CN106997553A - Multi-objective optimization-based commodity combination mode mining method - Google Patents

Multi-objective optimization-based commodity combination mode mining method Download PDF

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CN106997553A
CN106997553A CN201710237451.0A CN201710237451A CN106997553A CN 106997553 A CN106997553 A CN 106997553A CN 201710237451 A CN201710237451 A CN 201710237451A CN 106997553 A CN106997553 A CN 106997553A
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张磊
张鑫
张兴义
段富臣
程凡
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Anhui University
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Abstract

The invention discloses a method for mining a commodity combination mode based on multi-objective optimization, which converts the problem of mining the commodity combination mode in a commodity transaction database into the problem of multi-objective optimization and solves the problem of mining the commodity combination mode in the commodity transaction database through problem conversion, population initialization and population evolution. The invention solves the problem of singleness of the commodity combination mode in the commodity transaction database, provides various module combinations for users to select, and can improve the accuracy and effectiveness of mining the commodity combination mode in the commodity transaction database.

Description

A kind of method for digging of the grouping of commodities pattern based on multiple-objection optimization
Technical field
Recommend field the present invention relates to optimization model collection in grouping of commodities pattern, it is more specifically a kind of to be based on multiple target The method for digging of the grouping of commodities pattern of optimization.
Background technology
With the arrival of Internet era, the application of the task based access control driving in many reality emerges, in this field In, user just continuously attempts to realize that one constitutes task by the subtask in many daily record datas.This usual daily record data can Transaction database can be depicted as, each affairs contain the subtask selected by user.Based on this transaction database On the basis of, grouping of commodities mode excavation is directed to finding recommendation method frequently with most integrated pattern.At present, existing pattern is dug Dig in algorithm, it is desirable to which user specifies the support critical value min_sup, the occupancy critical value min_ of bottom line of bottom line Occ, and between two indexs, importance associated priority λ.However, for a user, selecting these Study firsts normal It is difficult often, especially in the case that the knowledge for not having priori in application scenarios is for reference.
Optimal grouping of commodities set of patterns in current grouping of commodities mode excavation recommends problem to include two class research methods：
One class research method is the DOFIA algorithms based on transaction database, and frequent mould is enumerated using " dictionary subset tree " Formula, the dictionary subset tree representation whole search space of algorithm, by depth-first traversal (Depth First Search, DFS) scanned for reference to the strategy of beta pruning, obtain the dictionary subset tree of final transaction database.But DOFIA needs user Preset necessary parameter, i.e. min_sup, min_occ and λ.Lack the premise of the priori in corresponding field in user Under, user is difficult to provide a rational parameter to run algorithm, and parameter set no matter for algorithm run time Or very big influence is suffered from operation result, algorithm operation can be caused if parameter setting is too small slowly, user is difficult to bear By, and if parameter setting it is excessive can make algorithm in search procedure excessive beta pruning so that optimal solution is cut up.
One class research method is that have many in the DOFRA algorithms based on time series database, DOFIA and DOFRA algorithm flows Similarity, just for data set it is different.Although algorithm can to dictionary subset tree carry out beta pruning, but the efficiency of beta pruning with Effect is influenceed very big by parameter, it is difficult to general.Finally, traditional algorithm is the mathematics in classic multiple-objection optimization period by the way of The mode of planning, search is optimized by being converted to multiple targets progress linear weighted function again after single goal.But this method As the defect of classic Multipurpose Optimal Method, each algorithm can only obtain an optimal solution, and user may more need What is wanted is to select the most suitable solution of oneself from one group of compromise solution, therefore can only be by changing mesh for traditional algorithm Weight proportion λ between mark obtains different solutions algorithm is run multiple times, and more bothers.
The content of the invention
There is provided a kind of=grouping of commodities pattern based on multiple-objection optimization to overcome in place of the deficiencies in the prior art by the present invention Method for digging, to which the accuracy and validity that grouping of commodities pattern in merchandising database is recommended can be improved, so as to be user Recommend one group of optimal Top-K set of patterns, user is selected optimal grouping of commodities pattern according to the demand of oneself.
