CN110826914A - Learning group grouping method based on difference - Google Patents
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Abstract
The invention discloses a learning group grouping method based on differences, which relates to the technical field of collaborative learning, personalized teaching and experimental grouping. The invention considers the difference among all the grouping members in the cooperative learning, provides a learning group grouping method based on the difference, and realizes that the elements with large difference are grouped into one group, and the elements with small difference are distributed to different groups, thereby expanding the application range of the grouping and being more suitable for the cooperative learning scene.
Description
Technical Field
The invention belongs to the technical field of collaborative learning, personalized teaching and experimental grouping, and particularly relates to a collaborative learning grouping method.
Background
In recent years, with the popularization of mobile intelligent devices (such as smart phones, tablet computers and the like) and the development of network communication technologies, online mobile learning modes (such as large-scale open network courses, namely admiration courses and small-scale restrictive online courses) are widely popularized and developed, and play a great role in promoting the realization of learning anytime and anywhere, namely learning of any content by anyone at any time and any place. Research researchers, governments and enterprises have conducted a great deal of research and application to mobile online learning, including: teaching mode, turnover classroom, online work correction, online examination, online project completion, experiment and the like.
Currently, many projects and experiments are performed in groups, not in individuals. The project and experiment taking the group as a unit can train and train a plurality of soft skills and soft abilities which play important roles in the future professional development, such as communication, cooperation, social interaction, problem solving and the like of learners, so that the grouping problem becomes an important research problem for implementing collaborative learning and personalized teaching at present. In addition, the grouping problem also plays an important role in grouping experiments of many disciplines, such as biological, physical, chemical and other experimental disciplines, and the quality of grouping often has an important influence on the experimental result.
The grouping problem is to divide a set containing N elements into K groups, wherein N is an integral multiple of K, and each group comprises N/K elements. From the existing research results, the current grouping method mainly has two types: one is a random grouping method, i.e. all elements are randomly and uniformly distributed into each group, for example, in an experiment, the elements are divided into a control group and an experimental group, and in various competitive games, random grouping by drawing is generally adopted. One type is a grouping method based on machine learning, such as a similarity-based K-Means method, a decision tree method, a support vector machine method and the like, but the method is mainly based on the similarity of two elements, and is calculated through a certain similarity formula, so that the similarity is divided into a group as much as possible. In fact, in cooperative learning, the differences of the panelists are significant, such as sex, age, knowledge structure, hobbies, learning ability, learning habits, learning specials, and the like. The group with larger difference can often obtain better learning effect in the cooperative learning, so that the group based on difference can obtain better learning effect in the cooperative learning than the group based on similarity. In addition, the existing grouping method does not consider the balance among the groups, which may cause large difference among the groups and is not beneficial to comprehensively improving the learning score of students. Therefore, the grouping method considering the difference and the grouping effect balance has important significance for improving the learning effect of students, training the soft abilities of student cooperation, communication and the like, and more effectively implementing cooperative learning.
Based on the method, in order to adapt to a collaborative learning scene in online mobile learning and improve the balance of grouping effects, a learning group grouping method based on difference is designed under the condition of considering element difference.
Disclosure of Invention
The technical problem to be solved by the present invention is to overcome the above disadvantages of the prior art, and to provide a learning group grouping method based on difference, which is simple in operation, fast in operation speed, and high in efficiency.
The technical scheme adopted for solving the technical problems comprises the following steps:
(1) collecting attribute features of N elements
Attribute feature v of ith elementiExpressed as a vector:
vi＝(ai1,ai2,...,aim,...,aiM)
wherein each component aimA quantized value, a, representing the element i corresponding to the mth attribute featureimFor real numbers, M represents the number of attribute features of an element, i ∈ {1, 2.. and N }, M ∈ {1, 2.. and M }, M, N are finite positive integers.
(2) Determining the number of groups and the number of elements contained
Determining the grouping number K according to the actual requirement, and determining the number f (K) of elements contained in the kth grouping according to the formula (1):
where K is in the range of {1, 2.,. K }, where N% K represents the remainder of N divided by K, and K is a finite positive integer.
