CN107122407A - The multi-field recommendation method of feature based selection - Google Patents
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Abstract
The invention discloses a kind of multi-field recommendation method of feature based selection, including:Multiple users are obtained to the rating matrix of multiple articles and the domain information of each article;Calculate the similarity matrix between similarity matrix and the domain between user;The complete model for optimizing default multi-field commending system obtains object function respectively for the partial derivative of the feature selecting vector in the similarity matrix between the similarity matrix between user, domain and domain until the condition of convergence obtains end user preferences matrix, finished article eigenmatrix and final feature selecting vector;Score in predicting is carried out according to end user preferences matrix, finished article eigenmatrix and final feature selecting vector, so as to according to appraisal result recommendation information.The invention has the advantages that:Alleviate the influence of the sparse performance to commending system of rating matrix, effectively eliminate the collective effect of original multi-field segmentation and recommendation for recommending to be constituted by two independent steps and have ignored field, effectively improve the accuracy of recommendation.
Description
Technical Field
The invention relates to the field of recommendation methods, in particular to a multi-field recommendation method based on feature selection.
Background
Nowadays, with the rapid increase of information on the internet, the problem of information overload (information overload) is becoming more and more serious. Both consumers and information producers have met with significant challenges: as information consumers, how to find out the content in which the consumers are interested from a large amount of information becomes a very difficult thing, especially in the case that the users have no clear needs; it is very difficult for information producers to make information produced by themselves stand out, and the information producers get attention from the wide range of users. The recommendation method is an important tool for solving the contradiction.
Among the wide variety of recommendation algorithms, collaborative filtering is one of the most successful algorithms, with the basic assumption that users with similar scoring behavior also have similar preferences in the selection of other items. Although collaborative filtering based recommendation methods have met with great success in the real world, they still suffer from certain drawbacks and limitations. The biggest challenge is the data sparsity problem, namely that in a huge scoring matrix, scoring data of a user is extremely sparse. In recent years, to alleviate such problems, a multi-domain based recommendation method has been proposed. Herein, a domain (also called a sub-group) refers to a group of users having similar preferences for a series of items. Such an approach improves the performance of collaborative filtering based recommendation algorithms to some extent by dividing users and items into overlapping subgroups and then generating recommendations independently on each subgroup. Conventional multi-domain based recommendation techniques require that users and items be classified into different categories and then the results produced by the various zones be combined. However, these two steps ignore their mutual roles in the recommendation process.
Disclosure of Invention
The present invention is directed to solving at least one of the above problems.
Therefore, the invention aims to provide a multi-field recommendation method based on feature selection to solve the problem of data sparsity.
In order to achieve the above object, an embodiment of the present invention discloses a multi-domain recommendation method based on feature selection, including the following steps: s1: acquiring a scoring matrix of a plurality of items by a plurality of users and domain information of each item; s2: calculating a similarity matrix between users according to the grading matrix, and calculating a similarity matrix between domains according to the domain information of each article; s3: optimizing a complete model of a preset multi-field recommendation system by adopting a random gradient descent algorithm to obtain partial derivatives of a target function respectively corresponding to a similarity matrix among users, a similarity matrix among fields and a feature selection vector of the fields until convergence conditions are met to obtain a final user preference matrix, a final article feature matrix and a final feature selection vector; s4: and performing grading prediction according to the final user preference matrix, the final article feature matrix and the final feature selection vector so as to recommend information to the users according to a grading result.
Further, a similarity matrix between the users is calculated by the following formula:
wherein s isijElements, r, representing the ith row and jth column in the similarity matrix between said usersi=[ri1,...,ric]Is the score distribution, rijIs the normalized number of user i's scores in the jth domain.
Further, calculating a similarity matrix between the domain information calculation domains of each article by the following formula:
wherein,is the similarity for user u, fields k and l, whereIndicating that user u has over-scored behavior in k domains.