The present invention adopts the following technical scheme that to solve technical problem：
A kind of the characteristics of method for digging of grouping of commodities pattern based on multiple-objection optimization of the present invention is to enter as follows OK：
Step 1, make commodity transaction database be D, D={ X1,X2,…,Xi,…,X|τ|Represent the commodity Transaction Information The set of all grouping of commodities patterns, X in storehouseiI-th of grouping of commodities pattern is represented, | τ | it is the sum of grouping of commodities pattern；Time Going through sum in commodity transaction database D is | τ | grouping of commodities pattern, obtain the item of merchandise number under each grouping of commodities pattern And in the commodity transaction database D variety classes item of merchandise number | N |；
Any one grouping of commodities pattern X Mining Problems are converted to the multi-objective optimization question as shown in formula (1) Maximize F(X)：
Maximize F (X)=(supp (X), occu (X), area (X))T (1)
In formula (1), supp (X) represents the support of the grouping of commodities pattern X, and has：
Supp (X)=freq (X)/| τ | (2)
In formula (2), freq (X) represents the frequency of the grouping of commodities pattern X；
In formula (1), occu (X) represents the occupancy of the grouping of commodities pattern X, and has：
In formula (3), | X | represent the number of item of merchandise in the grouping of commodities pattern X, τXBe it is all include grouping of commodities mould The support affairs of Formula X；T represents any one support affairs for including grouping of commodities pattern X；
In formula (1), area (X) represents the covering domain of the grouping of commodities pattern X, and：
Step 2, using the Multipurpose Optimal Method calculated based on fitness to all in the commodity transaction database D Grouping of commodities pattern changes optimizing for multi-objective optimization question, so as to obtain one group of optimal grouping of commodities set of patterns；
Step 2.1, kind group coding：
According to the item of merchandise species number of all grouping of commodities patterns in the commodity transaction database D, using binary system Mode is encoded to all item of merchandise in grouping of commodities pattern X, obtains the individual X={ x of grouping of commodities pattern1, x2,…,xi,…,x|N|}；xiI-th of item of merchandise in grouping of commodities pattern X is represented, if xiDeposited in=1 expression grouping of commodities pattern X In i-th of item of merchandise, if xi=0 represents that i-th of item of merchandise is not present in grouping of commodities pattern X；So as to right | τ | individual grouping of commodities Pattern is encoded, the commodity transaction database D ' after being encoded；
According to the number of variety classes item of merchandise in the commodity transaction database D | N |, make being encoded to for item of merchandise Y " 1 ", remaining | N | -1 item of merchandise is encoded to " 0 ", so as to obtain an individual for commodity meta schema；
Step 2.2, initialization population：
Step 2.2.1, definition Population Size are popSize；Make popSize=(| N |/50+1) × 50；
If popSize/2≤| N |, from commodity meta schema | N | random selection popSize/2 constitutes initial in individual Change the half of population；From commodity transaction mode | τ | random selection popSize/2 constitutes the another of initialization population in individual Half；
If popSize/2 ＞ | N |, in selection commodity meta schema | N | individual is used as the part for initializing population； Remainder is from commodity transaction mode | N | randomly choosed in individual；
Commodity transaction database D ' after step 2.2.2, the traversal coding, so as to the institute in the initialization population There is individual to be matched, and all individual corresponding supports obtained in the initialization population, frequency are calculated using formula (1) Numerous degree and covering domain；
Step 2.2.3, using non-dominated ranking algorithm to it is described initialization population be ranked up, having after being sorted The population of multiple leading surfaces；
Step 2.2.4, the crowding distance according to the population with multiple leading surfaces after the Euclidean distance calculating sequence, And according to resulting crowding distance, descending sort is carried out to the population with multiple leading surfaces after the sequence, obtained again The population with multiple leading surfaces after minor sort；
Step 2.3, Evolution of Population：
Step 2.3.1, initialization iterations L=0；
Step 2.3.2, using algorithm of tournament selection strategy to the population with multiple leading surfaces after the minor sort again Selected, obtain the pond that mates, be used as the population of the L times iteration；
