sets with discrete features, the k-means algorithm No longer applicable. Huang extended the k-means algorithm in 1998, using "modes" instead of "means", and proposed a k-modes algorithm suitable for categorical data clustering. The k-modes algorithm uses a simple Hamming distance to calculate the dissimilarity, which ignores the difference of the same classification feature between data objects, weakens the similarity within the cluster, and does not fully reflect the dissimilarity between two feature values under the same classification feature. , affecting the accuracy of clustering results. In addition, the k-modes algorithm uses a random selection method to determine the initial cluster center and k value, and uses a frequency-based method to recalculate and update the cluster center, which brings great uncertainty to the clustering results.

Contents of the invention

The present invention aims to solve the problem of the accuracy of the k-modes algorithm and the selection of the initial cluster center, and provides a classification data clustering method based on the dissimilarity between clusters within a cluster.

In order to solve the above problems, the present invention is achieved through the following technical solutions:

A clustering method for classified data based on intra-cluster and inter-cluster dissimilarity, comprising the following steps:

Step 1. For a classified data set D with n data objects, use the simple Hamming distance to calculate the dissimilarity d _i,j between every two data objects;

Step 2. For each data object x _i of the sub-type data set D, first sort the dissimilarity d _{i, j} between the data object x _i and other data correspondences in ascending order, and obtain the corresponding data object x _i Dissimilarity vector d′ _i,j =[d′ _i,1 ,d′ _i,2 ,...,d′ _i,n ]; then the two adjacent dissimilarity vectors d′ _i,j The maximum difference of the dissimilarity is taken as the cut-off distance d _c,i of the data object x _i ;

Step 3. Select the minimum value of the cut-off distance dc _,i of all data objects in the classification data set D as the cut-off distance _dc of the classification data set D;

Step 4. Calculate the local neighborhood density _ρ i of each data object x _i in the classification data set D based on the cut-off distance d _c of the classification data set D by using the square wave kernel function method or the Gaussian kernel function method;

Step 5. Calculate the relative distance L _i of each data object x _i in the classification data set D:

Step 6. For each data object _xi in the classification data set D, use the local neighborhood density ρ _i and the relative distance L _i of the data object _xi to obtain the decision graph Z _i of the data object _xi :

Z _i =ρ _i ×L _i

Step 7. First sort the decision graph Z _i of all data objects in the classification data set D in descending order to obtain a sorting sequence; then based on the sorting sequence, use the subscript i of the data object x _i as the abscissa, and the data object x The decision diagram _Z of _i is the vertical coordinate to draw the decision diagram of the classification data set D, and the abscissa at the inflection point in the decision diagram of the classification data set D is the selected number of clusters k;

Step 8, select k data objects from the classification data set D to form the current cluster center set;

Step 9. Based on the current set of cluster centers, calculate the dissimilarity d( _xi ,q _l ) between the remaining nk data objects _xi and k cluster centers q _l in the subtype data set D:

Step 10. According to the dissimilarity d( _xi ,q _l ) between the data object _xi and the cluster center q _l , and based on the principle of proximity, assign nk data objects to the nearest cluster. After the assignment is completed, Obtain k clusters, and mark the cluster labels of these nk data objects, thereby obtaining the clustering result based on the current cluster center set;

Step 11. For the formed k clusters, select the eigenvalue with the highest frequency of occurrence on each dimension feature from each cluster to form a new cluster center of the cluster, and obtain a new set of cluster centers;

Step 12. Repeat steps 9-11 until each cluster center no longer changes or reaches the specified maximum number of iterations, the algorithm terminates, and the clustering result based on the current cluster center set is output; otherwise, the obtained new cluster center Set as the current cluster center set, and skip to step 9 to continue iteration;

Iteration makes the selected cluster center closer to the real cluster center, so the iterative process will make the clustering effect better and better. The end conditions of the clustering algorithm can be specifically selected by the experimenter according to the actual situation: (1) iterate until the maximum number of iterations is reached; (2) iterate until the objective function threshold is terminated.

Among them, i, j=1,2,...,n, n is the number of data objects in the classification data set D; s=1,2,...,m, m is the number of features of the data objects; l=1 ,2,...,k, is the number of clusters; δ(A _i,s ,A _ql,s ) is the dissimilarity between the data object x _i and cluster center q _l under the s-th dimension feature; A _i,s is The s-th dimension feature of the data object x _i ; A _ql,s is the s-th dimension feature of the cluster center q _l ; is the number of data objects whose feature value is _As,t in cluster C _l ; |C _l | is the number of data objects in cluster C _l ; ζ _l is the adjustment coefficient.