Further, the preset complete model of the multi-domain recommendation system is as follows:
where P and Q are d-dimensional hidden variable expressions for users and goods, PiAnd q isiFeature vector, m, representing each user i or item jkA feature selection vector representing the domain k, α, β, γ, and λ are parameters that balance the terms;
the partial derivatives of the objective function with respect to the similarity matrix between users, the similarity matrix between domains, and the feature selection vector of the domain are respectively:
wherein D is dependent on mkThe value of the ith element on the diagonal is calculated by the following formula:
wherein, is a positive number for smoothing the target;
all variables P, Q and m are initialized to [0,1 ]]According to the step size parameter omegap、ωqAnd ωmAnd updating the variables until the algorithm converges to obtain a final user preference matrix, a final article feature matrix and a final feature selection vector.
Further, in step S1, each of the plurality of users possesses at least a first threshold amount of rating data and each of the plurality of items possesses at least a second threshold amount of rating.
According to the multi-domain recommendation method based on feature selection, provided by the embodiment of the invention, the multi-domain information of the commodity is utilized, and the feature selection vector is introduced on the basis of matrix decomposition so as to relieve the influence of the sparse scoring matrix on the performance of a recommendation system. The method effectively eliminates the problem that the original multi-field recommendation consists of two independent steps and neglects the combined action of field segmentation and recommendation, and the frame is used for recommending articles for the user, so that the recommendation accuracy can be effectively improved.
Additional aspects and advantages of the invention will be set forth in part in the description which follows and, in part, will be obvious from the description, or may be learned by practice of the invention.
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The above and/or additional aspects and advantages of the present invention will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings of which:
FIG. 1 is a flow chart of a multi-domain recommendation method based on feature selection according to an embodiment of the present invention;
fig. 2 is a model diagram of a multi-domain recommendation method based on feature selection according to an embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
These and other aspects of embodiments of the invention will be apparent with reference to the following description and attached drawings. In the description and drawings, particular embodiments of the invention have been disclosed in detail as being indicative of some of the ways in which the principles of the embodiments of the invention may be practiced, but it is understood that the scope of the embodiments of the invention is not limited correspondingly. On the contrary, the embodiments of the invention include all changes, modifications and equivalents coming within the spirit and terms of the claims appended hereto.
The invention is described below with reference to the accompanying drawings.
Fig. 1 is a flowchart of a multi-domain recommendation method based on feature selection according to an embodiment of the present invention. The multi-field recommendation method based on feature selection comprises the following steps:
s1: and acquiring a scoring matrix of a plurality of items by a plurality of users and the domain information of each item.
Specifically, in step S1, each of the plurality of users possesses at least a first threshold amount of scoring data and each of the plurality of items possesses at least a second threshold amount of scoring to reduce data sparseness. In one example of the present invention, the first threshold is 10 and the second threshold is 5.
As shown in fig. 2, a scoring matrix R is formed based on the scores of a plurality of items by a plurality of users. P is a user feature matrix, Q is an item feature matrix, and M is a feature selection vector. The first score 4 in the score matrix R represents the result of multiplying the first row of the user feature matrix P by the diagonal matrix generated by the feature selection vector and then by the first column of the item feature matrix Q.
S2: and calculating a similarity matrix between users according to the grading matrix, and calculating a similarity matrix between domains according to the domain information of each article.
Specifically, the embodiment of the present invention provides a complete model of a multi-domain recommendation system preset as follows:
where P and Q are d-dimensional hidden variable expressions for users and goods, PiAnd q isiFeature vector, m, representing each user i or item jkThe feature selection vectors representing the domain k, α, β, γ, and λ are parameters that balance the terms, whose values can be determined by five-fold cross-validation.S and T refer to the similarity matrix between users and the similarity matrix between domains, SijAnd TijRespectively, the ijth element in the similarity matrix.
SijAnd TijThe calculation is as follows:
wherein r isi=[ri1,...,ric]Is the score distribution, rijIs the normalized number of user i's scores in the jth domain. Once two users have resemblanceThe scores of (1) are distributed, they have a relatively high similarity.