(3) Normalizing attribute features of N elements
The m-th attribute feature value a of any element i according to equation (2)imAnd (4) carrying out standardization:
wherein, mumMean value of characteristic values of the m-th attribute representing all elements, i.e.
μm＝(a1m+a2m+...+aNm)/N，σmRepresents the standard deviation of the m-th attribute feature values of all elements,
(4) determining degrees of difference between pairs of elements and ordering
Degree of difference d between pairs of elements consisting of any two elements i, jijDetermined according to equation (3):
in the formula, biAnd bjThe normalized attribute feature vectors of the element i and the element j are respectively represented, i, j belongs to {1, 2.,. N }, i ≠ j.
bi＝(bi1,bi2,...,biM)
bj＝(bj1,bj2,...,bjM)
(bi－bj)TRepresents a vector (b)i－bj) Transposing; s represents covariance matrix among characteristic vectors of each attribute, the covariance matrix is M-dimensional matrix, and any element in S is Si'j'It is shown that,
Si'j'＝cov(ui',uj')/(m-1)
wherein u isi'And uj'Respectively representThe i 'th and j' th attribute features in all elements are normalized to form a vector, i.e. the vector
ui'＝(b1i',b2i',...,bNi')
uj'＝(b1j',b2j',...,bNj')
cov(ui',uj') Represents a vector ui'And uj'Covariance therebetween, i.e.
cov(ui',uj')＝E[(ui'-μi')(uj'-μj')]
Wherein, mui'And muj'The normalized mean values of the i 'th and j' th attribute feature values respectively representing all elements, i.e.
μi'＝(b1i'+b2i'+...+bNi')/N
μj'＝(b1j'+b2j'+...+bNj')/N
Where i ', j' is e {1, 2.
(5) Processing each element pair (i, j)
Grouping is performed using a diversity-based grouping method.
In the step (5) of processing each element pair (i, j) of the present invention, the diversity-based grouping method is:
one element of the element pair (i, j) is not assigned to the group, one element is assigned to the group, the unassigned element is s, where s ∈ { i, j }, and the group is grouped in the absence of a group that does not contain any element by:
1) determining the degree of dissimilarity d (s, k ') of the element s to the grouping k' of each allocable element as follows:
wherein S (k ') represents the set of allocated elements in the grouping k' of allocable elements, dscRepresenting the degree of disparity between element s and element c, groups of assignable elementsk ' means that the number of allocated elements in the group k ' is less than the number f (k) of elements contained in the group determined in step (2), i.e. | S (k '). luminance<f (k), the set Q(s) of groupings of allocable elements s is represented by:
Q(s)＝{k'||S(k')|<f(k)}；
2) allocating the element s to the grouping k 'with the largest difference degree in the grouping k' of the allocable elements, and processing the next element pair; k "is determined as follows:
where q(s) represents a grouped collection of allocable elements s.
In the step (5) of processing each element pair (i, j) of the present invention, the diversity-based grouping method is: processing each element pair (i, j) in step (5); the element pair (i, j) is: if both the i and j element pairs have been assigned to a group, the next element pair is processed.
In the step (5) of processing each element pair (i, j) of the present invention, the diversity-based grouping method is: processing each element pair (i, j) in step (5); the element pair (i, j) is: one element of the element pair (i, j) is not assigned to the group, one element is assigned to the group, the unassigned element is s, where s e { i, j }, and when there is a group l that does not contain any element, l e {1, 2.
In the step (5) of processing each element pair (i, j) of the present invention, the diversity-based grouping method is: processing each element pair (i, j) in step (5), the element pair (i, j) is: neither element of the pair (i, j) is assigned to a group, there is a group l "that does not contain any element, element j is assigned to the group l", i "e {1, 2.. multidata., K }, and step (5) is performed to process element pair (i, j) again.
In the step (5) of processing each element pair (i, j) of the present invention, the diversity-based grouping method is: neither element of the pair (i, j) of elements is assigned to a group, there is no group containing any element, further comprising the steps of:
1) determining a grouping set Q of allocable elements of the element i and the element j, wherein the grouping corresponding to each element in the grouping set Q of allocable elements can further contain at least one element.