Step 2.3.3, cross and variation is carried out to the individual in the population of the L times iteration produce the L+1 times iteration Population；
Commodity transaction database D ' after step 2.3.4, the traversal coding, so as to the kind of the L+1 times iteration All individuals in group are matched, and utilization formula (1) calculating obtains all individual corresponding in the population of the L+1 times iteration Support, frequency and covering domain；
Step 2.3.5, using non-dominated ranking the population of the L+1 times iteration is ranked up, after being sorted The population with multiple leading surfaces of the L+1 times iteration；
Step 2.3.6, the kind with multiple leading surfaces according to the L+1 times iteration after the Euclidean distance calculating sequence The crowding distance of group, and according to resulting crowding distance, there are multiple leading surfaces to the L+1 times iteration after the sequence Population carry out descending sort, obtain according to the L+1 time iteration after crowding distance descending sort with multiple leading surfaces Population；
Step 2.3.7, L+1 is assigned to L；And step 2.3.2 is repeated, until obtaining continuous σ between population Untill similarity meets threshold condition, so as to obtain the population after final iteration；
Step 2.4, using non-dominated ranking algorithm the individual in the population after final iteration is ranked up, sorted The candidate population with multiple leading surfaces afterwards；
Step 2.5, from the candidate population with multiple leading surfaces after the sequence select first leading surface in institute There is individual；
Step 2.6, Top-K individual of all individual choices is used as one group of optimal commodity from first leading surface Integrated mode collection is exported.
Compared with the prior art, the present invention has the beneficial effect that：
1st, the grouping of commodities mode excavation problem in commodity transaction database is converted into based on multiple-objection optimization by the present invention Grouping of commodities mode excavation problem, grouping of commodities mode excavation is solved the problems, such as by using multi-objective Evolutionary Algorithm；The party The calculating that method passes through correct objective function and fitness, it is possible to which one group obtained in commodity transaction database is optimal Grouping of commodities set of patterns, makes the selection variation of user；This method can solve search without the concern for the setting of Study first Efficiency with effect by the far-reaching problem of parameter, while can solve dictionary subset tree in DOFRA and DOFIA it is excessively huge and Cause the problem of search efficiency is greatly reduced, so as to greatly enhance the efficiency of grouping of commodities mode excavation.
2nd, in current method for digging, resulting Result is single pattern, very single, it is impossible to meet various use The demand at family, the present invention can be very good to solve this hardly possible by the method based on multiple-objection optimization using the calculating of fitness Topic, so as to recommend one group of optimal grouping of commodities set of patterns for user, selects according to the demand of oneself for user, makes the Result be in Existing diversity.
3rd, the present invention is not required to set Study first min_sup, min_occ and λ, it is to avoid Study first sets inaccurate band The problem of mining mode number come excessively or in mining process omits important model, makes Result more complete.
4th, the present invention is directed to grouping of commodities mode excavation problem, proposes an overall initialization strategy, and this strategy can be with Ensure that the individual of initialization generation is all useful, and remain a good diversity in actual applications.
5th, the present invention recommends optimal grouping of commodities mode issue using fitness calculating by multi-objective Evolutionary Algorithm, Methods described need not too worry that the space enumerated in DOFIA and DOFRA algorithms will be with the increasing of transaction database middle term Plus and show the trend of exponential growth, something which increases the validity of mode excavation and accuracy.
Brief description of the drawings
Fig. 1 is the inventive method flow chart；
Schematic diagram of the problem of Fig. 2 a is the present invention conversion with planting group coding；
Fig. 2 b are multi-objective Evolutionary Algorithm flow chart of the present invention；
Fig. 2 c recommend figure for optimal grouping of commodities pattern of the invention.