Wherein,is the similarity for user u, fields k and l, whereIndicating that user u has over-scored behavior in k domains. It should be noted that whenWhen the temperature of the water is higher than the set temperature,there is no value.
S3: optimizing a complete model of a preset multi-field recommendation system by adopting a random gradient descent algorithm to obtain partial derivatives of a target function respectively corresponding to a similarity matrix among users, a similarity matrix among fields and a feature selection vector of the fields until convergence conditions are met to obtain a final user preference matrix, a final article feature matrix and a final feature selection vector;
specifically, a random gradient descent method is used for optimizing a complete model of the preset multi-domain recommendation system, an objective function of the complete model of the preset multi-domain recommendation system is recorded as L, and then L is related to pi,qjAnd mkThe partial derivatives of (c) are as follows:
wherein D is dependent on mkThe value of the ith element on the diagonal is calculated by the following formula:
wherein, is a positive number for smoothing the target;
all variables P, Q and m are initialized to [0,1 ]]According to the step size parameter omegap、ωqAnd ωmAnd updating the variables until the algorithm converges to obtain a final user preference matrix, a final article feature matrix and a final feature selection vector. Omegap、ωqAnd ωmDetermined by a linear search algorithm.
S4: and performing grading prediction according to the final user preference matrix, the final article feature matrix and the final feature selection vector so as to recommend information to the users according to a grading result.
According to the multi-domain recommendation method based on feature selection, provided by the embodiment of the invention, the multi-domain information of the commodity is utilized, and the feature selection vector is introduced on the basis of matrix decomposition so as to relieve the influence of the sparse scoring matrix on the performance of a recommendation system. And effectively eliminates the prior multi-domain recommendation which is composed of two independent steps and neglects the joint action of the segmentation and the recommendation of the domain. The framework is used for recommending articles for the user, and the recommending accuracy can be effectively improved.
In addition, other configurations and functions of the multi-domain recommendation method based on feature selection according to the embodiment of the present invention are known to those skilled in the art, and are not described in detail for reducing redundancy.
In the description of the present invention, it is to be understood that the terms "first" and "second" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While embodiments of the invention have been shown and described, it will be understood by those of ordinary skill in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.
Claims (5)
1. A multi-field recommendation method based on feature selection is characterized by comprising the following steps:
s1: acquiring a scoring matrix of a plurality of items by a plurality of users and domain information of each item;
s2: calculating a similarity matrix between users according to the grading matrix, and calculating a similarity matrix between domains according to the domain information of each article;
s3: optimizing a complete model of a preset multi-field recommendation system by adopting a random gradient descent algorithm to obtain partial derivatives of a target function respectively corresponding to a similarity matrix among users, a similarity matrix among fields and a feature selection vector of the fields until convergence conditions are met to obtain a final user preference matrix, a final article feature matrix and a final feature selection vector;
s4: and performing grading prediction according to the final user preference matrix, the final article feature matrix and the final feature selection vector so as to recommend information to the users according to a grading result.
2. The multi-domain recommendation method based on feature selection according to claim 1, wherein the similarity matrix between the users is calculated by the following formula:
<mrow> <msub> <mi>S</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msubsup> <mi>r</mi> <mi>i</mi> <mi>T</mi> </msubsup> <msub> <mi>r</mi> <mi>j</mi> </msub> </mrow> <mrow> <mo>|</mo> <mo>|</mo> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>|</mo> <mo>|</mo> <msub> <mi>r</mi> <mi>j</mi> </msub> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> </mfrac> </mrow>
wherein s isijElements, r, representing the ith row and jth column in the similarity matrix between said usersi=[ri1,...,ric]Is the score distribution, rijIs the normalized number of user i's scores in the jth domain.