2) Determining the degree of disparity of element i and element j to each assignable element's grouping k', respectively, i.e.
Wherein k' is belonged to Q, dicAnd djcRespectively representing the degree of difference between elements i and j and element c.
3) Determining the element with the maximum difference degree and the grouping, dividing the element with the maximum difference degree into the grouping with the maximum difference degree, turning to the step (5), and processing the element pair (i, j); the element and the grouping with the greatest degree of difference are determined according to the following formula:
compared with the prior art, the invention has the following advantages:
the invention adopts a grouping method based on difference to carry out element grouping, so that the difference between elements in a group is larger, the difference between elements among groups is smaller, the method is suitable for large-item cooperative learning aiming at cultivating the soft ability of students, and the application range of the cooperative learning is expanded. The calculation of the difference between the two elements takes the correlation of each attribute characteristic of the elements into consideration, the covariance matrix is used for carrying out weighting calculation on the difference of the two elements, and compared with the existing calculation mode based on Euclidean distance and included angle cosine, the method eliminates the interference of the correlation of the attribute characteristics.
Compared with the existing similarity-based K-Means method, decision tree method and support vector machine method, the method can realize the separation of elements with larger differences into the same group, and better learning effect can be obtained in cooperative learning based on the difference grouping than the similarity grouping. The invention considers the balance among all groups, ensures that the difference among all groups is smaller, is beneficial to exerting the enthusiasm of all students of all groups, comprehensively improves the learning achievement of all students of all layers of all groups, improves the learning effect of the students, trains the abilities of student cooperation, communication and the like, and adapts to the future professional development.
The invention provides an efficient grouping method, and the most time-consuming operation of the method is to N2The element pairs are sorted by degree of disparity, with a time complexity of O (N)2log (N)), which is convenient for the computer to run; the time complexity of the traditional brute force search method is O (2)N) The time consumption is far higher than that of the method when N is larger. The method has the advantages of simple operation, high running speed, high efficiency and the like.
Drawings
FIG. 1 is a flowchart of example 1 of the present invention.
FIG. 2 is a graph of the results of a comparison experiment between the present invention and a random grouping method, a grouping method based on k-means clustering.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, but the present invention is not limited to the examples described below.
Example 1
Taking the example of the number of students N being 9, M being 4, and K being 3, the diversity-based learning group grouping method of this example consists of the following steps (see fig. 1):
(1) collecting attribute features of N elements
Attribute feature v of ith elementiExpressed as a vector:
vi＝(ai1,ai2,...,aim,...,aiM)
wherein each component aimA quantized value, a, representing the element i corresponding to the mth attribute featureimIn the case of a real number,m represents the number of attribute features of an element, i belongs to {1, 2., N }, M belongs to {1, 2., M }, in this embodiment, N is 9, M is 4, viThe values are as follows:
v1＝(a11,...,a14)＝(19,9,8,4)
v2＝(a21,...,a24)＝(19,8,8,5)
v3＝(a31,...,a34)＝(19,9,7,4)
v4＝(a41,...,a44)＝(20,6,8,6)
v5＝(a51,...,a54)＝(20,4,7,5)
v6＝(a61,...,a64)＝(20,6,9,4)
v7＝(a71,...,a74)＝(18,5,8,4)
v8＝(a81,...,a84)＝(18,7,6,9)
v9＝(a91,...,a94)＝(18,8,5,7)
(2) determining the number of groups and the number of elements contained
Determining the grouping number K according to the actual requirement, and determining the number f (K) of elements contained in the kth grouping according to the formula (1):
wherein K is ∈ {1,2,. and K }, N% K represents a remainder obtained by dividing N by K, K in this embodiment is 3, and f (K) ═ 3 is calculated, and K is ∈ {1,2,3 };
(3) normalizing attribute features of N elements
The m-th attribute feature value a of any element i according to equation (2)imAnd (4) carrying out standardization:
wherein, mumMean value of characteristic values of the m-th attribute representing all elements, i.e.
