CN106682963A - Recommendation system data completion method based on convex optimization local low-rank matrix approximation - Google Patents
Recommendation system data completion method based on convex optimization local low-rank matrix approximation Download PDFInfo
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- CN106682963A CN106682963A CN201611250239.XA CN201611250239A CN106682963A CN 106682963 A CN106682963 A CN 106682963A CN 201611250239 A CN201611250239 A CN 201611250239A CN 106682963 A CN106682963 A CN 106682963A
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q30/00—Commerce
- G06Q30/02—Marketing; Price estimation or determination; Fundraising
- G06Q30/0241—Advertisements
- G06Q30/0251—Targeted advertisements
- G06Q30/0269—Targeted advertisements based on user profile or attribute
- G06Q30/0271—Personalized advertisement
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q30/00—Commerce
- G06Q30/06—Buying, selling or leasing transactions
- G06Q30/0601—Electronic shopping [e-shopping]
- G06Q30/0631—Item recommendations
Abstract
The invention relates to a recommendation system data completion method based on convex optimization local low-rank matrix approximation. The method includes the steps of 1) constructing a recommendation system data matrix M according to the user's rating of a product in a recommendation system, and representing the data on unrated products by the user as 0 element in M; 2) selecting anchor points, dividing the recommendation system data matrix into a plurality of local matrices using a kernel smoothing method, the number of local matrices being the same as the number of the anchor points; and 3) solving a matrix completion model according to a convex optimization local low-rank matrix approximation algorithm, and completing the 0 element in the matrix M according to the matrix completion model to obtain a recommendation system data matrix X after completion. Compared with the prior art, the invention can finish the recommendation system matrix data completion while guaranteeing the operation speed and the accuracy.
Description
Technical field
The present invention relates to commending system field, more particularly, to a kind of recommendation approximate based on convex optimization local low-rank matrix
System data complementing method.
Background technology
Currently, personalized ventilation system is widely used in reality.The primary product of personalized ventilation system is exactly to recommend
System, commending system is, according to the passing record information of user, including purchaser record, to browse record, scoring etc., carrys out analyses and prediction
User excavates potential consumption demand for the fancy grade of other products.
Commending system does not only have very big learning value, and the focus studied, many electronics business are even more in e-commerce field
Business system recommends customized information by commending system to user, the every annual sales revenues of such as e-commerce website Amazon
20% -30% from commending system；Movie rental website Netflix has nearly 60% user to be found certainly by commending system
Oneself film interested.
1992, GoWberg et al. proposed first collaborative filtering, and establishes first personalized recommendation system
System.In March nineteen ninety-five, there is scholar to propose the Web Watcher systems of Personalized Navigation, the scholar of Stanford University then proposes
LIRA personalized recommendation systems.The research worker of University of Minnesota in 1997 creates online film commending system
MovieLens, is the progress of an initiative in the development of collaborative filtering recommending technology, and MovieLens is by using user to electricity
Shadow degree interested recommends it possible interested and film that is not seen with collaborative filtering recommending technology to user.
Calendar year 2001, Gediminas Adoavicius of New York University et al. are proposed based on the ecommerce of user modeling
Commending system 1Pro；IBM is realized based on the personalized recommendation system Webspheret of correlation rule.Calendar year 2001, Amazon will
Commending system is applied in e-commerce system, and personalized recommendation starts from academic research to march toward practical application, hereafter, cooperates with
Filter proposed algorithm obtains huge success and is widely applied in e-commerce system.2006, Netflix set up
NetflixPrize, it is desirable to which entrant realizes a commending system using the data set of its company's offer so that RMSE (Root
Mean Square Error) RMSE in mean square deviation error ratio NetFlix system improves 10%, and its bonus is 1,000,000 dollars,
The match causes very big sensation, and numerous research worker is bounded oneself to it.2007, Google was nearest according to user
The hobby of digging user is removed in search, so as to be supplied to user individual to push away in online advertisement AdWorks according to keyword
Recommend service.
1999, Tsing-Hua University's road hamming et al. proposed the hybrid intelligent personalized recommendation based on multi-agent technology and takes
Business.2000, bright and beautiful phoenix et al. Personalized service that begins one's study more than Peking University.Calendar year 2001, Pan Jingui of Nanjing University etc.