In the above step 4, for the large-scale classification data set D whose data object is greater than or equal to 10TB, use the square wave kernel function method to calculate the local neighborhood density ρ _i of the data object x _i ; for the small-scale classification data whose data object is less than 10TB Set D, use the Gaussian kernel function method to calculate the local neighborhood density ρ _i of the data object _xi . Note: Large-scale data generally refers to the amount of data above 10TB (1TB=1024GB).

Compared with prior art, the present invention has following characteristics:

1. The present invention proposes a new dissimilarity calculation method based on the similarity between clusters within a cluster, which can prevent the loss of important eigenvalues in the clustering process, strengthen the similarity between eigenvalues within a cluster, and weaken the similarity between clusters. Similarity between eigenvalues.

2. The automatic selection method of the cluster center proposed by the present invention greatly reduces the error brought to the clustering by randomly selecting the cluster center or manually selecting the cluster center.

3. The dissimilarity coefficient calculation method proposed by the present invention retains the characteristics of the data, achieves the standard of low intra-cluster dissimilarity and high inter-cluster dissimilarity, improves clustering accuracy, purity and recall rate, and effectively improves Clustering effect of categorical data.

Description of drawings

Figure 1 is a schematic diagram of the sensitivity of the k-modes algorithm to the selection of the initial cluster center, (a) the clustering result graph of k=1, (b) the clustering result graph of k=2, (c) the clustering result graph of k=3 Result graph.

Figure 2 is a diagram of the situation when the local neighborhood density of x _i is not the maximum density.

Figure 3 is a diagram of the situation when the local neighborhood density of x _i is the maximum density.

Figure 4 is a diagram of the determination of d _{c, i} values.

Figure 5 is a schematic diagram of a two-dimensional data set.

Figure 6 is a decision diagram.

Fig. 7 is a decision diagram of Z _i .

Figure 8 is a flowchart of IKMCA.

Detailed ways

In order to make the object, technical solution and advantages of the present invention clearer, the present invention will be further described in detail below in conjunction with specific examples.

The symbols used and their meanings are shown in Table 1.

Table 1 Symbol Description

Taking the data object _xi and the cluster center q _l as examples, define the simple Hamming distance of the classic k-modes algorithm, as shown in formula (1), this calculation gives each feature the same weight.

in:

The k-modes algorithm minimizes the objective function by simple Hamming distance. As shown in formula (2):

In terms of the dissimilarity coefficient, the dissimilarity coefficient of the classical k-modes algorithm does not consider the relative frequency of eigenvalues within a cluster, nor does it consider the intra-cluster and inter-cluster structure of each feature. In the process of partitioning new data objects, some clusters allocate less similar data. For the convenience of explanation, the artificial data set _D1 shown in Table 2 is used to demonstrate the dissimilarity coefficient. D ₁ is described by three features A={A ₁ , A ₂ , A ₃ }. Wherein, DOM(A ₁ )={A,B}, DOM(A ₂ )={E,F}, DOM(A ₃ )={H,I}. D ₁ has two clusters C ₁ and C ₂ , corresponding to cluster centers q ₁ (A,E,H) and q ₂ (A,E,H) respectively.

Table 2 Artificial Dataset D ₁

Assuming that x ₇ =(A,E,H) needs to be clustered, using the simple full-name distance, d(x ₇ ,q ₁ )=d(x ₇ ,q ₂ )=0+0+0=0 . But in terms of intra-cluster similarity, x ₇ should be assigned to cluster C ₁ .

In the selection of the initial cluster center, the classical k-modes algorithm is very sensitive to the initial cluster center, and the selection of the initial cluster center adopts random initialization method or manual setting method, both of which lead to unstable clustering results to a certain extent. Choosing initial cluster centers with different positions and k values will produce different clustering results. As shown in Figure 1, the true number of clusters for this dataset is 3. Selecting different initial cluster centers and setting different k values may produce different clustering results. The contents of Figure 1 from left to right are: random selection of initial cluster centers, clustering iteration process, and final clustering results. It can be seen that it is very important to find a suitable initial cluster center.