Embodiment
In the present embodiment, a kind of method for digging of the grouping of commodities pattern based on multiple-objection optimization is by commodity Transaction Information Tie-in sale problem is converted into the Mining Problems of the grouping of commodities pattern based on multiple-objection optimization in storehouse, passes through the calculating of fitness To solve the problems, such as the recommendation of optimal grouping of commodities pattern in commodity transaction database, so as to obtain final in commodity transaction database Optimal grouping of commodities set of patterns；As shown in figure 1, specifically carrying out as follows：
Step 1, make commodity transaction database be D, D={ X1,X2,…,Xi,…,X|τ|Represent the commodity Transaction Information The set of all grouping of commodities patterns, X in storehouseiI-th of grouping of commodities pattern is represented, | τ | it is the sum of grouping of commodities pattern；Time Going through sum in commodity transaction database D is | τ | grouping of commodities pattern, obtain the item of merchandise number under each grouping of commodities pattern And in the commodity transaction database D variety classes item of merchandise number | N |；
Any one grouping of commodities pattern X Mining Problems are converted to the multi-objective optimization question as shown in formula (1) Maximize F(X)：
Maximize F (X)=(supp (X), occu (X), area (X))T (1)
In formula (1), supp (X) represents the support of the grouping of commodities pattern X, and has：
Supp (X)=freq (X)/| τ | (2)
In formula (2), freq (X) represents the frequency of the grouping of commodities pattern X；
In formula (1), occu (X) represents the occupancy of the grouping of commodities pattern X, and has：
In formula (3), | X | represent the number of item of merchandise in the grouping of commodities pattern X, τXBe it is all include grouping of commodities mould The support affairs of Formula X；T represents any one support affairs for including grouping of commodities pattern X；
In formula (1), area (X) represents the covering domain of the grouping of commodities pattern X, and：
Step 2, using the Multipurpose Optimal Method calculated based on fitness to all in the commodity transaction database D Grouping of commodities pattern changes optimizing for multi-objective optimization question, so as to obtain one group of optimal grouping of commodities set of patterns； Fig. 2 a, Fig. 2 b and Fig. 2 c are the quick-reading flow sheets schematic diagram of the present invention, and such as Fig. 2 a top halfs show many after conversion Objective optimisation problems；
Step 2.1, kind group coding：
According to the item of merchandise species number of all grouping of commodities patterns in the commodity transaction database D, using binary system Mode is encoded to all item of merchandise in grouping of commodities pattern X, obtains the individual X={ x of grouping of commodities pattern1, x2,…,xi,…,x|N|}；xiI-th of item of merchandise in grouping of commodities pattern X is represented, if xiDeposited in=1 expression grouping of commodities pattern X In i-th of item of merchandise, if xi=0 represents that i-th of item of merchandise is not present in grouping of commodities pattern X；So as to right | τ | individual grouping of commodities Pattern is encoded, the commodity transaction database D ' after being encoded；As Fig. 2 a the latter half show commodity transaction database D In certain five grouping of commodities pattern encoding examples, by taking one of commodity transaction mode W={ A, B, D } as an example, because commodity Item { C, E } does not occur, so that commodity transaction mode W's is encoded to { 1,1,0,1,0 }；
According to the number of variety classes item of merchandise in the commodity transaction database D | N |, make being encoded to for item of merchandise Y " 1 ", remaining | N | -1 item of merchandise is encoded to " 0 ", so as to obtain an individual for commodity meta schema；
Step 2.2, initialization population：
Step 2.2.1, definition Population Size are popSize；Make popSize=(| N |/50+1) × 50；
If popSize/2≤| N |, from commodity meta schema | N | random selection popSize/2 constitutes initial in individual Change the half of population；From commodity transaction mode | τ | random selection popSize/2 constitutes the another of initialization population in individual Half；
If popSize/2 ＞ | N |, in selection commodity meta schema | N | individual is used as the part for initializing population； Remainder is from commodity transaction mode | N | randomly choosed in individual；
Commodity transaction database D ' after step 2.2.2, the traversal coding, so as to the institute in the initialization population There is individual to be matched, and all individual corresponding supports obtained in the initialization population, frequency are calculated using formula (1) Numerous degree and covering domain；