People have developed personalized information retrieval intelligence system DOLTRI-AgentPW；Tsing-Hua University Feng Korea Spro et al. devises mixing and recommends system
System OpenBookmarkPU, the system mixed vector space law is recommended with collaborative filtering method.2002, Shanghai University of Science and Technology
Old generation equality people devises the intelligent retrieval system Myspy of domain-oriented, and using multi-agent technology Web document index number is ingeniously managed
According to storehouse.Deng Ailin's in 2003 et al.《Collaborative Filtering Recommendation Algorithm based on article score in predicting》；Surplus energy in 2004 etc.《Electricity
Sub- commercial affairs personalized recommendation research》；Peng Yu's in 2007 etc.《Item-based collaborative filterings based on attribute similarity》；
The towering grades of Peng De in 2009《It is a kind of based on user characteristicses and the Collaborative Filtering Recommendation Algorithm of time》These outstanding papers are represented
Development of china academia circle in personalization technology.2008, the Taobao under Alibaba was proposed personalized recommendation system
System, it is intended to help user that oneself article interested is searched in substantial amounts of commodity.2011, Baidu was proposed personalized recommendation
Homepage, according to the interest of user and behavior the information of its demand is met to its recommendation.2014, Alibaba held ＂ days cats and pushes away
Algorithm contest ＂ is recommended, the research boom of the country has been started.
But, recently as developing rapidly for the Internet and ecommerce, number of users and number of articles all become
Very huge numeral, and this two groups of huge numerals are combined into huger user-article rating matrix, but, by
The article that can be contacted in each user is limited, by user beat it is undue can only account for minority so that the user-article is commented
Most numbers in sub-matrix are presented vacancy, and then it is higher openness that the user-article rating matrix is had, so
User is predicted when data recommendation system to during the scoring of a certain article, due to the scoring between user overlap it is less, by similar
The obvious accuracy of scoring that the score data of user carrys out a certain article prediction for user is not high.Therefore, how data to be set up
Comprehensively commending system is a need for the problem for solving.
The content of the invention
The purpose of the present invention is exactly the defect in order to overcome above-mentioned prior art to exist and provides a kind of based on convex optimization office
The approximate commending system Supplementing Data method of portion's low-rank matrix, can complete under conditions of arithmetic speed and accuracy is ensured
Commending system matrix data completion.
The purpose of the present invention can be achieved through the following technical solutions：
A kind of commending system Supplementing Data method approximate based on convex optimization local low-rank matrix, comprises the following steps：
1) scoring according to user in commending system to product builds commending system data matrix M, and user is not commented product
The data divided are in M with 0 element representation；
2) anchor point is chosen, the commending system data matrix is divided into by several local matrixes using core smoothing method,
The number of local matrix is identical with the number of the anchor point；
3) according to convex optimization local low-rank matrix approximate data solution matrix completion model, according to the matrix completion model
0 element in completion matrix M, obtains the commending system data matrix X after completion.
The step 1) it is specially：
Scoring of the user in commending system to product is divided into into five grades, is represented with 1 to 5, grade superelevation represents user
It is higher to the favorable rating of product, represent that user does not score product with 0, so as to form commending system data matrix M, and M ∈
Rm×n, meet condition：
Wherein, m, n represent the ranks value of user's number and product number, i.e. matrix M in commending system data, ПA(M) come
Represent that, from subscript to the mapping for corresponding to numerical value in M, A represents known data in M,
(ai,bi) represent M in known element.
The step 2) in anchor point be the uniform sample point for extracting from training set, wherein training set is from commending system
Data matrix M, size is the 50% of M.
The step 2) in, the core smooth function K that core smoothing method is adoptedhFor：
Kh(s1,s2)=(1-d (s1,s2)2)1[d(s1,s2) ＜ h]
Wherein, h is bandwidth, s1、s2Two elements in respectively matrix M, d (s1,s2) represent element s1,s2Between phase
Like property.
The step 2) in, have between each local matrix of acquisition and overlap.
The step 3) in, the matrix completion model for obtaining is solved according to convex optimization local low-rank matrix approximate data is：
s.t.XΩ=MΩ
Wherein, q is local matrix number,To seek trace norm,Represent the local moment of i-th anchor point determination
Matrix data after battle array completion, known element in Ω representing matrixs.
Compared with prior art, the present invention has advantages below：
(1) present invention based on the approximate method of local low-rank matrix reduce matrix be global low-rank it is assumed that, based on square
The global low-rank of battle array is assumed often to be limited to large-scale matrix, and assumes that matrix is Local approximation, more tallies with the actual situation, and more
Suitable for large-scale matrix data；
(2) it is that completely convex optimization is asked based on the approximate commending system Supplementing Data method of convex optimization local low-rank matrix
Topic, it is easier to solve and obtain optimal solution, improves the accuracy of completion matrix；
(3) the inventive method can be applied easily on personalized recommendation system, additionally, applying also for image recovery.
Description of the drawings
Fig. 1 is the schematic flow sheet of the present invention；
Fig. 2 is the schematic diagram that overall situation matrix of the invention is divided into multiple local matrixes.
Specific embodiment
Below in conjunction with the accompanying drawings the present invention is described in detail with specific embodiment.The present embodiment is with technical solution of the present invention
Premised on implemented, give detailed embodiment and specific operating process, but protection scope of the present invention is not limited to
Following embodiments.