If the selected dissimilarity coefficient can discover all or part of the potential modes in the data set, then the division-based k-modes algorithm will do more with less, so that the k-modes algorithm can produce efficient clustering results that meet the requirements of the data objects in the cluster. The minimum dissimilarity between clusters; the condition for the largest dissimilarity between data objects between clusters. Therefore, the present invention proposes a new dissimilarity coefficient "intra-cluster dissimilarity coefficient" based on intra-cluster and inter-cluster similarity. The k-modes algorithm (IKMCA) algorithm based on intra-cluster and inter-cluster dissimilarity uses the improved density peak algorithm to determine the initial cluster center, and uses the intra-cluster inter-cluster dissimilarity coefficient to calculate the dissimilarity between each data object and the cluster center degree, and update the cluster centers.

The within-cluster, between-cluster dissimilarity coefficient takes into account the relative frequency with which eigenvalues are distributed within the same cluster. Data objects belonging to the same cluster have higher frequency of occurrence of the same eigenvalue, and higher similarity within the cluster. The definition of intra-cluster dissimilarity is shown in formula (3):

Among them: 1≤i≤n, 1≤s≤m.

Using data set D ₁ , according to formula (3), d(x ₁₀ ,q ₁ )=(1-2/3)+(1-2/3)+(1-1)=2/3, d( x ₁₀ ,q ₂ )=(1-2/3)+(1-2/3)+(1-2/3)=1. It can be seen from the calculation results that x ₇ has the minimum dissimilarity with cluster C ₁ , so x ₇ should be divided into cluster C ₁ . Although formula (3) considers the relative frequency of eigenvalues within a cluster, it does not consider the distribution of eigenvalues between clusters. The flaw of not considering the inter-cluster similarity is discussed using the artificial dataset _D2 shown in Table 3. D ₂ is described by three categorical features A={A ₁ , A ₂ , A ₃ }. Wherein, DOM=(A ₁ )={A,B,C}, DOM(A ₂ )={E,F}, DOM(A ₃ )={H,I,J}. D ₂ has three clusters C ₁ , C ₂ and C ₃ respectively corresponding to cluster centers q ₁ =(A,E,H), q ₂ =(A,E,H) and q ₃ =(B,E,I ).

Table 3 Artificial dataset D ₂

Assume that x ₁₀ =(A, E, H) needs to be divided into clusters. Using the simple Hamming distance, d(x ₁₀ ,q ₁ )=d(x ₁₀ ,q ₂ )=d(x ₁₀ ,q ₃ )=0+0+0=0 can be obtained. Using formula (3), d(x ₁₀ ,q ₁ )=(1-2/3)+(1-2/3)+(1-3/3)=2/3, d(x ₁₀ ,q ₂ )=(1-2/3)+(1-3/3)+(1-2/3)=2/3, d(x ₁₀ ,q ₃ )=1+0+1=2. From the above calculation results, we can see that simple Hamming distance cannot cluster x ₁₀ ; formula (3) can divide x ₁₀ into cluster C ₁ or cluster C ₂ , that is, formula (3) cannot accurately determine the correctness of x ₁₀ cluster division. Observing the data set D ₂ from the perspective of "low intra-cluster dissimilarity and high inter-cluster dissimilarity", it can be seen that it is more appropriate to assign x ₁₀ to cluster C ₁ . Because after assigning x ₁₀ to cluster C ₁ , the dissimilarity between cluster C ₁ and cluster C ₂ will be maximized.

Between-cluster dissimilarity considers the total frequency of feature values relative to all cluster distributions. Assuming that the eigenvalues are frequently distributed in only one cluster, it means that the eigenvalues are very different from other clusters. The definition of intra-cluster and inter-cluster dissimilarity coefficient is shown in formula (4):

Among them: 1≤i≤n, 1≤s≤m.

Use formula (4) to calculate data set D ₂ d(x ₁₀ ,q ₁ )=(1-2/3×2/4)+(1-2/3×2/8)+(1-3/3 ×3/5)=1.9; d(x ₁₀ ,q ₂ )=(1-2/3×2/4)+(1-3/3×3/8)+(1-2/3×2/ 5)=2.025; d(x ₁₀ ,q ₃ )=(1-0×1)+(1-3/3×3/8)+(1-0×1)=2.625. According to the calculation result of formula (4), it can be seen that the dissimilarity between x ₁₀ and cluster C ₁ is smaller. This result is consistent with the previous analysis, and x ₁₀ has been clustered successfully. Next, formula (4) is used to verify the more special artificial data set D ₃ . As shown in Table 4, D ₃ is described by three features A={A ₁ , A ₂ , A ₃ }. Among them, DOM=(A ₁ )={A,B}, DOM(A ₂ )={E,F}, DOM(A ₃ )={H,I}, three clusters C ₁ , C ₂ and C ₃ corresponds to cluster centers q ₁ = (A, E, H), q ₂ = (A, E, H) and q ₃ = (A, E, H), respectively, A, E and H are uniformly distributed in D ₃ , appearing 6 times.

