CN110310185B - Weighted bipartite graph-based popular and novel commodity recommendation method - Google Patents

Weighted bipartite graph-based popular and novel commodity recommendation method Download PDF

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CN110310185B
CN110310185B CN201910620567.1A CN201910620567A CN110310185B CN 110310185 B CN110310185 B CN 110310185B CN 201910620567 A CN201910620567 A CN 201910620567A CN 110310185 B CN110310185 B CN 110310185B
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郁湧
骆永军
于倩
刘金卓
赵娜
谢仲文
刘强
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Yunnan University YNU
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Abstract

The invention discloses a weighted bipartite graph-based popular and novel commodity recommendation method, which specifically comprises the following steps: step 1, establishing a weighted bipartite graph according to a purchasing relationship and a score between a commodity and a user; step 2, establishing a single-mode projection network from the commodity to the user; step 3, calculating the similarity between the user to be recommended and the recommending system user, and counting the similar user set of the user to be recommended; step 4, counting commodity sets of similar users; step 5, calculating a recommended predicted value of each commodity in the commodity set, and recommending commodities to the user to be recommended according to the recommended predicted value; the method weakens the influence of popular commodities on the similarity of the users, provides reasonable measurement for the similarity of the users, enables the calculation result of the similarity of the users to be more accurate, and enables the recommendation result of commodity recommendation of the users to be more accurate, and to be better in diversity and novelty based on the similarity.

Description

Weighted bipartite graph-based popular and novel commodity recommendation method
Technical Field
The invention belongs to the technical field of data processing, and particularly relates to a popular and novel commodity recommendation method based on a weighted bipartite graph.
Background
The 'explosive' growth of Web information resources accumulates massive data, so that severe information overload is caused, how to help a user to more accurately screen massive information is a hotspot direction of current research, and the personalized recommendation system is an effective method for solving the problem, and information which is possibly interested is recommended for the user by analyzing the behavior characteristics of the user to predict the interest, so that the screening efficiency of the user is improved, and the information screening time is saved.
The current recommendation algorithm mainly includes a Collaborative Filtering recommendation algorithm (CF), a content-based recommendation algorithm, a hybrid recommendation algorithm, a network structure-based recommendation algorithm, and the like, and has been widely applied in a commercial environment; the collaborative filtering recommendation algorithm is to calculate the similarity between users through the evaluation of the users on commodities, search neighbor users and then recommend according to the information of the neighbor users, but the problems of data sparsity and the like often exist; the method comprises the steps of finding out commodities with highest similarity according to commodity information liked by a user based on a content recommendation algorithm, recommending the commodities to the user, respectively establishing configuration files for the user and the commodities by a recommendation system based on the content, analyzing the commodities purchased or browsed by the user, establishing or updating a configuration file system of the user, comparing the similarity between the user and the commodity configuration files, and directly recommending the commodities which are most similar to the configuration files to the user.
Disclosure of Invention
The invention aims to provide a weighted bipartite graph-based popular and novel commodity recommendation method, which is used for weakening the influence of popular commodities on the similarity between different users, selecting popular recommendation or novel recommendation through the change of parameter values, and enabling recommendation results to be more accurate and to meet the living requirements of the users.