μm＝(a1m+a2m+...+aNm)/N，σmRepresents the standard deviation of the m-th attribute feature values of all elements,
b is calculated in this exampleimThe following were used:
(b11,b12,b13,b14)＝(0,1.27,0.58,-0.82)
(b21,b22,b23,b24)＝(0,0.67,0.58,-0.20)
(b31,b32,b33,b34)＝(0,1.27,-0.29,-0.82)
(b41,b42,b43,b44)＝(1.22,-0.53,0.58,0.41)
(b51,b52,b53,b54)＝(1.22,-1.74,-0.29,-0.20)
(b61,b62,b63,b64)＝(1,22,-0.53,1.43,-0.82)
(b71,b72,b73,b74)＝(-1.22,-1.14,0.58,-0.82)
(b81,b82,b83,b84)＝(-1.22,0.07,-1.15,2.25)
(b91,b92,b93,b94)＝(-1.22,0.67,-2.02,1.02)
(4) determining degrees of difference between pairs of elements and ordering
Degree of difference d between pairs of elements consisting of any two elements i, jijDetermined according to equation (3):
wherein, biAnd bjRespectively representing normalized attribute feature vectors for element i and element j, i, j ∈ {1, 2.i ≠ j, i ∈ {1,2,. 9} of this embodiment, j ∈ {1,2,. 9 };
bi＝(bi1,bi2,...,biM)
bj＝(bj1,bj2,...,bjM)
(bi－bj)Trepresents a vector (b)i－bj) Transposing; s represents covariance matrix among characteristic vectors of each attribute, the covariance matrix is M-dimensional matrix, and any element in S is Si'j'It is shown that,
Si'j'＝cov(ui',uj')/(m-1)
the covariance matrix S of the present embodiment is expressed as follows:
wherein u isi'And uj'Respectively representing the vectors formed by normalizing the ith' and jth attribute features in all elements, i.e.
ui'＝(b1i',b2i',...,bNi')
uj'＝(b1j',b2j',...,bNj')
cov(ui',uj') Represents a vector ui'And uj'Covariance therebetween, i.e.
cov(ui',uj')＝E[(ui'-μi')(uj'-μj')]
Wherein, mui'And muj'The normalized mean values of the i 'th and j' th attribute feature values respectively representing all elements, i.e.
μi'＝(b1i'+b2i'+...+bNi')/N
μj'＝(b1j'+b2j'+...+bNj')/N
Where i ', j' is e {1, 2.
Degree of difference d in the present embodimentijThe following were used:
in this embodiment, the sorting is performed from small to large according to the difference, and the sorting result is as follows:
(1，2，0.30)，(1，3，0.31)，(2，3，0.34)，(8，9，0.41)，(4，5，0.42)，(2，7，0.62)，(2，4，0.67)，(4，6，0.68)，(4，7，0.74)，(5，7，0.81)，(1，7，0.82)，(5，6，0.82)，(3，7，0.85)，(1，4，0.89)，(3，4，0.97)，(2，5，0.99)，(2，6，1.01)，(6，7，1.03)，(1，6，1.05)，(1，5，1.21)，(3，5，1.26)，(3，6，1.28)，(3，9，1.42)，(2，9，1.55)，(3，8，1.57)，(2，8，1.62)，(7，9，1.67)，(7，8，1.67)，(1，9，1.70)，(1，8，1.82)，(4，8，1.85)，(4，9，1.90)，(5，8，1.94)，(5，9，2.02)，(6，8，2.48)，(6，9，2.48)。
in the components of each triplet, the first two components all represent the serial numbers of students, and the third component is the difference between the two corresponding students.
(5) Processing each element pair (i, j)
Grouping is performed using a diversity-based grouping method.