Table 4 Artificial Dataset D ₃

Use the simple Hamming distance, formula (3) and formula (4) to cluster and divide x ₁₀ (A, E, H). Use simple Hamming distance to get d(x ₁₀ ,q ₁ )=d(x ₁₀ ,q ₂ )=d(x ₁₀ ,q ₃ )=0+0+0=0; use formula (3) to get d (x ₁₀ ,q ₁ )=d(x ₁₀ ,q ₂ )=d(x ₁₀ ,q ₃ )=(1-2/3)+(1-2/3)+(1-2/3)= 1; use formula (4) to get d(x ₁₀ ,q ₁ )=d(x ₁₀ ,q ₂ )=d(x ₁₀ ,q ₃ )=(1-2/3×2/6)+(1 -2/3×2/6)+(1-2/3×2/6)=21/9. From the above calculation results, it can be known that when the eigenvalues are evenly distributed, none of the above three dissimilarity coefficients can correctly cluster x ₁₀ . Therefore, once again consider improving the intra-cluster and inter-cluster dissimilarity coefficient.

Take the eigenvalue distribution of the data object x _i and compare it with the overall eigenvalue distribution of the cluster. The definition of the perfect part is shown in formula (5):

Among them: x _i is the data object to be divided, x _j is the data object in the cluster C _l . The redefined intra-cluster and inter-cluster dissimilarity coefficient is shown in formula (6):

For any x _i, x _j ∈ D, d has the following properties:

Self-distance: For all x _i , the distance of each object to itself is equal to zero d(x _i , x _i )=0.

Symmetry: For all x _i and x _j , the distance from x _i to x _j is equal to the distance d( _{xi , x j )} =d(x _j , x _i ) from x j to x i.

Non-negativity: for all x _i , x _j , the distance d is a non-negative value, and d( _xi , x _j )=0 if and only when x _i =x _j .

Satisfy the triangle inequality: for all x _i and x _j , d(x _i , x _j )≤d(x _i , x _h )+d(x _h , x _j ).

Using formula (6) to calculate D ₃ again, we can get Therefore, the calculation result of the new dissimilarity coefficient is d(x ₁₀ ,q ₁ )=21/9+ζ ₁ =2.6666, d(x ₁₀ ,q ₂ )=21/9+ζ ₂ =2.8148, d(x ₁₀ ,q ₃ )=21/9+ζ ₃ =2.8888. From the above calculation results, it can be seen that x ₁₀ should be divided into cluster C ₁ . The result of clustering and division conforms to the actual situation, which shows that the dissimilarity coefficient scheme proposed by the present invention is feasible.

In 2014, Rodriguez et al. proposed the Density Peak (DP) algorithm. DP algorithm is a new type of clustering algorithm based on relative distance and local neighborhood density. It deals with numerical data, and its input is the dissimilarity matrix between data objects. Therefore, the classification is calculated by appropriate dissimilarity coefficient. The degree of dissimilarity between the data can be used to apply the DP algorithm to the classification data clustering. In this section, the DP algorithm can automatically determine the advantages of the number of clusters to determine the initial cluster center.

The value of the local neighborhood density ρ _i of the data object _xi is equivalent to the number of data objects in the area with the data object _xi as the center and the cut-off distance d _c as the radius. The local neighborhood density of data object x _i has two definition methods: square wave kernel function method and Gaussian kernel function method:

The square wave kernel function method is suitable for large-scale data sets. The definition of _ρi obtained by the square wave kernel function method is shown in formula (7):

Where: when d _i,j -d _c ≤0, χ(x)=1; otherwise, χ(x)=0.

If the number of objects in the data set is small, the calculation of _ρi using the square wave kernel function is likely to be affected by statistical errors and cause inaccurate clustering results. At this time, the Gaussian kernel function method can be used. The Gaussian kernel function is a commonly used density estimation method and is widely used in the analysis of density-based clustering algorithms. The definition of Gaussian kernel function method to calculate the local neighborhood density _ρi is shown in formula (8):

Where: K(x)=exp{-x ² }.