As shown in figure 1, the present embodiment provides a kind of commending system data approximate based on convex optimization local low-rank matrix mending
Full method, comprises the following steps：
(1) scoring according to user in commending system to product builds commending system data matrix M, specifically, will recommend
Scoring of the user to product in system is divided into five grades, represents with 1 to 5, and grade superelevation represents that user likes journey to product
Degree is higher, represents that user does not score product with 0, so as to form commending system data matrix M, and M ∈ Rm×n, meet condition：
Wherein, m, n represent the ranks value of user's number and product number, i.e. matrix M in commending system data, ∏A(M) come
Represent that, from subscript to the mapping for corresponding to numerical value in M, A represents known data in M,
(ai,bi) represent M in known element.
0 element representation unknown data in matrix M, is the data for needing completion.
(2) anchor point is chosen, the commending system data matrix is divided into by several local matrixes using core smoothing method,
The number of local matrix is identical with the number of the anchor point, and has overlap between each local matrix for obtaining.Detailed process is such as
Under：
201) select anchor point first, there is that three kinds of methods are uniform from sample to extract anchor point here, first method be from
It is uniform in sample [m] × [n] to extract anchor point；Second method is that anchor point is extracted from training set；The third method is from survey
Choose on examination collection.The present invention is to adopt second method, and selects q anchor point.
202) the core smooth function for adopting is determined, conventional core smooth function has uniform kernel, triangular
Kernel and Epanechnikov kernel, the present invention uses Epanechnikov kernel, and formula is：
Kh(s1,s2)=(1-d (s1,s2)2)1[d(s1,s2) ＜ h]
Wherein, h is bandwidth, s1、s2Two elements in respectively matrix M, d (s1,s2) represent element s1,s2Between phase
Like property.
For the ranks of anchor point, the core SMOOTHING FORMULAE of concrete employing is：
Wherein, (a, b) and (c, d) is the ranks coordinate of two elements in matrix M, and K and K ' is respectively the core on row and column
Smooth function, h1,h2Bandwidth is represented, h is taken1=0.8, h2=0.8.
D in Epanechnikov kernel formula represents the similarity between element, for example, ask for user i and user j
Between similarity, formula is：
For the specific coordinate of q anchor point is (at,bt) wherein t=1 ..., q, solved as follows respectively：
From the rows of matrix M the 1st to the m rows of matrix：Calculate
Arrange to the n-th of matrix from matrix M the 1st and arrange：Calculate
203) finally calculateQ matrix of corresponding anchor is obtained, division result is as shown in Figure 2.
(3) according to convex optimization local low-rank matrix approximate data solution matrix completion model, according to the matrix completion mould
0 element in type completion matrix M, obtains the commending system data matrix X after completion.
The matrix completion model for obtaining is solved according to convex optimization local low-rank matrix approximate data is：
s.t.XΩ=MΩ
Wherein, q is local matrix number,To seek trace norm,Represent the local moment of i-th anchor point determination
Matrix data after battle array completion, known element in Ω representing matrixs.
The solution of above-mentioned matrix completion model is a convex optimization problem, can be solved using ADMM methods, so as to obtain
Matrix data X after completion.
Calculation is evaluated in commending system generally by the way that whether the prediction scoring and the actual scoring of user of proposed algorithm are close to
The accuracy of method.The accuracy for commonly using RMSE (root-mean-square error) now to judge to predict：
Calculate the value that matrix X and original matrix M in the embodiment of the present invention after completion calculate RMSE.
It is compared with the svd algorithm and LLORMA algorithms of current popular, as shown in table 1, RMSE is less for the result for obtaining
The accuracy for representing algorithm is better, finds that embodiment of the present invention effect is better than svd algorithm and LLORMA algorithms, explanation by result
The accuracy of the inventive method matrix completion is substantially better than and compares outstanding svd algorithm and LLORMA algorithms now.
Table 1
| SVD | LLORMA | The present invention | |
| R=5 | 0.8835 | 0.8604 | 0.8580 |
| R=10 | 0.8764 | 0.8444 | 0.8385 |
| R=15 | 0.8758 | 0.8365 | 0.8333 |
The above, the only specific embodiment of the present invention, but protection scope of the present invention is not limited thereto, any
Those familiar with the art the invention discloses technical scope in, the change or replacement that can be readily occurred in, all should
It is included within the scope of the present invention.Therefore, protection scope of the present invention should be with the scope of the claims
It is accurate.
Claims (6)
1. a kind of commending system Supplementing Data method approximate based on convex optimization local low-rank matrix, it is characterised in that include with
Lower step：
1) scoring according to user in commending system to product builds commending system data matrix M, and user does not score product
Data are in M with 0 element representation；
2) anchor point is chosen, the commending system data matrix is divided into by several local matrixes using core smoothing method, local
The number of matrix is identical with the number of the anchor point；
3) according to convex optimization local low-rank matrix approximate data solution matrix completion model, according to the matrix completion model completion
0 element in matrix M, obtains the commending system data matrix X after completion.