The grouping method based on the differences in the embodiment is as follows: processing each element pair (i, j) in step (5). The element pair (i, j) of this example is: one element of the element pair (i, j) is not assigned to the group, one element is assigned to the group, the unassigned element is s, where s ∈ { i, j }, and the group is grouped in the absence of a group that does not contain any element by:
1) determining the degree of dissimilarity d (s, k ') of the element s to the grouping k' of each allocable element as follows:
wherein S (k ') represents the set of allocated elements in the grouping k' of allocable elements，dscRepresenting the difference between the element S and the element c, the group k ' of allocable elements means that the number of the allocated elements in the group k ' is less than the number f (k) of the elements contained in the group determined in step (2), i.e. | S (k '), (k;) is<f (k), the set Q(s) of groupings of allocable elements s is represented by:
Q(s)＝{k'||S(k')|<f(k)}；
2) allocating the element s to the grouping k 'with the largest difference degree in the grouping k' of the allocable elements, and processing the next element pair; k "is determined as follows:
where q(s) represents a set of grouped constituents of allocable element s.
The grouping result of this embodiment is: g1 ═ {1, 4, 8}, G2 ═ 2, 6, 9}, and G3 ═ 3, 5, 7 }.
Example 2
Taking the number of students N as 9, M as 4, and K as 3 as an example, the difference-based learning group grouping method of this example comprises the following steps:
(1) collecting attribute features of N elements
This procedure is the same as in example 1.
(2) Determining the number of groups and the number of elements contained
This procedure is the same as in example 1.
(3) Normalizing attribute features of N elements
This procedure is the same as in example 1.
(4) Determining degrees of difference between pairs of elements and ordering
This procedure is the same as in example 1.
(5) Processing each element pair (i, j)
The grouping method based on the differences in the embodiment is as follows: processing each element pair (i, j) in step (5). The element pair (i, j) of this example is: if both the i and j element pairs have been assigned to a group, the next element pair is processed.
Example 3
Taking the number of students N as 9, M as 4, and K as 3 as an example, the difference-based learning group grouping method of this example comprises the following steps:
(1) collecting attribute features of N elements
This procedure is the same as in example 1.
(2) Determining the number of groups and the number of elements contained
This procedure is the same as in example 1.
(3) Normalizing attribute features of N elements
This procedure is the same as in example 1.
(4) Determining degrees of difference between pairs of elements and ordering
This procedure is the same as in example 1.
(5) Processing each element pair (i, j)
The grouping method based on the differences in the embodiment is as follows: processing each element pair (i, j) in step (5). The element pair (i, j) of this example is: one element of the element pair (i, j) is not assigned to the group, one element is assigned to the group, the unassigned element is s, where s e { i, j }, and when there is a group l that does not contain any element, l e {1, 2.
Example 4
Taking the number of students N as 9, M as 4, and K as 3 as an example, the difference-based learning group grouping method of this example comprises the following steps:
(1) collecting attribute features of N elements
This procedure is the same as in example 1.
(2) Determining the number of groups and the number of elements contained
This procedure is the same as in example 1.
(3) Normalizing attribute features of N elements
This procedure is the same as in example 1.
(4) Determining degrees of difference between pairs of elements and ordering
This procedure is the same as in example 1.
(5) Processing each element pair (i, j)
The grouping method based on the differences in the embodiment is as follows: processing each element pair (i, j) in step (5). The element pair (i, j) of this example is: neither element of the pair (i, j) is assigned to a group, there is a group l "that does not contain any element, element j is assigned to the group l", i "e {1, 2.. multidata., K }, and step (5) is performed to process element pair (i, j) again.
Example 5
Taking the number of students N as 9, M as 4, and K as 3 as an example, the difference-based learning group grouping method of this example comprises the following steps:
(1) collecting attribute features of N elements
This procedure is the same as in example 1.
(2) Determining the number of groups and the number of elements contained
This procedure is the same as in example 1.
(3) Normalizing attribute features of N elements
This procedure is the same as in example 1.
(4) Determining degrees of difference between pairs of elements and ordering
This procedure is the same as in example 1.
(5) Processing each element pair (i, j)
The grouping method based on the differences in the embodiment is as follows: neither element of the pair (i, j) of elements is assigned to a group, there is no group containing any element, further comprising the steps of:
1) determining a grouping set Q of allocable elements of the element i and the element j, wherein the grouping corresponding to each element in the grouping set Q of allocable elements can further contain at least one element.
2) Determining the degree of disparity of element i and element j to each assignable element's grouping k', respectively, i.e.