The technical scheme adopted by the invention is that the popularization and novelty commodity recommendation method based on the weighted bipartite graph specifically comprises the following steps:
step 1, according to the userEstablishing a weighted bipartite graph G ═ of (U ^ I, E, W) of a recommendation system according to the purchase relation between commodities and the scores of the commodities by usersM) Wherein U ═ { U ═1,…,ui,…,umU denotes a set of m elements in the recommendation system, I is a variable 1 ≦ I ≦ m representing the user, I ≦ m1,…,Ij,…InI represents a commodity set containing n elements, j is a variable 1 ≦ j ≦ n representing commodities, E represents an edge formed by a purchase relationship between a user and commodities, W represents a purchase relationship matrix between a user and commodities, and W (I, j) ≦ 1 represents a user uiPurchased goods IjW (i, j) ═ 0 denotes user uiHas not purchased commodity Ij；WMFor the scoring matrix between the user and the purchased goods, representing the weight of the corresponding edge of the user-goods weighted bipartite graph, WM(i, j) ≠ 0 denotes user uiPurchases goods IjAnd scored as WM(i,j)；WM(i, j) ═ 0 denotes user uiHas not purchased commodity Ij；
Step 2, in the user-commodity weighted bipartite graph, a commodity-to-user single-mode projection network is constructed according to the purchase relation between the user and the commodity, and is recorded as GI→U＝(U,EU,WU) In which EURepresenting an edge, W, formed by an associative relationship between two different users based on a single mode projectionUA weight matrix, W, for associations between different usersU(i, a) represents a user u to be recommendedaWith user u in the recommendation systemiSimilarity between them;
step 3, calculating the user u to be recommended based on the single-mode projection networkaSimilarity with all users in the recommendation system is screened out, and the users u to be recommended in the recommendation system are screened outaForming a similar user set U by the K similar users with the highest similaritya＝{ua1,…,uak,…,uaKK is a variable representing similar users, and is more than or equal to 1 and less than or equal to K;
step 4, counting the commodity sets purchased by the K similar users, and screening out the users u to be recommendedaThe purchased commodities are marked as commodity set I(ua)＝Γ(ua1)∪…∪Γ(uak)∪…∪Γ(uaK)-Γ(ua)；
Step 5, calculating commodity set I (u)a) The recommended predicted value of each commodity is beta & gt 0 when popular recommendation is needed for the user to be recommended, beta & lt 0 when novelty recommendation is needed, and the commodity set I (u) is not considereda) And (3) taking beta as 0 when the sales volume of the inner commodities is recommended to the user only according to the grading difference of the user, and recommending the commodities to the user to be recommended in sequence from large to small according to the recommended predicted value.
Further, only weighted bipartite graph G ═ (U ═ I, E, W is considered in step 3M) The purchasing relationship in (1) does not consider the scoring matrix WMIn time, the user u to be recommendedaWith user u in the recommendation systemiSimilarity between WU(i, a) the calculation is shown in equation (1):
Figure GDA0003373053760000021
Γ (u) in equation (1)i) Representing user uiSet of purchased goods, Γ (u)a) Representing a user u to be recommendedaSet of purchased goods IlFor user uiWith the user u to be recommendedaThe goods that have been purchased together are,
Figure GDA0003373053760000031
for purchased goods I in the recommendation systemlThe total number of users.
Further, the user u to be recommended is calculated in the step 3aWith user u in the recommendation systemiWhen the purchasing relationship and the scoring matrix in the weighted bipartite graph are considered comprehensively, the calculation is as shown in formula (2):
Figure GDA0003373053760000032
w in formula (2)M(i, l) represents user uiPurchases goods IlAnd scored as WM(i,l)，WM(a, l) represents user uaPurchases goods IlAnd scored as WM(a, l), alpha is a number greater than 0,
Figure GDA0003373053760000033
representing user u versus scores made by different users for the same itemiWith the user u to be recommendedaThe correction coefficient of the similarity is calculated,
Figure GDA0003373053760000034
further, the user u to be recommended in the step 3aAnd carrying out normalization processing on the similarity between the recommendation system and all users, wherein a normalization equation is shown as a formula (3):
Figure GDA0003373053760000035
WU(i, a) has a value in the range of [0,1 ]]。
Further, in the step 5, the commodity set I (u) isa) The weighted average value of the scores of the commodity users is used as a recommendation prediction value, and the recommendation prediction value R (a, k) is calculated as shown in formula (4):