It can be seen from formula (7) and formula (8) that the value of d _c will directly affect the size of ρ _i , and then affect the selection of cluster center and the whole clustering result. Therefore, it is very important for the algorithm to determine the appropriate d _c value.

The value of _Li is calculated according to the Alex-Li formula, and the relative distance _Li between data objects x _i and x _j is defined as shown in formula (9):

When ρ _i of xi is not the maximum density, L _i is defined as the distance between the data object closest _{to xi} and _xi among all data objects whose local neighborhood density is larger than _xi , as in the formula (10 ) and as shown in Figure 2:

When ρ _i of xi is the maximum density, _{Li is} defined as the distance between the data object farthest _from xi and _xi among all the data objects whose local neighborhood density is larger than _xi , such as the formula (11 ) and Figure 3. The data object with high L _i and high ρ _i at the same time is the cluster center.

The cutoff distance _dc is a critical value that limits the distance search range. The d _c value of the DP algorithm needs to be determined manually. The distance between two data objects in the data set is arranged in ascending order, and the value at the top 1% to 2% position is the d _c value, which is an approximate range. In the actual clustering problem, if the value of d _c is set too large, the obtained ρ _i will overlap, and if the value of d _c is set too small, the distribution of clusters will be sparse. The present invention provides a detailed d _c value determination method. Set d _i,j =[d _i,1 ,d _i,2 ,..,d _i,n ] as the degree of dissimilarity between data objects x _i and x _j . Use formula (1) to calculate d _i,j values, and then sort d _i,j in ascending order to obtain d′ _i,j =[d′ _i,1 ,d′ _i,2 ,...,d′ _i,n ] . The cut-off distance d _c,i of x _i is defined as shown in formula (12):

Among them: max(d′ _i,j+1 -d′ _i,j ) is the maximum difference of adjacent dissimilarity in d′ _i,j .

Let d′ _i,j =d _a , d′ _i,j+1 =d _b 12 . As shown in Figure 4, the data object x _i has a small dissimilarity with data objects in the same cluster as it, and a large dissimilarity with data objects in a different cluster with it. Therefore, at d′ _i,j =[d′ _i,1 ,d′ _i,2 ,...,d′ _i,j ,d′ _i,j+1 ,...,d′ _i,n ] There must be a critical position in which the difference between d′ _i,j+1 and d′ _i,j is the largest. It is considered that data object x _i and data object a belong to the same cluster, and data object b belongs to a different cluster. Calculate the _dc,i value of the data object x _i according to the Shuang YF formula, as shown in formula (13):

The value of d _c is defined as the minimum value of set d _c,i as shown in formula (14).

d _c =min(d _c,i ) (14)

IKMCA determines initial cluster centers based on the following two assumptions: (1) The local neighborhood density of cluster centers is higher than that of surrounding non-cluster centers. (2) The relative distance between the cluster centers is relatively large. Based on the above assumptions, this section presents a method for automatic determination of initial cluster centers. As shown in Figure 5, it is a two-dimensional example data set, with a total of 93 data objects, 2 clusters, corresponding to 2 cluster centers.

The selection of the cluster center of the DP algorithm is determined through the decision diagram. As shown in Fig. 6, the horizontal axis of the decision graph is the local neighborhood density ρ _i of the data object x _i , and the vertical axis is the relative distance L _i . The value of ρ _i and L _i that are large at the same time is the cluster center of the data set. The two points in the upper right corner of Figure 6 are the cluster centers corresponding to the two clusters in Figure 6. The cluster center is surrounded by a large number of data objects, and its local neighborhood density ρ _i and relative distance L _i are both large.

In order to observe and determine the cluster center more intuitively, consider using the Z _i decision diagram to select the cluster center. The local neighborhood density and relative distance of each data object are obtained by formula (8) and formula (9). Calculate the Z _i values of all data objects according to the formula Z _i =ρ _i ×L _i , sort the Z _i values in descending order to obtain the sorting sequence Z ⁽¹⁾ >Z ⁽²⁾ >...Z ⁽ⁿ⁾ , where Z ^{( 1)} >Z ⁽²⁾ >...Z ^(k) , the point corresponding to (k<n) is the cluster center. As shown in Figure 7, the horizontal axis of the Zi decision diagram is the subscript of the data object xi, and the vertical axis is the value of _Zi . The larger the value of _Zi , the more likely it is the cluster center. From the cluster center to the non-cluster center, there is a very obvious inflection point on the Z _i diagram, the abscissa corresponding to the inflection point is the number of clusters k, the data object on the left side of the inflection point is the cluster center point, and the data object on the right side of the inflection point is the non-cluster center point. As shown in Figure 7, the two points on the upper left are cluster center points, and the points on the lower right with very smooth distribution are all non-cluster center points.

