CN104933595A - Collaborative filtering recommendation method based on Markov prediction model - Google Patents

Abstract

The invention discloses a collaborative filtering recommendation method based on a Markov prediction model. The specific realization process is as follows: firstly, a user-personalized transferring matrix is obtained by using the Markov prediction model; secondly, the personalized matrix is processed by using tensor decomposition, namely standard decomposition, and the preference degree of a user to a project is analyzed; and finally, the collaborative recommendation is carried out on the basis and the recommended project is obtained. Compared to the prior art, the collaborative filtering recommendation method based on the Markov predication model sufficiently utilizes each piece of existing data, so that the relatively good recommendation effect can be generated; and the method is high in practicability and easy to popularize.

Description

A kind of collaborative filtering recommending method based on Markov prediction model

Technical field

The present invention relates to e-commerce field, specifically a kind of practical collaborative filtering recommending method based on Markov prediction model.

Background technology

Along with the development of ecommerce, personalized recommendation is subject to increasing user favor, thereby produce a lot of personalized recommendation algorithm, wherein Collaborative Filtering Recommendation Algorithm applies the most successfully one, its basic thought is: by the scoring of the score in predicting destination item of the neighborhood high with destination item similarity, thus produces final individual character recommendation.Along with the change of website structure, the increase of content complexity and increasing of user, how to improve the extensibility of algorithm and how to improve the recommendation quality of collaborative filtering, the subject matter of the systems face based on collaborative filtering. much different solutions is proposed for head it off researchist, under specific occasion, some algorithm can obtain good effect.As time-based data weight and item similarity-based data weight two kinds of improvement quantity algorithms, the dimension in minimizing project space, the project of user after dimensionality reduction is made spatially to have scoring to solve the openness problem of data, the preselected algorithm of the neighbour based on K-means clustering algorithm to each project.Although above-mentioned algorithm can be recommended accordingly, but it often only adopts score information, closely-related time sequence information and relation information are then left in the basket with it, effectively utilize these information can improve the precision of proposed algorithm further. and when score data is more sparse, there is various drawback, cause neighbourhood to gather inaccurate, thus affect the recommendation quality of commending system.

Existing many a lot of algorithms, in order to solve recommendation precision problem, have following several method: 1) based on the proposed algorithm of user (user-based).Based on the system that the recommend method of user constantly changes in the face of number of users, need the similarity matrix often recalculated between user, thus time complexity is high, and extensibility is poor.2) based on the proposed algorithm of project (item-based), website user's quantity constantly increases, the recommended number of entry then keeps relative stability, the item similarity matrix update frequency calculated is low, can use within long period of time. propose the proposed algorithm based on project (item-based) for this reason, but when number of entry Rapid Variable Design in commending system (online news is as recommended project), project-based algorithm is faced with scalability problem equally.

Based on this, the invention provides a kind of collaborative filtering recommending method based on Markov prediction model, pass through the method, the proposed algorithm of user and Markov prediction model, obtain the transition matrix of user interest, thus recommend the items of interest of user on this basis, algorithm simply and directly, and when Sparse, recommendation can be completed preferably.

Summary of the invention

Technical assignment of the present invention is for above weak point, provide a kind of practical, based on the collaborative filtering recommending method of Markov prediction model.

Based on a collaborative filtering recommending method for Markov prediction model, its specific implementation process is,

First Markov prediction model is utilized to obtain user individual transition matrix;

Then use tensor resolution, namely Standard Decomposition processes personalized matrix, analyzes user to the fancy grade of project;

Finally carry out Collaborative Recommendation on this basis, obtain recommended project thus.

The transition matrix construction process of described user is:

Structure Markov chain, is set to m=1 by the length of chain, tries to achieve user and buys l to the transition probability model buying i, then obtain the transition matrix of user.