Figure GDA0003373053760000036
u in formula (4)akRepresenting a user u to be recommendedaSimilar users of, WU(a, ak) represents the user u to be recommendedaUser u similar theretoakSimilarity between them, W (ak, k) represents similar users uakPurchased goods Ik，Ik∈I(ua)，Γ(I(ua) Show purchased goods IkIs given as the set of users, | Γ (I (u)a))∩UaI represents the purchased goods IkUser set and user u to be recommendedaThe intersection of the set of similar users of (c),
Figure GDA0003373053760000037
is the correction of the weighted average value of the scores, and the value range of the correction coefficient beta is [ -1,1]。
Further, the matrix representation form of the recommended predicted value is as follows:
Figure GDA0003373053760000041
wherein I is an identity matrix, a matrix
Figure GDA0003373053760000042
The element in (A) is
Figure GDA0003373053760000043
W (ak, k) represents similar user uakPurchased goods Ik。
The invention has the advantages that (1) when single-mode projection is carried out, the number of users who purchase commodities is considered, so that the influence of popular commodities on the similarity among different users is weakened; (2) taking the scores of the users on the commodities as the weight of a bipartite graph, considering the differences of the scores of the different users on the commodities, and providing a method capable of reasonably measuring the similarity between the users; (3) compared with the original method, the recommendation algorithm can select whether to carry out popular recommendation or novelty recommendation according to the value of the parameter in the same model, and the recommendation result has better accuracy, diversity and novelty.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a flow chart of the present invention.
Fig. 2 is a graph showing the variation of the parameter α according to the embodiment of the present invention.
Fig. 3 is a graph showing the variation of the parameter β according to the embodiment of the present invention.
FIG. 4 is a graph comparing the recommended effects of the present invention with the conventional CF algorithm and NBI algorithm.
FIG. 5 is a graph showing the effect of the MAE, RMSE and HD of the present invention compared with the CF algorithm and NBI algorithm.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The flow of the weighted bipartite graph-based popularization and novelty commodity recommendation method is shown in fig. 1, and specifically comprises the following steps:
step 1, establishing a weighted bipartite graph G (U I, E, W) of a recommendation system by using a purchase relation between a user and a commodity and a score of the user on the commodityM)；
Wherein U is { U ═1,…,ui,…,umU denotes a set of m elements in the recommendation system, I is a variable 1 ≦ I ≦ m representing the user, I ≦ m1,…,Ij,…InI represents a commodity set containing n elements, j is a variable 1 ≦ j ≦ n representing commodities, E represents an edge formed by a purchase relationship between a user and commodities, W represents a purchase relationship matrix between a user and commodities, and W (I, j) ≦ 1 represents a user uiPurchased goods IjW (i, j) ═ 0 denotes user uiHas not purchased commodity Ij；WMFor the scoring matrix between the user and the purchased goods, representing the weight of the corresponding edge of the user-goods weighted bipartite graph, WM(i, j) ≠ 0 denotes user uiPurchases goods IjAnd scored as WM(i,j)；WM(i, j) ═ 0 denotes user uiHas not purchased commodity Ij；
Step 2, in the user-commodity weighted bipartite graph, a single-mode projection network from the commodity to the user based on the purchase relation is constructed according to the purchase relation between the user and the commodity, so that the different users who have purchased the same commodity generate correlation, and the single-mode projection network is marked as GI→U＝(U,EU,WU) In which EURepresenting an edge, W, formed by an associative relationship between two different users based on a single mode projectionUA similarity matrix representing the similarity between different users, i.e. a weight matrix of the associations of different users, WU(i, a) represents a user u to be recommendedaWith user u in the recommendation systemiSimilarity between them;
step 3, calculating the user u to be recommended based on the single-mode projection networkaSimilarity with all users in the recommendation system is screened out, and the users u to be recommended in the recommendation system are screened outaForming a similar user set U by the K similar users with the highest similaritya＝{ua1,…,uak,…,uaKK is a variable representing similar users, and is more than or equal to 1 and less than or equal to K;