Step 2.2.3, using non-dominated ranking algorithm to it is described initialization population be ranked up, having after being sorted The population of multiple leading surfaces；
Step 2.2.4, the crowding distance according to the multifaceted population after the Euclidean distance calculating sequence, and according to institute Obtained crowding distance, descending sort is carried out to the population with multiple leading surfaces after the sequence, obtain according to it is crowded away from From the population with multiple leading surfaces after descending sort；
Step 2.3, Evolution of Population：
Step 2.3.1, initialization iterations L=0；
Step 2.3.2, using algorithm of tournament selection strategy to after the descending sort according to crowding distance have it is multiple The population of leading surface is selected, and obtains mate pond, i.e., the population of the L times iteration；
Step 2.3.3, cross and variation is carried out to the individual in the population of the L times iteration produce the L+1 times iteration Population；
Commodity transaction database D ' after step 2.3.4, the traversal coding, so as to the kind of the L+1 times iteration All individuals in group are matched, and utilization formula (1) calculating obtains all individual corresponding in the population of the L+1 times iteration Support, frequency and covering domain；
Step 2.3.5, using non-dominated ranking the population of the L+1 times iteration is ranked up, after being sorted The population with multiple leading surfaces of the L+1 times iteration；
Step 2.3.6, the kind with multiple leading surfaces according to the L+1 times iteration after the Euclidean distance calculating sequence The crowding distance of group, and according to resulting crowding distance, there are multiple leading surfaces to the L+1 times iteration after the sequence Population carry out descending sort, obtain according to the L+1 time iteration after crowding distance descending sort with multiple leading surfaces Population；
Step 2.3.7, L+1 is assigned to L；And step 2.3.2 is repeated, until obtaining continuous σ between population Untill similarity meets threshold condition, so as to obtain the population after final iteration；As shown in Figure 2 b, iteration terminates, and obtains most Population after whole iteration；
Step 2.4, using non-dominated ranking algorithm the individual in the population after final iteration is ranked up, sorted The candidate population with multiple leading surfaces afterwards；
Step 2.5, from the candidate population with multiple leading surfaces after the sequence select first leading surface in institute There is individual；
Step 2.6, Top-K individual of all individual choices is used as one group of optimal commodity from first leading surface Integrated mode collection is exported.As shown in Figure 2 c, grouping of commodities patterns all in first leading surface are obtained, and select Top-K Grouping of commodities pattern recommends user as one group of optimal grouping of commodities pattern, is selected for user.

Claims (1)

1. a kind of method for digging of the grouping of commodities pattern based on multiple-objection optimization, it is characterized in that carrying out as follows：
Step 1, make commodity transaction database be D, D={ X1,X2,…,Xi,…,X|τ|Represent in the commodity transaction database The set of all grouping of commodities patterns, XiI-th of grouping of commodities pattern is represented, | τ | it is the sum of grouping of commodities pattern；Travel through business Sum is in product transaction database D | τ | grouping of commodities pattern, obtain item of merchandise number under each grouping of commodities pattern and The number of variety classes item of merchandise in the commodity transaction database D | N |；
Any one grouping of commodities pattern X Mining Problems are converted to the multi-objective optimization question as shown in formula (1) MaximizeF(X)：
MaximizeF (X)=(supp (X), occu (X), area (X))T (1)
In formula (1), supp (X) represents the support of the grouping of commodities pattern X, and has：
Supp (X)=freq (X)/| τ | (2)
In formula (2), freq (X) represents the frequency of the grouping of commodities pattern X；
In formula (1), occu (X) represents the occupancy of the grouping of commodities pattern X, and has：
o c c u ( X ) = 1 | τ X | Σ t ∈ τ X | X | t - - - ( 3 )
In formula (3), | X | represent the number of item of merchandise in the grouping of commodities pattern X, τXBe it is all include grouping of commodities pattern X Support affairs；T represents any one support affairs for including grouping of commodities pattern X；
In formula (1), area (X) represents the covering domain of the grouping of commodities pattern X, and：
a r e a ( X ) = f r e q ( X ) · | X | Σ t ∈ τ X | t | - - - ( 4 )