The processing procedure of described personalized matrix is:

1) transition matrix obtained carries out tensor resolution;

2) then the formula of tensor resolution is combined with Markov model, obtain new transition matrix, use the similarity between associated similarity calculating user;

3) after calculating similarity, obtain the neighbours of user, thus adopt the method for collaborative filtering to recommend user.

Described step 2) in Similarity measures adopt following formula:

$sim(u1,u2)=\frac{{\mathrm{\Σ}}_{u\∈C_{u1,u2}}(R_{u1,i,j}-{\stackrel{\‾}{R}}_i)(R_{u2,i,j}-{\stackrel{\‾}{R}}_i)}{\sqrt{{\mathrm{\Σ}}_{u\∈C_{u1}}{(R_{u1,i}-{\stackrel{\‾}{R}}_i)}^2}\sqrt{{\mathrm{\Σ}}_{u\∈C_{u2}}{(R_{u2,j}-{\stackrel{\‾}{R}}_j)}^2}}$

Wherein: C _{u1, u2}represent that user u1 and user u2 has the set of identical transfer item, R _{u1, i, j}and R _{u2, i, j}represent that user's previous step buys the probability of i and next step purchase j respectively, with represent that user buys the average probability of i, j respectively.

After using associated similarity to calculate the similarity between two two users, its result is kept at user's similarity matrix R_sim (N, N) in, this R_sim is N × N square formation, N represents N number of user, and the value of its element is that rotational symmetry distributes with principal diagonal, i.e. sim_ (k, m)=sim_ (m, k).

Described step 3) detailed process be:

What calculate user u does not purchase Item Sets N _k=I-I _k(1≤k≤M), I is Item Sets, I _kfor user purchases Item Sets;

According to R _simthe nearest-neighbors set U={u of (N, N) select target user u ₁, u ₂..., u _p, make and sim (u, u ₁) maximum, sim (u, u ₂) take second place, by that analogy;

Calculate according to the set U of the nearest-neighbors p of targeted customer u and recommend collection accordingly:

Item Sets N is not purchased for user u _kin each i, utilize the probability of following formula predictions user bought item:

$P_{u,i}=\stackrel{\‾}{R_u}+\frac{{\mathrm{\Σ}}_{u_k\∈U}sim(u,u_k)(R_{u_k,i}-\stackrel{\‾}{R_{u_k}})}{{\mathrm{\Σ}}_{u_k\∈U}\left(\right|sim(u,u_k)\left|\right)};$

Wherein sim (u, u _k) represent user u and its nearest-neighbors user u _kbetween comprehensive similarity, represent user u _kto the purchase probability of project i, with represent user u, u respectively _kto the average purchase probability of project;

To N _kthe prediction probability of middle element sorts according to order from big to small, gets front p item design and recommends collection I _rec={ i ₁, i ₂..., i _p, recommend targeted customer u.

A kind of collaborative filtering recommending method based on Markov prediction model of the present invention, has the following advantages:

A kind of collaborative filtering recommending method based on Markov prediction model that the present invention proposes, Markov prediction model is combined with collaborative filtering, and in the process combined, tensor resolution is taken to sparse matrix, make full use of existing every bar data, thus good recommendation effect can be produced, practical, be easy to promote.

Accompanying drawing explanation

Accompanying drawing 1 is the purchase history lists of 4 users.

Accompanying drawing 2 is the transition matrix figure of user 1.

Accompanying drawing 3 is the transition matrix figure of user 2.

Accompanying drawing 4 is the transition matrix figure of user 3.

Accompanying drawing 5 is the transition matrix figure of user 4.

Embodiment

Below in conjunction with the drawings and specific embodiments, the invention will be further described.

The invention provides a kind of collaborative filtering recommending method based on Markov prediction model, the explanation of nouns related in the method is as follows:

Markov prediction model: be that in applied probability, markovian Theories and methods research random occurrence changes and a kind of model of analyses and prediction future trends whereby.

Collaborative filtering: be utilize certain to have similar tastes and interests, have the hobby of the colony of the common experience interested information of person of coming recommendation.