when considering only the weighted bipartite graph G ═ (UvI, E, W)M) The purchasing relationship in (1) does not consider the scoring matrix WMIn time, the user u to be recommendedaWith user u in the recommendation systemiSimilarity between WU(i, a) the calculation is shown in equation (1-1):
Figure GDA0003373053760000051
Γ (u) in equation (1-1)i) For user uiSet of purchased goods, Γ (u)a) Representing a user u to be recommendedaSet of purchased goods IlFor user uiWith the user u to be recommendedaThe goods that have been purchased together are,
Figure GDA0003373053760000052
for purchased goods I in the recommendation systemlThe total number of users;
at the moment, the user to be recommendedSimilarity W to users in a recommendation systemUThe value of (i, a) not only takes into account the user uiWith the user u to be recommendedaThe quantity of the commodities purchased together and the commodities IlThe number of purchasing users, i.e. the weighted bipartite graph G ═ (UUI, E, W)M) Chinese merchandise IlTaking into account the degree of (c); when the commodity I is purchasedlWhen the number of users is large, the commodity IlIn order to be a popular commodity, the method is that,
Figure GDA0003373053760000061
for user uiWith the user u to be recommendedaThe similarity contribution value of (1) is reduced, user uiWith the user u to be recommendedaSimilarity between WU(i, a) becomes indirectly smaller; when the commodity I is purchasedlWhen the number of users is small, the product IlIs a novel commodity and is characterized in that,
Figure GDA0003373053760000062
for user uiWith the user u to be recommendedaThe similarity contribution value of (b) increases, user uiWith the user u to be recommendedaSimilarity between WU(i, a) will be indirectly larger; therefore, the influence of popular commodities, namely commodities with a large number of purchased users on the similarity among different users can be weakened, the probability that the commodities with novelty are recommended is increased, and the result of obtaining the similarity of the users is more reasonable;
when considering both weighted bipartite graph G ═ U ═ E, WM) The purchasing relationship in (1) and the scoring matrix w are consideredMIn time, the user u to be recommendedaWith user u in the recommendation systemiSimilarity between WUThe value of (i, a) is shown in the formula (1-2):
Figure GDA0003373053760000063
in the formula (1-2), α is a number greater than 0, WM(i, l) represents user uiPurchases goods IlAnd scored as WM(i，l)，WM(a, l) represents a user u to be recommendedaPurchases goods IlAnd scored as WM(a, l), user uiWith the user u to be recommendedaThe closer the scores of the same item purchased, the closer WUThe larger the value of (i, a) is, the user uiWith the user u to be recommendedaThe higher the similarity of (A); when the score difference values are the same, the contribution of the popular commodities purchased by the users to the similarity among the users is smaller than the contribution of the novel commodities to the similarity of different users,
Figure GDA0003373053760000064
is user uiWith the user u to be recommendedaScoring the same item purchased to user uiWith the user u to be recommendedaThe correction coefficient of the similarity is calculated,
Figure GDA0003373053760000065
has a value range of [0,1 ]]；
To WU(i, a) carrying out normalization treatment, wherein a normalization equation is shown as a formula (1-3), and obtaining the W with unified standardU(i，a)，WU(i, a) has a value in the range of [0,1 ]]；
Figure GDA0003373053760000071
Step 4, counting the commodity sets purchased by the K similar users, and screening out the users u to be recommendedaThe purchased commodities are marked as commodity set I (u)a)＝Γ(ua1)∪…∪Γ(uak)∪…∪Γ(uaK)-Γ(ua)；
Step 5, calculating commodity set I (u)a) The recommended predicted value of each commodity is beta & gt 0 when popular recommendation is needed for the user to be recommended, beta & lt 0 when novelty recommendation is needed, and the commodity set I (u) is not considereda) Taking beta as 0 when recommending the user according to the grading difference of the user, and recommending the commodities to the user to be recommended in sequence from large to small according to a recommended predicted value;
collecting the commodities I (u)a) Taking the weighted average value of each commodity as a recommendation prediction value, evaluating the recommendation sequence and the commodity set I (u)a) The calculation of the recommended predicted value R (a, k) of the medium commodity is shown in the formula (1-4):
Figure GDA0003373053760000072
Γ (I (u) in equations (1-4)a) Show purchased goods IkOf a user set ofk∈I(ua)，|Γ(I(ua))∩UaI represents the purchased goods IkUser set and user u to be recommendedaW (ak, k) represents a similar user uakPurchased goods Ik，WU(a, ak) represents the user u to be recommendedaUser u similar theretoakThe similarity between the two groups is similar to each other,