3. The multi-domain recommendation method based on feature selection according to claim 1, wherein the similarity matrix between the domain information calculation domains of each item is calculated by the following formula:
<mrow> <msubsup> <mi>T</mi> <mrow> <mi>k</mi> <mi>l</mi> </mrow> <mi>u</mi> </msubsup> <mo>=</mo> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mo>(</mo> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>N</mi> <mi>k</mi> <mi>u</mi> </msubsup> <mo>,</mo> <msubsup> <mi>N</mi> <mi>l</mi> <mi>u</mi> </msubsup> </mrow> <mo>)</mo> </mrow> <mo>/</mo> <mi>m</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>N</mi> <mi>k</mi> <mi>u</mi> </msubsup> <mo>,</mo> <msubsup> <mi>N</mi> <mi>l</mi> <mi>u</mi> </msubsup> </mrow> <mo>)</mo> </mrow> <mo>-</mo> <mn>1</mn> </mrow> <mo>)</mo> <mo>)</mo> </mrow> </mrow>
wherein,is the similarity for user u, fields k and l, whereIndicating that user u has over-scored behavior in k domains.
4. The multi-domain recommendation method based on feature selection according to claim 1, wherein in step S3:
the complete model of the preset multi-domain recommendation system is as follows:
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <munder> <mi>min</mi> <mrow> <mi>P</mi> <mo>,</mo> <mi>Q</mi> <mo>,</mo> <mi>m</mi> </mrow> </munder> <munder> <mi>&Sigma;</mi> <mrow> <mo>{</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>}</mo> <mo>&Element;</mo> <mi>O</mi> </mrow> </munder> <msup> <mrow> <mo>(</mo> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msubsup> <mi>p</mi> <mi>i</mi> <mi>T</mi> </msubsup> <mi>d</mi> <mi>i</mi> <mi>a</mi> <mi>g</mi> <mo>(</mo> <msub> <mi>m</mi> <mi>k</mi> </msub> <mo>)</mo> <msub> <mi>q</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <mi>&alpha;</mi> <munder> <mi>&Sigma;</mi> <mi>k</mi> </munder> <mo>|</mo> <mo>|</mo> <msub> <mi>m</mi> <mi>k</mi> </msub> <mo>|</mo> <msub> <mo>|</mo> <mn>1</mn> </msub> <mo>+</mo> <mi>&beta;</mi> <munder> <mi>&Sigma;</mi> <mi>i</mi> </munder> <munder> <mi>&Sigma;</mi> <mi>j</mi> </munder> <msub> <mi>S</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>|</mo> <mo>|</mo> <msub> <mi>p</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>p</mi> <mi>j</mi> </msub> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <mi>&gamma;</mi> <munder> <mi>&Sigma;</mi> <mi>i</mi> </munder> <munder> <mi>&Sigma;</mi> <mi>j</mi> </munder> <msub> <mi>T</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>|</mo> <mo>|</mo> <msub> <mi>m</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>m</mi> <mi>j</mi> </msub> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>+</mo> <mi>&lambda;</mi> <mrow> <mo>(</mo> <mo>|</mo> <mo>|</mo> <mi>P</mi> <mo>|</mo> <msubsup> <mo>|</mo> <mi>F</mi> <mn>2</mn> </msubsup> <mo>+</mo> <mo>|</mo> <mo>|</mo> <mi>Q</mi> <mo>|</mo> <msubsup> <mo>|</mo> <mi>F</mi> <mn>2</mn> </msubsup> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced>
where P and Q are d-dimensional steganography of users and itemsExpression of variables, piAnd q isiFeature vector, m, representing each user i or item jkA feature selection vector representing the domain k, α, β, γ, and λ are parameters that balance the terms;
the partial derivatives of the objective function with respect to the similarity matrix between users, the similarity matrix between domains, and the feature selection vector of the domain are respectively:
