CN113010800B - Combined coding-based collaborative ranking recommendation method - Google Patents

Combined coding-based collaborative ranking recommendation method Download PDF

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CN113010800B
CN113010800B CN202110240166.0A CN202110240166A CN113010800B CN 113010800 B CN113010800 B CN 113010800B CN 202110240166 A CN202110240166 A CN 202110240166A CN 113010800 B CN113010800 B CN 113010800B
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卢涛
刘成昊
孙建伶
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Zhejiang University ZJU
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Abstract

The invention discloses a collaborative sequencing recommendation method based on combinatorial coding, which aims to represent users and articles by fully utilizing the accuracy of real-value vectors and the high efficiency of binary vectors on the premise of not influencing model performance so as to improve the accuracy and efficiency of the recommendation method. In order to keep consistent with the final goal of the recommendation system for obtaining top-k recommendation results, the CCCR adopts a paired sorting loss function, so that the method has better performance on sorting indexes. In order to obtain faster convergence speed and better convergence result than the traditional discrete coordinate descent method, the CCCR uses a new efficient optimization method and adopts a mode of updating binary vectors integrally rather than updating bit by bit. Finally, experimental results on the published data set show that the accuracy of the results in the top-k recommendation task is significantly improved while the high efficiency of retrieval and training is maintained by the CCCR.