Step 2, using the Multipurpose Optimal Method calculated based on fitness to commodity all in the commodity transaction database D Integrated mode changes optimizing for multi-objective optimization question, so as to obtain one group of optimal grouping of commodities set of patterns；
Step 2.1, kind group coding：
According to the item of merchandise species number of all grouping of commodities patterns in the commodity transaction database D, using binary mode All item of merchandise in grouping of commodities pattern X are encoded, the individual X={ x of grouping of commodities pattern are obtained1,x2,…, xi,…,xN}；xiI-th of item of merchandise in grouping of commodities pattern X is represented, if xi=1 represents exist i-th in grouping of commodities pattern X Item of merchandise, if xi=0 represents that i-th of item of merchandise is not present in grouping of commodities pattern X；So as to right | τ | individual grouping of commodities pattern is entered Row coding, the commodity transaction database D ' after being encoded；
According to the number of variety classes item of merchandise in the commodity transaction database D | N |, make item of merchandise Y's to be encoded to " 1 ", its It is remaining | N | -1 item of merchandise is encoded to " 0 ", so as to obtain an individual for commodity meta schema；
Step 2.2, initialization population：
Step 2.2.1, definition Population Size are popSize；Make popSize=(| N |/50+1) × 50；
If popSize/2≤| N |, from commodity meta schema | N | random selection popSize/2 constitutes initialization kind in individual The half of group；From commodity transaction mode | τ | random selection popSize/2 constitutes second half of initialization population in individual；
If popSize/2 ＞ | N |, in selection commodity meta schema | N | individual is used as the part for initializing population；It is remaining Partly from commodity transaction mode | N | randomly choosed in individual；
Commodity transaction database D ' after step 2.2.2, the traversal coding, so as to all in the initialization population Body is matched, and all individual corresponding supports, the frequency obtained in the initialization population is calculated using formula (1) And covering domain；
Step 2.2.3, using non-dominated ranking algorithm the initialization population is ranked up, after sort with multiple The population of leading surface；
Step 2.2.4, the crowding distance according to the population with multiple leading surfaces after the Euclidean distance calculating sequence, and root According to resulting crowding distance, descending sort is carried out to the population with multiple leading surfaces after the sequence, arranged again The population with multiple leading surfaces after sequence；
Step 2.3, Evolution of Population：
Step 2.3.1, initialization iterations L=0；
Step 2.3.2, the tactful progress of the population with multiple leading surfaces to after the minor sort again using algorithm of tournament selection Selection, obtains the pond that mates, is used as the population of the L times iteration；
Step 2.3.3, the population that cross and variation the L+1 times iteration of generation is carried out to the individual in the population of the L times iteration；
Commodity transaction database D ' after step 2.3.4, the traversal coding, so that in the population of the L+1 times iteration All individuals matched, and all individual corresponding branch obtained in the population of the L+1 times iteration are calculated using formula (1) Degree of holding, frequency and covering domain；
Step 2.3.5, using non-dominated ranking the population of the L+1 times iteration is ranked up, the L+1 after being sorted The population with multiple leading surfaces of secondary iteration；
Step 2.3.6, the population with multiple leading surfaces for calculating according to Euclidean distance the L+1 times iteration after the sequence Crowding distance, and according to resulting crowding distance, to the kind with multiple leading surfaces of the L+1 times iteration after the sequence Group carries out descending sort, obtains the population with multiple leading surfaces according to the L+1 times iteration after crowding distance descending sort；
Step 2.3.7, L+1 is assigned to L；And step 2.3.2 is repeated, until obtaining continuous σ for similar between population Untill degree meets threshold condition, so as to obtain the population after final iteration；
Step 2.4, using non-dominated ranking algorithm the individual in the population after final iteration is ranked up, after being sorted Candidate population with multiple leading surfaces；
Step 2.5, from the candidate population with multiple leading surfaces after the sequence select all in first leading surface Body；
Step 2.6, Top-K individual of all individual choices is used as one group of optimal grouping of commodities from first leading surface Set of patterns is exported.
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