Wherein k' is belonged to Q, dicAnd djcRespectively representing the degree of difference between elements i and j and element c.
3) Determining the element with the maximum difference degree and the grouping, dividing the element with the maximum difference degree into the grouping with the maximum difference degree, turning to the step (5), and processing the element pair (i, j); the element and the grouping with the greatest degree of difference are determined according to the following formula:
in order to verify the beneficial effects of the invention, the inventor carries out a comparison experiment by adopting the method of the embodiment 1 of the invention and a traditional random grouping method and a grouping method based on k-means clustering, and the experimental method is as follows:
the number of students N is 10-90, M is 4, the interval is 10, the grouping number K is 2-18, the interval is 2, and the attribute characteristic value of each student is randomly selected from 1-50. The grouping method used for 9 groups was the same as in example 1, each group of experiments was performed 100 times, and the average was taken as the final performance.
The number of students was the same as in example 1, and experiments were conducted according to the method of example 1, the conventional random grouping method, and the grouping method based on k-means clustering.
The indexes of the minimum difference degree in the group of the 3 methods are compared, wherein the minimum difference degree in the group MinGroupDiff can be represented by the following formula:
where K is the number of groups, S (K) is the set of elements contained in the kth group, dijRepresenting the degree of difference between element i and element j. As can be seen from this formula, in one division result, the index value is larger if the minimum degree of difference between elements included in all the groups is larger. The method for improving the index is to improve the minimum difference degree between elements of each group, and the difference degree of all the innermost elements needs to be improved.As can be seen, the index can reflect whether the degree of difference between all the elements in the group is increased.
The results of the performance comparison of the three methods on the minimum difference index within the group are shown in fig. 2. In fig. 2, ours represents grouping results using the method of embodiment 1, random represents grouping results using a conventional random grouping method, and kmeans represents grouping results using a k-means clustering-based grouping method. As can be seen from fig. 2, the minimum difference degree within the group of the three methods gradually decreases as the number of elements increases. The experimental group has a remarkable improvement effect under the condition of various different element numbers, and particularly when the element number is more than 30, the minimum difference degree in the experimental group is more than 2 times of that of other methods.
The present disclosure has been described in detail, and the principles and embodiments of the present disclosure have been explained herein by using specific examples, which are provided only for the purpose of helping understanding the method and the core concept of the present disclosure; meanwhile, for those skilled in the art, according to the idea of the present disclosure, there may be variations in the specific embodiments and the application range, and the content of the present specification should not be construed as a limitation of the present disclosure.
Claims (6)
1. A difference-based learning group grouping method is characterized by comprising the following steps:
(1) collecting attribute features of N elements
Attribute feature v of ith elementiExpressed as a vector:
vi＝(ai1,ai2,...,aim,...,aiM)
wherein each component aimA quantized value, a, representing the element i corresponding to the mth attribute featureimThe method comprises the following steps that M represents attribute feature numbers of elements, i belongs to {1,2,. and N }, M belongs to {1,2,. and M }, and M, N is a finite positive integer;
(2) determining the number of groups and the number of elements contained
Determining the grouping number K according to the actual requirement, and determining the number f (K) of elements contained in the kth grouping according to the formula (1):
wherein K belongs to {1, 2.,. K }, N mod K represents a remainder obtained by dividing N by K, and K is a finite positive integer;
(3) normalizing attribute features of N elements
The m-th attribute feature value a of any element i according to equation (2)imAnd (4) carrying out standardization:
wherein, mumMean value of characteristic values of the m-th attribute representing all elements, i.e.