Description

Combined coding-based collaborative ranking recommendation method
Technical Field
The invention belongs to the field of discrete recommendation, and particularly relates to a collaborative sequencing recommendation method based on combined coding.
Background
In these scenes, the recommendation system mainly plays a role in mining out potential interesting items of a user according to existing information of the user and the items and recommending the potentially interesting items to the user, so that the user experience, the flow rate of the platform, the advertising income and the like are improved.
In order to improve the recommendation efficiency of the algorithm in a large-scale recommendation scene, a lot of research works in this respect have been done in recent years. One of the research directions is to use a hash method. The hash method uses binary vectors to represent users and goods, so that the inner product operation of the feature vectors of the users and goods can be realized in the Hamming space by a fast bit operation mode. However, compared to real-valued vectors, binary vectors are inherently less accurate due to their limited expressive power per bit, which prevents them from modeling complex relationships between users and objects.
In order to fully utilize the advantages of real-valued vectors in precision and binary vectors in efficiency, a cooperative filtering method (CCCF) based on combinatorial coding is proposed. Although the CCCF approach has a better balance between recommendation accuracy and efficiency than the existing recommendation methods, it has two limitations. First, the objective function of this method is a squared error point-by-point loss function, which is inconsistent with the final objective of the recommendation system (i.e., the ordering objective of accurately recommending the top-k items that the user likes best). Secondly, due to the discrete constraint, the method is optimized in a discrete coordinate descending manner, and the method for updating the hash code according to the bits can cause the method to have slow convergence speed and easily fall into a local minimum value.
Disclosure of Invention
The present invention is directed to a method for collaborative ranking recommendation based on combinatorial coding, which addresses the limitations and disadvantages of the prior art. The invention solves the problem that the traditional binary code expression capability is not enough and the optimization target and the recommendation target of the existing method based on the combined coding are not consistent, and aims to improve the recommendation efficiency and accuracy.
The purpose of the invention is realized by the following technical scheme: a collaborative ranking recommendation method based on combined coding comprises a training phase and an online recommendation phase.
In the training phase, according to a scoring matrix M epsilon R formed by M users and n articlesm×nTo obtain a combined code of the user and the article, wherein the combined code comprises G binary vectors with r dimensions and a real number weight vector with G dimensions. The combined coding for the u-th user is represented as:
Figure GDA0003010187200000011
wherein, bu (k)∈{±1}rIs the kth binary vector, η, of user uuFor user u, the number of weight vectors, k is 1 to G, and r is the dimension of the real-valued eigenvector.
The combined code for the ith item is represented as:
Figure GDA0003010187200000021
wherein the content of the first and second substances,
Figure GDA0003010187200000022
is the kth binary vector, ξ, of item iiA weight vector is real for item i.
With A { (u, i) | Mui>0 represents a set pair of a user and an article corresponding to each score in M, u is 1 to M, i is 1 to n, and M isuiRepresenting the user u's rating of item i. Representing all item pairs i and j scored by user u with a triplet (u, i, j) all triplets are represented using Ω { (u, i, j) | (u, i), (u, j) ∈ a }, j ═ 1 to n. Definition of Yu,i,jTo express the relative relationship of the preference degrees of the two items by the user, the specific definition is as follows:
Figure GDA0003010187200000023
with B ═ B1,…,bm]∈{±1}m×rAnd D ═ D1,…,dn]∈{±1}n×rTo represent binary vectors of users and items in dimension r, respectively. The optimized objective function is as follows:
Figure GDA0003010187200000024
Figure GDA0003010187200000025
B(k)∈{±1}m×r,D(k)∈{±1}n×r,k＝1,…,G.
Figure GDA0003010187200000026
wherein the content of the first and second substances,
Figure GDA0003010187200000027
respectively representing the score estimation of the user u on the items i and j; b is(k)An r-dimensional user binary vector representing a kth local model; d(k)An r-dimensional bin vector representing the kth local model.
And (3) an online recommendation stage: according to the combined codes of the users and the items obtained by training, for each accessed user, the scores of the user and all the items are calculated, and the score calculation formula of the user u on the item i is as follows:
Figure GDA0003010187200000028
and sorting all the scores from high to low, selecting top-k articles as recommendation results and returning the recommendation results to the user, and finishing online recommendation.
Further, the training phase specifically comprises the following steps:
(1) an anchor point is selected. Obtaining initial real-value feature vectors of users and goods by using a collaborative filtering algorithm, and selecting G anchor points (u 'by using a k-means algorithm'1,i′1),…,(u′G,i′G) Corresponding to G local models.
(2) The weights are calculated. For each user and item, a weight is calculated based on its distance from the anchor point, the user weight for the kth local model
Figure GDA0003010187200000031
The calculation formula is as follows:
Figure GDA0003010187200000032
wherein u is0Is an initialized real value feature vector u 'corresponding to the user u'kIs the real-valued eigenvector of the user corresponding to the k-th anchor point,
Figure GDA0003010187200000033
h is a hyperparameter used to control the sparsity of the weights. II is an indication function, and the weight calculation formula of the article is similar to that of the user.
(3) And optimizing the target function, and circularly updating the binary vectors of each local model in turn in a mode of an overall closed solution until all the binary vectors are converged to construct the combined code.
Further, the step (1) is specifically as follows: obtaining an initial real-value feature vector u of the user by using a collaborative filtering algorithm for M0And an initial real-valued feature vector i of the item0(ii) a And then selecting G anchor points (u'1,i′1),…,(u′G,i′G) To correspond to G local models; wherein u'k∈RrIs the real-valued feature vector i 'of the user corresponding to the k-th local model'k∈RrIs the real-valued feature vector of the item corresponding to the kth local model.
Further, the step (3) specifically comprises the following sub-steps:
(3.1) initializing binary vectors of users and articles in the G local models;
(3.2) sequentially updating the binary vectors of the users and the articles of each local model in an overall closed solution mode by optimizing an objective function based on the initial values of the binary vectors; and repeatedly and circularly updating all the local models until all the binary vectors are converged to obtain the final binary vectors of the user and the article.
And (3.3) constructing a combined code of the user and the article.
Further, in step (3.1), initializing binary vectors of users and articles in the G local models, which may be implemented in the following two ways:
(3.3.1) initializing the initial value of the binary vector at random.