The new intra-cluster and inter-cluster dissimilarity coefficient makes the dissimilarity calculation of subcategory data more accurate. The autonomous selection of the initial cluster center avoids the uncertainty of the clustering results caused by the random selection of the classic k-modes algorithm or manual setting. The DP algorithm only gives the approximate range of d _c , and the present invention provides a definite determination method of d _c on the basis of the DP algorithm. The intra-cluster and inter-cluster dissimilarity coefficient is applied to the classical k-modes algorithm, and its objective function is defined as shown in formula (15). Theorem 1 shows how to minimize the objective function F(U,Q).

u _il ∈ {0,1}, 1≤i≤n, 1≤l≤k (16)

U _n×k is a membership degree matrix satisfying the constraints (16~18), and u _il =1 means that x _i belongs to cluster C _l . When the constraint conditions (16-18) are met, the objective function F(U, Q) reaches the minimum value, and at this time, it can be judged that the clustering algorithm ends.

Theorem 1: The cluster center selection of IKMCA should minimize the function F(U,Q) if and only if t _s ≠t _h (1≤s≤m). The text description is that each eigenvalue of the cluster center should select the eigenvalue with the highest frequency of occurrence on each feature in the data set.

f _s,t ( _xi )(1≤s≤m,1≤t≤n _s ) indicates the number of x _i taking the value A _s,t under the sth feature, as shown in formula (19):

f _s,t ( _xi )＝|{ _xi ∈D,xi _,s ＝A _s,t }| (19)

The function F(U,Q) is minimized if and only if q _l =DOM(A _s ), 1≤s≤m and formula (20) is satisfied:

In order to make the objective function F(U,Q) reach the minimum value, the improved k-modes algorithm based on intra-cluster dissimilarity between clusters (IKMCA) is a classification data aggregation method based on intra-cluster dissimilarity. The class method, as shown in Figure 8, is described as follows:

Input: a categorical dataset D with n data objects and m categorical features. Output: the completed cluster set C={C ₁ ,C ₂ ,...,C _k }.

step1. Calculate the degree of dissimilarity d _i,j by formula (1), and obtain the dissimilarity matrix d _n×n ;

step2. Calculate the cut-off distance dc according to formula (14);

step3. Use formula (7) or formula (8) to calculate the local neighborhood density ρ _i ;

step4. Utilize the formula (9) to calculate the relative distance L _i ;

step5. According to the formula Z _i =ρ _i ×L _i , calculate Z _i ={Z ₁ ,Z ₂ ,...,Z _n };

step6. Sort Z _i in descending order to obtain the sorted sequence Z ^(1)> Z ⁽²⁾ >...>Z ⁽ⁿ⁾ . Use the subscript of the data object x _i as the abscissa, and Z _i as the ordinate to draw the Z _i decision-making diagram, determine the inflection point in the graph, and the abscissa value at the inflection point is the optimal k value.

Step7. Determine k value and initial cluster center set q ⁽⁰⁾ ={q ₁ ,q ₂ ,...,q _k };

Step8. Calculate the dissimilarity d(x _i , q _l ) between nk data objects and k initial cluster centers in the data set according to formula (6);

Step9. According to the principle of proximity, allocate the data object to the initial cluster closest to it. After the allocation is completed, k clusters C ⁽¹⁾ = {C ₁ ,C ₂ ,...,C _k } are obtained, marked The cluster label of these (nk) data objects;

Step10. Update the cluster center q ⁽¹⁾ ={q ₁ ,q ₂ ,..,q _k } according to Theorem 1 on the newly formed cluster;

Step11. Repeat steps 8-11 until the objective function value no longer changes. If the objective function value no longer changes, the algorithm ends; otherwise, repeat Step8 to continue execution;

Step12. The algorithm ends and the clustering is completed.