<mrow> <mfrac> <mrow> <mo>&part;</mo> <mi>L</mi> </mrow> <mrow> <mo>&part;</mo> <msub> <mi>p</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>=</mo> <mo>-</mo> <mn>2</mn> <mrow> <mo>(</mo> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msubsup> <mi>p</mi> <mi>i</mi> <mi>T</mi> </msubsup> <mi>d</mi> <mi>i</mi> <mi>a</mi> <mi>g</mi> <mo>(</mo> <msub> <mi>m</mi> <mi>k</mi> </msub> <mo>)</mo> <msub> <mi>q</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mi>d</mi> <mi>i</mi> <mi>a</mi> <mi>g</mi> <mrow> <mo>(</mo> <msub> <mi>m</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>q</mi> <mi>j</mi> </msub> <mo>+</mo> <mn>2</mn> <msub> <mi>&lambda;p</mi> <mi>i</mi> </msub> <mo>+</mo> <mn>2</mn> <mi>&beta;</mi> <munder> <mi>&Sigma;</mi> <mi>i</mi> </munder> <msub> <mi>S</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>p</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>p</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> </mrow>
<mrow> <mfrac> <mrow> <mo>&part;</mo> <mi>L</mi> </mrow> <mrow> <mo>&part;</mo> <msub> <mi>q</mi> <mi>j</mi> </msub> </mrow> </mfrac> <mo>=</mo> <mo>-</mo> <mn>2</mn> <mrow> <mo>(</mo> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msubsup> <mi>p</mi> <mi>i</mi> <mi>T</mi> </msubsup> <mi>d</mi> <mi>i</mi> <mi>a</mi> <mi>g</mi> <mo>(</mo> <msub> <mi>m</mi> <mi>k</mi> </msub> <mo>)</mo> <msub> <mi>q</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <mi>d</mi> <mi>i</mi> <mi>a</mi> <mi>g</mi> <mrow> <mo>(</mo> <msub> <mi>m</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>p</mi> <mi>i</mi> </msub> <mo>+</mo> <mn>2</mn> <msub> <mi>&lambda;q</mi> <mi>j</mi> </msub> </mrow>
<mrow> <mfrac> <mrow> <mo>&part;</mo> <mi>L</mi> </mrow> <mrow> <mo>&part;</mo> <msub> <mi>m</mi> <mi>k</mi> </msub> </mrow> </mfrac> <mo>=</mo> <mo>-</mo> <mn>2</mn> <mrow> <mo>(</mo> <msub> <mi>r</mi> <mrow> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>-</mo> <msubsup> <mi>p</mi> <mi>i</mi> <mi>T</mi> </msubsup> <mi>d</mi> <mi>i</mi> <mi>a</mi> <mi>g</mi> <mo>(</mo> <msub> <mi>m</mi> <mi>k</mi> </msub> <mo>)</mo> <msub> <mi>q</mi> <mi>j</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>p</mi> <mi>i</mi> </msub> <msub> <mi>q</mi> <mi>j</mi> </msub> <mo>+</mo> <mn>2</mn> <msub> <mi>&alpha;Dm</mi> <mi>k</mi> </msub> <mo>+</mo> <mn>2</mn> <mi>&gamma;</mi> <munder> <mi>&Sigma;</mi> <mi>i</mi> </munder> <msub> <mi>T</mi> <mrow> <mi>k</mi> <mi>l</mi> </mrow> </msub> <mrow> <mo>(</mo> <msub> <mi>m</mi> <mi>k</mi> </msub> <mo>-</mo> <msub> <mi>m</mi> <mi>l</mi> </msub> <mo>)</mo> </mrow> </mrow>
wherein D is dependent on mkThe value of the ith element on the diagonal is calculated by the following formula:
<mrow> <msub> <mi>D</mi> <mrow> <mi>i</mi> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <msqrt> <mrow> <msubsup> <mi>m</mi> <mrow> <mi>k</mi> <mi>i</mi> </mrow> <mn>2</mn> </msubsup> <mo>+</mo> <mi>&epsiv;</mi> </mrow> </msqrt> </mrow> </mfrac> </mrow>
wherein, is a positive number for smoothing the target;
all variables P, Q and m are initialized to [0,1 ]]According to the step size parameter omegap、ωqAnd ωmAnd updating the variables until the algorithm converges to obtain a final user preference matrix, a final article feature matrix and a final feature selection vector.
5. The multi-domain recommendation method based on feature selection according to claim 1, wherein in step S1, each of said plurality of users has at least a first threshold number of scores and each of said plurality of items has at least a second threshold number of scores.
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