(3.3.2) substituting the real-value feature vector into the target function constructed in the step (3.2) instead of the binary vector, optimizing the target function to obtain a new real-value feature vector, and taking the sign bit of the new real-value feature vector as the initial value of the binary vector.
The invention has the beneficial effects that: the method utilizes the advantages brought by the combined coding, simultaneously uses the sequencing loss as the target function, and further improves the performance on the sequencing index compared with a collaborative filtering algorithm using the square error point-by-point loss. In addition, on the basis of the optimization updating method of the binary vector, because the convergence speed of the traditional bit-by-bit updating form is low and the local optimal solution is easy to fall into, the invention adopts the block-wise overall updating method, has higher convergence speed and can obtain a more optimal solution.
Drawings
FIG. 1 is a training flow diagram of the present invention;
FIG. 2 is a flow diagram of an online recommendation of the present invention;
FIG. 3 is a schematic diagram of the manner in which weights are calculated;
FIG. 4 is a schematic diagram of a method for updating binary vectors for users and items;
FIG. 5 is a graph showing the comparison of the NDCG index between the method of the present invention (CCCR) and the conventional recommended methods (CCCF, Primal-CR + +, DRMF, DCF, PPH).
Detailed Description
The objects and effects of the present invention will become more apparent from the following detailed description of the present invention when taken in conjunction with the accompanying drawings.
The invention relates to a collaborative ranking recommendation method based on combined coding.
The training process is shown in fig. 1, and comprises the following specific steps:
(1) as shown in fig. 3, an anchor point is selected.
(1.1) M users and n items form a scoring matrix M e Rm×nBy A { (u, i) | Mui>0 to represent the set pair of user and item corresponding to each score in M; wherein u is 1 to M, i is 1 to n, MuiRepresenting the rating of item i by user u;
(1.2) using a collaborative filtering algorithm to M to obtain an initial real-value feature vector u of the user0And an initial real-valued feature vector i of the item0(ii) a And then selecting G anchor points (u'1,i′1),…,(u′G,i′G) To correspond to G local models; wherein u'k∈RrIs the real-valued feature vector i 'of the user corresponding to the k-th local model'k∈RrThe k-th local model is a real-valued eigenvector of the article corresponding to the k-th local model, where k is 1 to G, and r is a dimension of the real-valued eigenvector.
(2) The weights are calculated. As shown in fig. 3, for each user and item, a weight is calculated based on the distance of the real-valued eigenvectors of the user and item from the anchor point.
User weight of kth local model
Figure GDA0003010187200000041
And weight of the item
Figure GDA0003010187200000042
The calculation formula is as follows:
Figure GDA0003010187200000043
Figure GDA0003010187200000044
where II is an indicator function, and the hyperparameter h is used to control the sparsity of the weights, distance (u)s,ut) As a function of the calculated distance:
Figure GDA0003010187200000045
wherein the content of the first and second substances,<us,ut>represents the dot product and represents the modulus of the vector.
(3) As shown in fig. 4, the binary vectors of the user and the object of each local model are updated by optimizing the objective function, so as to obtain the combined code.
(3.1) representing all item pairs i and j scored by user u with a triplet (u, i, j) using Ω { (u, i, j) | (u, i), (u, j) ∈ jA } to represent all triples, define Yu,i,jTo express the relative relationship between the preference degrees of the two items, the score is proportional to the preference degree, and is specifically defined as follows:
Figure GDA0003010187200000051
wherein j is 1 to n.
(3.2) construct the objective function as follows:
Figure GDA0003010187200000052
Figure GDA0003010187200000053
B(k)＝[b1 (k),…,bm (k)]∈{±1}m×r,D(k)＝[d1 (k),…,dn (k)]∈{±1}n×r,k＝1,…,G
Figure GDA0003010187200000054
wherein the content of the first and second substances,
Figure GDA0003010187200000055
respectively represent the score estimates, Δ f, of user u for items i, ju,i,jRepresenting the estimated score difference of the user to the item i, j; balanced partitioning is an imposed balance constraint and decorrelation is an imposed decorrelation constraint, both aiming to make the learned binary more compact and carry more information; 1m,1nRepresenting all 1 matrices, I, of m x m and n x nrAn identity matrix representing a dimension r; b is(k)R-dimensional user binary vector representing kth local model, bu (k)∈{±1}rBinary direction of user u as k local modelAn amount; d(k)An r-dimensional bin vector representing the kth local model,
Figure GDA0003010187200000056
is the binary vector of item i of the kth local model.
(3.3) initializing binary vectors of users and articles in the G local models, which can adopt the following two ways:
(3.3.1) initializing the initial value of the binary vector at random.
(3.3.2) substituting the real-value feature vector into the target function constructed in the step (3.2) instead of the binary vector, optimizing the target function to obtain a new real-value feature vector, and taking the sign bit of the new real-value feature vector as the initial value of the binary vector.
(3.4) sequentially updating the binary vectors of the users and the articles of each local model in an overall closed solution mode by optimizing an objective function based on the initial values of the binary vectors; and repeatedly and circularly updating all the local models until all the binary vectors are converged to obtain the final binary vectors of the user and the article.
And (3.5) constructing a combined code of the user and the article, wherein the combined code comprises G binary vectors with r dimensions and a real number weight vector with G dimensions.
The combined coding for the u-th user is represented as:
Figure GDA0003010187200000057
wherein eta isuA weight vector is real for user u.
The combined code for the ith item is represented as:
Figure GDA0003010187200000058
wherein ξiA weight vector is real for item i.
During the online recommendation stage, as shown in fig. 2, according to the combined codes of the users and the articles obtained by training, for each visiting user, calculating the score estimation of the user and all articles; and sorting all the score estimates from high to low, selecting top-k articles as recommendation results and returning the recommendation results to the user to complete online recommendation. The score estimation calculation formula of the user u for the item i is as follows:
Figure GDA0003010187200000061
in the embodiment of the invention, Movielens 1m, Yelp and Netflix are used as data sets. The method is called as CCCR, the comparison result of the repeated detection result of the method with the NDCG indexes of the methods such as CCCF, Primal-CR + +, DRMF, DCF and PPH is shown in figure 5, and the comparison result with the methods such as Primal-CR + +, DRMF and the like in the retrieval time is shown in table 1, and the result shows that the method is not only much less than the existing real-value algorithm in the retrieval time, but also superior to the existing hash-based and real-value recommendation algorithm in the recommendation accuracy. Therefore, the invention maintains higher recommendation efficiency and accuracy in a discrete recommendation system.
Table 1: compared result of the invention and the traditional method on retrieval time
Figure GDA0003010187200000062