Figure GDA0003373053760000073
representing a user u to be recommendedaOf similar users who purchased the commodity IkTo the commodity IkIs the weighted average of the score values of (a),
Figure GDA0003373053760000074
is to consider the user u to be recommendedaSimilar user set U ofaPurchased goods IkIn the case of the number of users, the weighted average of the scores is corrected, and the value range of the correction coefficient beta is [ -1,1]。
Beta is greater than 0
Figure GDA0003373053760000075
Is | Γ (I (u)a))∩UaAn increasing function of | recommending a predicted value R (a, k) with | Γ (I (u)a))∩UaIncreased by an increase in i, i.e. the user u to be recommendedaOf similar users who purchased the commodity IkIncreased number of users, item IkIs increased, when the predicted recommended value of the commodity I is increasedkBelonging to popular commodities, for commodity IkThe recommendation of (2) belongs to a popular recommendation.
When the beta is less than 0,
Figure GDA0003373053760000076
is | Γ (I (u)a))∩UaA decreasing function of |, the user u to be recommendedaOf similar users who purchased the commodity IkReduced number of users, commodity IkIs reduced, when the goods I are in the marketkBelonging to a novel commodity, to commodity IkThe recommendation belongs to novelty recommendation, and in the case that the weighted average of the scores of the commodities by the users is the same, the user u to be recommendedaSimilar users who purchased the commodity I collectivelykThe number of the users is reduced, and the recommendation prediction value is larger, so that the recommendation is easier.
When β is 0, it means that the recommended result does not take into consideration the product IkThe recommended forecast value R (a, k) is equal to the weighted average of the scores of the items.
The novelty recommendation and the popular recommendation of the invention are to assume a similar user set Ua＝{ua1,…,uak,…,uaKUser to commodity IkThe purchase condition can reflect the whole user to the commodity IkIf more accurate effect is needed, the value of K can be increased properly.
For convenience of expressing and calculating the commodity recommendation prediction value, a similarity matrix W is applied to the userUIs processed to obtain WU＝W′UI, enabling the invention to treat the recommended users uaWhen recommending commodities, user u to be recommendedaThe purchased commodities do not influence the recommended predicted value, wherein I is an identity matrix, and any commodity IkThe prediction value recommended to the user to be recommended is expressed as:
Figure GDA0003373053760000081
w in the formula (1-5)MA purchase scoring matrix between the user and the commodity is represented by the weight of the corresponding edge in the bipartite user-commodity purchase relation graph, WM(ak, k) ≠ 0 denotesHuu (household)akPurchases goods IkAnd scored as WM(ak,k)，WM(ak, k) ═ 0 denotes user uakHas not purchased commodity Ik(ii) a W is a purchase relation matrix between the user and the commodity, and W (ak, k) is 1 to represent the user uakPurchases goods IkW (ak, k) ═ 0 denotes user uakHas not purchased commodity Ik。
Definition matrix
Figure GDA0003373053760000082
Wherein the corresponding element is
Figure GDA0003373053760000083
Matrix W ″)UWM、W″UW and
Figure GDA0003373053760000084
for the homomorphic matrix, the operation of multiplication and division of the homomorphic matrix is as follows:
Figure GDA0003373053760000085
that is, the operation of the two homotype matrixes is the multiplication of the corresponding elements of the two matrixes;
Figure GDA0003373053760000091
that is, the operation of the two matrixes of the same type is the division of the corresponding elements of the two matrixes, and the value is 0 when the divisor is 0;
therefore, the matrix representation of the recommended predicted value between the user and the commodity is as follows:
Figure GDA0003373053760000092
beta is less than 0 when novelty recommendation is carried out in the recommendation process, and a user u to be recommended is selected from the obtained recommendation matrix RaCorresponding commodity set I (u) with maximum commodity recommendation predicted valuea) Recommending commodities to user u to be recommendedaTaking beta > (beta) when making popular recommendations0; if the popular recommendation and the novelty recommendation are to be performed simultaneously, the commodity set I (u) corresponding to beta < 0a) Recommending commodity set I (u) from high to low according to commodity prediction valuea) One half of the commodities, commodity set I (u) corresponding to beta > 0a) Recommending commodity set I (u) from high to low according to commodity prediction valuea) One half of the commodities are combined to obtain a recommended commodity; beta < 0 was taken for novelty recommendations.