2. the commending system Supplementing Data method approximate based on convex optimization local low-rank matrix according to claim 1, its
It is characterised by, the step 1) it is specially：
Scoring of the user in commending system to product is divided into into five grades, is represented with 1 to 5, grade superelevation represents user to producing
The favorable rating of product is higher, represents that user does not score product with 0, so as to form commending system data matrix M, and M ∈ Rm×n,
Meet condition：
Wherein, m, n represent the ranks value of user's number and product number, i.e. matrix M in commending system data, ПA(M) representing M
In from subscript to the mapping of correspondence numerical value, A represents known data in M,(ai,
bi) represent M in known element.
3. the commending system Supplementing Data method approximate based on convex optimization local low-rank matrix according to claim 1, its
Be characterised by, the step 2) in anchor point be the uniform sample point for extracting from training set, wherein training set is from recommending system
System data matrix M, size is the 50% of M.
4. the commending system Supplementing Data method approximate based on convex optimization local low-rank matrix according to claim 1, its
It is characterised by, the step 2) in, the core smooth function K that core smoothing method is adoptedhFor：
Kh(s1,s2)=(1-d (s1,s2)2)1[d(s1,s2) ＜ h]
Wherein, h is bandwidth, s1、s2Two elements in respectively matrix M, d (s1,s2) represent element s1,s2Between it is similar
Property.
5. the commending system Supplementing Data method approximate based on convex optimization local low-rank matrix according to claim 1, its
It is characterised by, the step 2) in, have between each local matrix of acquisition and overlap.
6. the commending system Supplementing Data method approximate based on convex optimization local low-rank matrix according to claim 1, its
It is characterised by, the step 3) in, the matrix completion model for obtaining is solved according to convex optimization local low-rank matrix approximate data is：
Wherein, q is local matrix number,To seek trace norm,The local matrix for representing i-th anchor point determination is mended
Matrix data after complete, known element in Ω representing matrixs.
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|---|---|---|---|---|
| CN107689960A (en) * | 2017-09-11 | 2018-02-13 | 南京大学 | A kind of attack detection method for inorganization malicious attack |
| CN109785656A (en) * | 2019-03-18 | 2019-05-21 | 南京大学 | A kind of traffic programme and air navigation aid based on Local approximation order |
| CN110322053A (en) * | 2019-06-13 | 2019-10-11 | 华中科技大学 | A kind of score in predicting method constructing local matrix based on figure random walk |
| CN110580316A (en) * | 2019-09-09 | 2019-12-17 | 河南戎磐网络科技有限公司 | Recommendation method based on quantum heuristic |
| CN111402003A (en) * | 2020-03-13 | 2020-07-10 | 第四范式（北京）技术有限公司 | System and method for realizing user-related recommendation |
| CN111612572A (en) * | 2020-04-28 | 2020-09-01 | 北京交通大学 | Adaptive local low-rank matrix approximate modeling method based on recommendation system |
| CN113139571A (en) * | 2021-03-09 | 2021-07-20 | 河海大学 | Dam safety monitoring data completion method based on space-time multi-view fusion |
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| CN107689960A (en) * | 2017-09-11 | 2018-02-13 | 南京大学 | A kind of attack detection method for inorganization malicious attack |
| CN109785656A (en) * | 2019-03-18 | 2019-05-21 | 南京大学 | A kind of traffic programme and air navigation aid based on Local approximation order |
| CN110322053A (en) * | 2019-06-13 | 2019-10-11 | 华中科技大学 | A kind of score in predicting method constructing local matrix based on figure random walk |
| CN110322053B (en) * | 2019-06-13 | 2022-02-15 | 华中科技大学 | Scoring prediction method for constructing local matrix based on graph random walk |
| CN110580316A (en) * | 2019-09-09 | 2019-12-17 | 河南戎磐网络科技有限公司 | Recommendation method based on quantum heuristic |
| CN111402003A (en) * | 2020-03-13 | 2020-07-10 | 第四范式（北京）技术有限公司 | System and method for realizing user-related recommendation |
| CN111402003B (en) * | 2020-03-13 | 2023-06-13 | 第四范式（北京）技术有限公司 | System and method for realizing user-related recommendation |
| CN111612572A (en) * | 2020-04-28 | 2020-09-01 | 北京交通大学 | Adaptive local low-rank matrix approximate modeling method based on recommendation system |
| CN113139571A (en) * | 2021-03-09 | 2021-07-20 | 河海大学 | Dam safety monitoring data completion method based on space-time multi-view fusion |
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Application publication date: 20170517 |