Suppose l is the number of iterations required for the algorithm to converge, usually n>>m,k,l. The time complexity of the IKMAC algorithm is mainly to update the cluster center and dissimilarity in each iteration. Initializing the cluster center requires manual observation of the decision graph, so the time complexity at this stage is not considered in the overall algorithm for the time being. The time complexity of updating the cluster center and dissimilarity calculation in each iteration using intra-cluster and inter-cluster dissimilarity is l(O(nmk)+O(nmk))=O(nmkl), so the total time complexity of IKMCA The degree is O(nmkl). From the above analysis, it can be found that the time complexity of the IKMCA algorithm that makes the intra-cluster and inter-cluster dissimilarity is linearly scalable with respect to the number of data objects, the number of clusters and the number of features.

In order to evaluate the effectiveness of the proposed algorithm, the clustering results are evaluated from the following three indicators: clustering accuracy AC, purity PR, and recall RE, as shown in formula (21) to formula (23). NUM+ indicates the number of data objects that are correctly divided into cluster _C1 ; NUM- indicates the number of data objects that are not correctly divided into cluster _C1 ; NUM* indicates that they should be divided into cluster _C1 but are not actually divided into clusters The number of data objects of C _l . The closer the clustering result is to the real division of the data set, the greater the values of AC, PE and RE, and the more effective the algorithm is.

The algorithm is implemented in Python language, and all experiments are run on the intel(R) Core(TM) processor i7-8700K CPU@3.70GHz, Windows 10 operating system. The datasets used are from real datasets. UCI is a real-world dataset dedicated to machine learning provided by the University of California, Irvine. In order to test the effectiveness of the algorithm, Mushroom (Mus for short), Breast-cancer (Bre for short), Car and Soybean-small (Soy for short) data sets were selected from the UCI data set for experimental verification. Table 5 lists these dataset details.

Table 5 Dataset description

The IKMCA algorithm proposed by the present invention and the k-modes algorithm proposed by Huang, the IDMKCA algorithm proposed by Ng et al. and the EKACMD algorithm proposed by Ravi et al. were run 30 times to obtain the average value. The calculation results of AC, PE and RE are shown in Table 6 to Table 9.

Table 6 Experimental results of the four algorithms in the Mus dataset

Table 7 Experimental results of four algorithms in Bre dataset

Table 8 Experimental results of the four algorithms in the Car dataset

Table 9 Experimental results of the four algorithms in the Soy dataset

From the above experimental results, it can be seen that for the Mus, Bre, Car, and Soy datasets, IKMCA outperforms the k-modes algorithm, IDMKCA algorithm, and EKACMD algorithm in AC, PR, and RE in most cases. The reason why the IMKCA algorithm is superior to the classic k-modes algorithm is that the preprocessing of the k-modes algorithm destroys the original structure of the classification feature. Calculating the dissimilarity coefficient using simple Hamming distance for transformed categorical feature values does not reveal the dissimilarity between categorical data. When there are many features in the data set, a simple 0-1 comparison may produce a very large degree of dissimilarity, or may produce a very small degree of dissimilarity or even a degree of dissimilarity. Compared with the classical k-modes algorithm and the IDMKCA and EKACMD algorithms, the proposed intra-cluster and inter-cluster dissimilarity can better reveal the structure of the data set.

The classic k-modes algorithm uses simple Hamming distance to calculate the dissimilarity, which weakens the intra-class similarity and ignores the inter-cluster similarity. To solve these problems, the present invention proposes a new calculation method of dissimilarity based on the similarity between clusters within a cluster. This method can prevent the loss of important eigenvalues in the clustering process, strengthen the similarity between eigenvalues within a cluster, and weaken the similarity between eigenvalues between clusters. The proposed automatic cluster center selection method greatly reduces the errors brought by random selection of cluster centers or manual selection of cluster centers to clustering. The present invention discusses the limitation of using other dissimilarity coefficients such as simple Hamming distance in the k-modes algorithm with some illustrative examples, and proposes a new dissimilarity coefficient. The classification data clustering algorithm based on the improved dissimilarity coefficient proposed by the present invention and the k-modes algorithm based on other dissimilarity coefficients are tested on the UCI data set. Experimental results show that the dissimilarity coefficient calculation method proposed by the present invention retains the characteristics of the data, achieves the standard of low intra-cluster dissimilarity and high inter-cluster dissimilarity, and improves clustering accuracy, purity and recall. Effectively improve the clustering effect of classified data.

The algorithm (IKMCA) proposed by the present invention can be applied to a rehabilitation treatment plan recommendation system containing massive pure classification data. On the rehabilitation treatment plan recommendation system, classification data clustering can help analysts distinguish different patients from the patient database. Patient groups, discover some in-depth information distributed in the database, and formulate personalized rehabilitation plans.