Examples
The method adopts a MovieLens data set established by a GroupLens research group as test data, wherein the data set comprises 10 ten thousand pieces of rating data of 943 users for 1628 movies, each user at least evaluates 20 movies, the rating value is an integer between 1 and 5, the rating height represents the like degree of the user to the movie, and the higher the rating is, the more the user likes the movie; the invention divides the selected data into 80% training set and 20% testing set, each record in the data set includes the following fields: a user ID, a commodity ID, a user score, and a timestamp;
recommending the film to a corresponding user by using the recommending method of the invention to obtain a recommending result list, evaluating the quality of the popular recommending result of the invention by using an average absolute error MAE, a root mean square error RMSE and a Hamming distance, and evaluating the quality of the novel recommending result by using average popularity;
1. representing the recommended accuracy according to the deviation of the predicted value from the actual error value:
the smaller the deviation is, the higher the prediction accuracy is, the recommendation is carried out according to the size of the predicted value, the higher the recommendation accuracy is, and the grade set of the predicted user is assumed to be { p }1,p2,p3,p4,…pN-1,pNThe actual evaluation diversity of the users is as { q }1,q2,q3,q4,…qN-1,qNAnd the mean absolute error MAE and the root mean square error RMSE are:
Figure GDA0003373053760000093
Figure GDA0003373053760000101
the Hamming distance HD evaluates the diversity of the prediction results according to the number of the same commodities in different user recommendation lists, and the user uiAnd ujIs a hamming distance HD between the recommendation listsijComprises the following steps:
Figure GDA0003373053760000102
wherein QijRepresentative user uiAnd ujThe recommendation list of (1) has a common commodity set, | QijI represents the set QijThe number of the middle elements, L represents the length of the recommendation list; if user uiAnd ujIf the recommendation lists are completely consistent, Q isijIf u is 0iAnd ujIf the recommendation list of (1) does not contain the same item, Q ij1 is ═ 1; the average value of the Hamming distances of all the users is the Hamming distance of the whole data set
Figure GDA0003373053760000103
Wherein m represents the number of users, and the bigger the Hamming distance is, the higher the diversity of the recommendation result is;
as can be seen from fig. 2, in this embodiment, the MAE and RMSE values of the recommendation result generated by the recommendation system change when the dynamically adjustable parameter α changes, and the recommendation result is the best when the dynamically adjustable parameter α is 0.6;
2. the novelty of the recommendation is evaluated using the average popularity of the recommendation:
the popularity performance reflects the recommendation condition of the recommendation system to cold commodities, the probability that the less popular commodities are novel for the user is higher, and the popularity of the recommendation system can utilize the average value of the recommendation commodity degree<k>It is shown that,<k>higher indicates more popular items in the recommended items and the average value of the degree of the items<k>Can be expressed as:
Figure GDA0003373053760000104
wherein n representsNumber of users, L represents length of recommendation list, p (I) represents item IiThe lower the average value of the commodity degree is, the higher the novelty of the commodity is;
FIG. 3 shows the influence of the correction coefficient β on the novelty of the recommendation algorithm, wherein the neighbor number is set to 60, top _10 indicates that the length of the recommendation list is 10, as can be seen from FIG. 3, the mean value < k > of the recommended commodity degree changes when the correction coefficient β changes, and the value of < k > tends to be stable when the correction coefficient β is less than or equal to-0.5, in this embodiment, the correction coefficient β is-0.6;