μm＝(a1m+a2m+...+aNm)/N，σmRepresents the standard deviation of the m-th attribute feature values of all elements,
(4) determining degrees of difference between pairs of elements and ordering
Degree of difference d between pairs of elements consisting of any two elements i, jijDetermined according to equation (3):
wherein, biAnd bjRespectively representing standardized attribute feature vectors of an element i and an element j, wherein i, j belongs to {1, 2.. once, N }, i is not equal to j;
bi＝(bi1,bi2,...,biM)
bj＝(bj1,bj2,...,bjM)
(bi－bj)Trepresents a vector (b)i－bj) Transposing; s represents the sum of the feature vectors of the respective attributesCovariance matrix is M dimensional matrix, and arbitrary element in S is Si'j'Represents:
Si'j'＝cov(ui',uj')/(m-1)
wherein u isi'And uj'Respectively representing the vectors formed by normalizing the ith' and jth attribute features in all elements, i.e.
ui'＝(b1i',b2i',...,bNi')
uj'＝(b1j',b2j',...,bNj')
cov(ui',uj') Represents a vector ui'And uj'Covariance therebetween, i.e.
cov(ui',uj')＝E[(ui'-μi')(uj'-μj')]
Wherein, mui'And muj'The normalized mean values of the i 'th and j' th attribute feature values respectively representing all elements, i.e.
μi'＝(b1i'+b2i'+...+bNi')/N
μj'＝(b1j'+b2j'+...+bNj')/N
Wherein i ', j' is e {1, 2.., M };
(5) processing each element pair (i, j)
Grouping is performed using a diversity-based grouping method.
2. The variability-based learning group grouping method of claim 1, wherein in the step (5) of processing each element pair (i, j), the variability-based learning group grouping method is:
one element of the element pair (i, j) is not assigned to the group, one element is assigned to the group, the unassigned element is s, where s ∈ { i, j }, and the group is grouped in the absence of a group that does not contain any element by:
1) determining the degree of dissimilarity d (s, k ') of the element s to the grouping k' of each allocable element as follows:
wherein S (k ') represents the set of allocated elements in the grouping k' of allocable elements, dscRepresenting the difference between the element S and the element c, the group k ' of allocable elements means that the number of the allocated elements in the group k ' is less than the number f (k) of the elements contained in the group determined in step (2), i.e. | S (k '), (k;) is<f (k), the set Q(s) of groupings of allocable elements s is represented by:
Q(s)＝{k'||S(k')|<f(k)}；
2) allocating the element s to the grouping k 'with the largest difference degree in the grouping k' of the allocable elements, and processing the next element pair; k "is determined as follows:
where q(s) represents a grouped collection of allocable elements s.
3. The variability-based learning group grouping method of claim 1, wherein in the step (5) of processing each element pair (i, j), the variability-based learning group grouping method is: processing each element pair (i, j) in step (5); the element pair (i, j) is: if both the i and j element pairs have been assigned to a group, the next element pair is processed.
4. The variability-based learning group grouping method of claim 1, wherein in the step (5) of processing each element pair (i, j), the variability-based learning group grouping method is: processing each element pair (i, j) in step (5); the element pair (i, j) is: one element of the element pair (i, j) is not assigned to the group, one element is assigned to the group, the unassigned element is s, where s e { i, j }, and when there is a group l that does not contain any element, l e {1, 2.
5. The variability-based learning group grouping method of claim 1, wherein in the step (5) of processing each element pair (i, j), the variability-based learning group grouping method is: processing each element pair (i, j) in step (5), the element pair (i, j) is: neither element of the pair (i, j) is assigned to a group, there is a group l "that does not contain any element, element j is assigned to the group l", i "e {1, 2.. multidata., K }, and step (5) is performed to process element pair (i, j) again.
6. The variability-based learning group grouping method of claim 1, wherein in the step (5) of processing each element pair (i, j), the variability-based learning group grouping method is: neither element of the pair (i, j) of elements is assigned to a group, there is no group containing any element, further comprising the steps of:
1) determining a grouping set Q of allocable elements of the element i and the element j, wherein the grouping corresponding to each element in the grouping set Q of the allocable elements can further contain at least one element;
2) determining the degree of disparity of element i and element j to each assignable element's grouping k', respectively, i.e.
Wherein k' is belonged to Q, dicAnd djcRespectively representing the difference degrees of the elements i and j and the element c;
3) determining the element with the maximum difference degree and the grouping, dividing the element with the maximum difference degree into the grouping with the maximum difference degree, turning to the step (5), and processing the element pair (i, j); the element and the grouping with the greatest degree of difference are determined according to the following formula:
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