Claims (5)

1. A collaborative ranking recommendation method based on combinatorial coding is characterized by comprising a training phase and an online recommendation phase;
in the training phase, according to a scoring matrix M epsilon R formed by M users and n articlesm×nTo obtain a combined code of the user and the article, wherein the combined code comprises G binary vectors with r dimensions and a real number weight vector with G dimensions; the combined coding for the u-th user is represented as:
Figure FDA0003420057980000011
wherein, bu (k)∈{±1}rIs the kth binary vector, η, of user uuA user u real number weight vector is represented, k is 1-G, and r is the dimension of a real value feature vector;
the combined code for the ith item is represented as:
Figure FDA0003420057980000012
wherein the content of the first and second substances,
Figure FDA0003420057980000013
is the kth binary vector, ξ, of item iiReal number weight vector for article i;
with A { (u, i) | MuiGreater than 0, represents a set pair of users and items corresponding to each score in M, u is 1 to M, i is 1 to n, M isuiRepresenting the rating of item i by user u; representing all the item pairs i and j scored by the user u by a triplet (u, i, j), wherein the triplet is represented by using omega { (u, i, j) | (u, i), (u, j) ∈ A }, and j is 1-n; definition of Yu，i，jTo express the relative relationship of the preference degrees of the two items by the user, the specific definition is as follows:
Figure FDA0003420057980000014
with B ═ B1，...，bm]∈{±1}m×rAnd D ═ D1，...，dn]∈{±1}n×rTo represent binary vectors of users and items in dimension r, respectively; the optimized objective function is as follows:
Figure FDA0003420057980000015
Figure FDA0003420057980000016
B(k)∈{±1}m×r，D(k)∈{±1}n×r，k＝1，...，G.
Figure FDA0003420057980000017
wherein the content of the first and second substances,
Figure FDA0003420057980000018
respectively representing the score estimation of the user u on the items i and j; b is(k)An r-dimensional user binary vector representing a kth local model; d(k)An r-dimensional commodity binary vector representing a kth local model;
and (3) an online recommendation stage: according to the combined codes of the users and the items obtained by training, for each accessed user, the scores of the user and all the items are calculated, and the score calculation formula of the user u on the item i is as follows:
Figure FDA0003420057980000021
and sorting all the scores from high to low, selecting top-k articles as recommendation results and returning the recommendation results to the user, and finishing online recommendation.
2. The co-ranking recommendation method based on combinatorial coding as claimed in claim 1, characterized in that the training phase specifically comprises the steps of:
(1) selecting an anchor point; obtaining initial real-value feature vectors of users and goods by using a collaborative filtering algorithm, and selecting G anchor points (u 'by using a k-means algorithm'1，i′1)，...，(u′G，i′G) To correspond to G local models;
(2) calculating the weight; for each user and item, according toIts distance from the anchor point to calculate the weight, the user weight of the kth local model
Figure FDA0003420057980000022
The calculation formula is as follows:
Figure FDA0003420057980000023
wherein u is0Is an initialized real value feature vector u 'corresponding to the user u'kIs the real-valued eigenvector of the user corresponding to the k-th anchor point,
Figure FDA0003420057980000024
h is a hyperparameter used to control the sparsity of the weights; II is an indication function, and the weight calculation formula of the article is similar to that of the user;
(3) and optimizing the target function, and circularly updating the binary vectors of each local model in turn in a mode of an overall closed solution until all the binary vectors are converged to construct the combined code.
3. The collaborative ranking recommendation method based on combinatorial coding according to claim 2, wherein the step (1) is specifically: obtaining an initial real-value feature vector u of the user by using a collaborative filtering algorithm for M0And an initial real-valued feature vector i of the item0(ii) a And then selecting G anchor points (u'1，i′1)，...，(u′G，i′G) To correspond to G local models; wherein u'k∈RrIs the real-valued feature vector i 'of the user corresponding to the k-th local model'k∈RrIs the real-valued feature vector of the item corresponding to the kth local model.
4. The co-ranking recommendation method based on combinatorial coding as claimed in claim 3, characterized in that step (3) comprises the following sub-steps:
(3.1) initializing binary vectors of users and articles in the G local models;
(3.2) sequentially updating the binary vectors of the users and the articles of each local model in an overall closed solution mode by optimizing an objective function based on the initial values of the binary vectors; repeatedly and circularly updating all local models until all binary vectors are converged to obtain final binary vectors of the user and the article;
and (3.3) constructing a combined code of the user and the article.
5. The co-ranking recommendation method based on combinatorial coding according to claim 4, characterized in that in step (3.1), the binary vectors of users and articles in the G local models are initialized in the following two ways:
(3.3.1) randomly initializing an initial value of the binary vector;
(3.3.2) substituting the real-value feature vector into the target function constructed in the step (3.2) instead of the binary vector, optimizing the target function to obtain a new real-value feature vector, and taking the sign bit of the new real-value feature vector as the initial value of the binary vector.
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