comparing the recommendation result obtained by the invention with the recommendation effect of the traditional CF algorithm and NBI algorithm on the cold commodity, the invention can effectively reduce the popularity of the recommended commodity when beta is less than 0, the individuation degree and novelty of the recommended commodity are improved, and the commodity with low stream travel degree in the recommendation system can also be recommended according to the graph shown in FIG. 4;
FIG. 5 is a graph showing the comparison effect between the MAE, RMSE and HD of the CF algorithm, NBI algorithm and the algorithm of the present invention, and it can be seen from FIG. 5 that the present invention is significantly superior to the CF algorithm and NBI algorithm in the recommendation accuracy, and can recommend suitable commodities to users better, and the recommendation result has better diversity;
by combining the experimental results, the recommendation diversity of the algorithm is obviously improved, and the influence of the degree of the user and the commodity is considered, so that the recommendation degree of popular movies in movie recommendation is effectively inhibited, users contributing to target users are more accurate, the recommendation individuality is improved, and the multi-interest requirements of different users are met.
All the embodiments in the present specification are described in a related manner, and the same and similar parts among the embodiments may be referred to each other, and each embodiment focuses on the differences from the other embodiments. In particular, for the system embodiment, since it is substantially similar to the method embodiment, the description is simple, and for the relevant points, reference may be made to the partial description of the method embodiment.
The above description is only for the preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention shall fall within the protection scope of the present invention.

Claims (5)

1. The popular and novel commodity recommendation method based on the weighted bipartite graph is characterized by comprising the following steps:
step 1, establishing a weighted bipartite graph G (U I, E, W) of a recommendation system according to a purchase relation between a user and a commodity and a grade of the user on the commodityM) Wherein U ═ { U ═1,…,ui,…,umU denotes a set of m elements in the recommendation system, I is a variable 1 ≦ I ≦ m representing the user, I ≦ m1,…,Ij,…InI represents a commodity set containing n elements, j is a variable 1 ≦ j ≦ n representing commodities, E represents an edge formed by a purchase relationship between a user and commodities, W represents a purchase relationship matrix between a user and commodities, and W (I, j) ≦ 1 represents a user uiPurchased goods IjW (i, j) ═ 0 denotes user uiHas not purchased commodity Ij；WMFor the scoring matrix between the user and the purchased goods, representing the weight of the corresponding edge of the user-goods weighted bipartite graph, WM(i, j) ≠ 0 denotes user uiPurchases goods IjAnd scored as WM(i,j)；WM(i, j) ═ 0 denotes user uiHas not purchased commodity Ij；
Step 2, in the user-commodity weighted bipartite graph, a commodity-to-user single-mode projection network is constructed according to the purchase relation between the user and the commodity, and is recorded as GI→U＝(U,EU,WU) In which EURepresenting an edge, W, formed by an associative relationship between two different users based on a single mode projectionUA weight matrix, W, for associations between different usersU(i, a) represents a user u to be recommendedaWith user u in the recommendation systemiSimilarity between them;
step 3, calculating the user u to be recommended based on the single-mode projection networkaSimilarity with all users in the recommendation system is screened out for use in the recommendation system and to be recommendedHuu (household)aForming a similar user set U by the K similar users with the highest similaritya＝{ua1,…,uak,…,uaKK is a variable representing similar users, and is more than or equal to 1 and less than or equal to K;
step 4, counting the commodity sets purchased by the K similar users, and screening out the users u to be recommendedaThe purchased commodities are marked as commodity set I (u)a)＝Γ(ua1)∪…∪Γ(uak)∪…∪Γ(uaK)-Γ(ua)；