It should be noted that although the above-mentioned embodiments of the present invention are illustrative, they are not intended to limit the present invention, so the present invention is not limited to the above specific implementation manners. Without departing from the principles of the present invention, all other implementations obtained by those skilled in the art under the inspiration of the present invention are deemed to be within the protection of the present invention.

Claims (2)

1. A classification data clustering method based on intra-cluster and inter-cluster dissimilarity, which is applied to a rehabilitation treatment program recommendation system containing massive pure classification data. In the rehabilitation treatment program recommendation system, classification data clustering can help The analyst distinguishes different patient groups from the patient database, and formulates a personalized rehabilitation plan; the feature is that it includes the following steps: Step 1. For a classified data set D with n data objects, use the simple Hamming distance to calculate the dissimilarity d _i,j between every two data objects; Step 2. For each data object x _i of the sub-type data set D, first sort the dissimilarity d _{i, j} between the data object x _i and other data correspondences in ascending order, and obtain the corresponding data object x _i Dissimilarity vector d' _i,j ＝[d' _i,1 ,d' _i,2 ,...,d' _i,n ]; then two adjacent dissimilarity vectors d' _i,j The maximum difference of the dissimilarity is taken as the cut-off distance d _c,i of the data object x _i ; Step 3. Select the minimum value of the cut-off distance dc _,i of all data objects in the classification data set D as the cut-off distance _dc of the classification data set D; Step 4. Calculate the local neighborhood density _ρ i of each data object x _i in the classification data set D based on the cut-off distance d _c of the classification data set D by using the square wave kernel function method or the Gaussian kernel function method; Step 5. Calculate the relative distance L _i of each data object x _i in the classification data set D: Step 6. For each data object _xi in the classification data set D, use the local neighborhood density ρ _i and the relative distance L _i of the data object _xi to obtain the decision graph Z _i of the data object _xi : Z _i =ρ _i ×L _i Step 7. First sort the decision graph Z _i of all data objects in the classification data set D in descending order to obtain a sorting sequence; then based on the sorting sequence, use the subscript i of the data object x _i as the abscissa, and the data object x The decision diagram _Z of _i is the vertical coordinate to draw the decision diagram of the classification data set D, and the abscissa at the inflection point in the decision diagram of the classification data set D is the selected number of clusters k; Step 8, select k data objects from the classification data set D to form the current cluster center set; Step 9. Based on the current set of cluster centers, calculate the dissimilarity d( _xi ,q _l ) between the remaining nk data objects _xi and k cluster centers q _l in the subtype data set D: Step 10. According to the dissimilarity d( _xi ,q _l ) between the data object _xi and the cluster center q _l , and based on the principle of proximity, assign nk data objects to the nearest cluster. After the assignment is completed, Obtain k clusters, and mark the cluster labels of these nk data objects, thereby obtaining the clustering result based on the current cluster center set; Step 11. For the formed k clusters, select the eigenvalue with the highest frequency of occurrence on each dimension feature from each cluster to form a new cluster center of the cluster, and obtain a new set of cluster centers; Step 12. Repeat steps 9-11 until each cluster center no longer changes or reaches the specified maximum number of iterations, the algorithm terminates, and the clustering result based on the current cluster center set is output; otherwise, the obtained new cluster center Set as the current cluster center set, and skip to step 9 to continue iteration; Among them, i, j=1,2,...,n, n is the number of data objects in the classification data set D; s=1,2,...,m, m is the number of features of the data objects; l=1 ,2,...,k, is the number of clusters; δ(A _i,s ,A _ql,s ) is the dissimilarity between the data object x _i and cluster center q _l under the s-th dimension feature; A _i,s is The s-th dimension feature of the data object x _i ; A _ql,s is the s-th dimension feature of the cluster center q _l ; is the number of data objects whose feature value is _As,t in cluster C _l ; |C _l | is the number of data objects in cluster C _l ; ζ _l is the adjustment coefficient. 2. a kind of classification data clustering method based on the dissimilarity between clusters in a cluster according to claim 1, is characterized in that, in step 4, for the large-scale classification data set D that data object is greater than or equal to 10TB, Use the square wave kernel function method to calculate the local neighborhood density ρ _i of the data object x _i ; for the small-scale classification data set D with the data object less than 10TB, use the Gaussian kernel function method to calculate the local neighborhood density ρ _i of the data object x _i .