Step 5, calculating commodity set I (u)a) When the recommended predicted value of each commodity is in the set I (u)a) The weighted average value of the scores of the commodity users is used as a recommendation prediction value, and the recommendation prediction value R (a, k) is calculated as shown in formula (4):
Figure FDA0003373053750000011
u in formula (4)akRepresenting a user u to be recommendedaSimilar users of, UaRepresenting a user u to be recommendedaSimilar user set of WU(a, ak) represents the user u to be recommendedaUser u similar theretoakSimilarity between them, W (ak, k) represents similar users uakPurchased goods Ik，Ik∈I(ua)，Γ(I(ua) Show purchased goods IkIs given as the set of users, | Γ (I (u)a))∩UaI represents the purchased goods IkUser set and user u to be recommendedaSimilar user set U ofaThe intersection of the two lines of intersection of the two lines,
Figure FDA0003373053750000021
is the correction of the weighted average value of the scores, and the value range of the correction coefficient beta is [ -1,1]；
When the popular recommendation is needed to be performed on the user to be recommended, beta is more than 0, when the novelty recommendation is needed, beta is less than 0, and when the commodity set I (u) is not considereda) Taking the selling amount of the inner commodity when recommending the user according to the grading difference of the userAnd beta is 0, and recommending the commodities to the user to be recommended from large to small according to the recommended predicted value.
2. The weighted bipartite graph-based commodity recommendation method according to claim 1, wherein only weighted bipartite graph G ═ (uu I, E, W) is considered in step 3M) The purchasing relationship in (1) does not consider the scoring matrix WMIn time, the user u to be recommendedaWith user u in the recommendation systemiSimilarity between WU(i, a) the calculation is shown in equation (1):
Figure FDA0003373053750000022
Γ (u) in equation (1)i) Representing user uiSet of purchased goods, Γ (u)a) Representing a user u to be recommendedaSet of purchased goods IlFor user uiWith the user u to be recommendedaThe goods that have been purchased together are,
Figure FDA0003373053750000023
for purchased goods I in the recommendation systemlThe total number of users.
3. The method as claimed in claim 1, wherein the step 3 of calculating the user u to be recommended is a method for recommending popular and novel commodities based on weighted bipartite graphaWith user u in the recommendation systemiWhen the purchasing relationship and the scoring matrix in the weighted bipartite graph are considered comprehensively, the calculation is as shown in formula (2):
Figure FDA0003373053750000024
Γ (u) in equation (2)i) Representing user uiSet of purchased goods, Γ (u)a) Representing a user u to be recommendedaSet of purchased goods IlFor user uiWith the user u to be recommendedaThe goods that have been purchased together are,
Figure FDA0003373053750000025
for purchased goods I in the recommendation systemlTotal number of users, WM(i, l) represents user uiPurchases goods IlAnd scored as WM(i,l)，WM(a, l) represents a user u to be recommendedaPurchases goods IlAnd scored as WM(a, l), alpha is a number greater than 0,
Figure FDA0003373053750000031
representing user u versus scores made by different users for the same itemiWith the user u to be recommendedaThe correction coefficient of the similarity is calculated,
Figure FDA0003373053750000032
4. the method as claimed in claim 1, wherein the user u to be recommended in step 3 is a commodity recommendation method based on weighted bipartite graphaAnd carrying out normalization processing on the similarity between the recommendation system and all users, wherein a normalization equation is shown as a formula (3):
Figure FDA0003373053750000033
wherein WU(i, a) represents a user u to be recommendedaWith user u in the recommendation systemiSimilarity between, WU(i, a) has a value in the range of [0,1 ]]。
5. The weighted bipartite graph-based commodity recommendation method for popularity and novelty according to claim 1, wherein the recommendation prediction values are represented in a matrix form as follows:
Figure FDA0003373053750000034
wherein I is an identity matrix, a matrix
Figure FDA0003373053750000035
The element in (A) is
Figure FDA0003373053750000036
W (ak, k) represents similar user uakPurchased goods Ik。
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