Recommend method: the project obtained by collaborative filtering (commodity) is recommended user.

In existing recommend method, the cold start-up problem of user, commodity is difficult problems, and the method generally used in recommend method is all collaborative filtering.This method of collaborative filtering builds user's commodity matrix, and then through similarity process, thus user is recommended.But when customer volume is huge, time commodity amount is equally also very large, user's commodity matrix is exactly a sparse matrix, and how the interested commodity of user that dope correct in sparse matrix are equally also difficult problems.And the information of the sequential ignored in classic method, thus user's commodity interested cannot be doped accurately, also cannot accurately for user recommends.

In method of the present invention, first utilize Markov prediction model to obtain user individual transition matrix, then with tensor resolution, personalized matrix is processed, analyze user to the fancy grade of project, and then Collaborative Recommendation is carried out on this basis, obtain better recommended project thus.

Based on this, specific implementation process of the present invention is:

First Markov prediction model is utilized to obtain user individual transition matrix;

Then use tensor resolution, namely Standard Decomposition processes personalized matrix, analyzes user to the fancy grade of project;

Finally carry out Collaborative Recommendation on this basis, obtain recommended project thus.

The transition matrix construction process of described user is:

Structure Markov chain, is set to m=1 by the length of chain, tries to achieve user and buys l to the transition probability model buying i, then obtain the transition matrix of user.

Based on this construction process, fig. 1 illustrates the example of a Continuous behavior.Existing 4 users bought article, and the article that system finally will be bought according to user are recommended.Time wherein in table is a kind of relative time.

Use after above-mentioned steps, the transition matrix of accompanying drawing 2, accompanying drawing 3, accompanying drawing 4, the user 1 shown in accompanying drawing 5, user 2, user 3 and user 4 can be obtained.

The processing procedure of described personalized matrix is:

1) transition matrix obtained carries out tensor resolution;

2) then the formula of tensor resolution is combined with Markov model, obtain new transition matrix, use the similarity between associated similarity calculating user;

3) after calculating similarity, obtain the neighbours of user, thus adopt the method for collaborative filtering to recommend user.

Described step 2) in Similarity measures adopt following formula:

$sim(u1,u2)=\frac{{\mathrm{\Σ}}_{u\∈C_{u1,u2}}(R_{u1,i,j}-{\stackrel{\‾}{R}}_i)(R_{u2,i,j}-{\stackrel{\‾}{R}}_j)}{\sqrt{{\mathrm{\Σ}}_{u\∈C_{u1}}{(R_{u1,i}-{\stackrel{\‾}{R}}_i)}^2}\sqrt{{\mathrm{\Σ}}_{u\∈C_{u2}}{(R_{u2,j}-{\stackrel{\‾}{R}}_j)}^2}}$

Wherein: C _{u1, u2}represent that user u1 and user u2 has the set of identical transfer item, R _{u1, i, j}and R _{u2, i, j}represent that user's previous step buys the probability of i and next step purchase j respectively, with represent that user buys the average probability of i, j respectively.

After using associated similarity to calculate the similarity between two two users, its result is kept at user's similarity matrix R_sim (N, N) in, this R_sim is N × N square formation, N represents N number of user, and the value of its element is that rotational symmetry distributes with principal diagonal, i.e. sim_ (k, m)=sim_ (m, k).

Described step 3) detailed process be:

What calculate user u does not purchase Item Sets N _k=I-I _k(1≤k≤M), I is Item Sets, I _kfor user purchases Item Sets;

According to R _simthe nearest-neighbors set U={u of (N, N) select target user u ₁, u ₂..., u _p, make and sim (u, u ₁) maximum, sim (u, u ₂) take second place, by that analogy;

Calculate according to the set U of the nearest-neighbors p of targeted customer u and recommend collection accordingly:

Item Sets N is not purchased for user u _kin each i, utilize the probability of following formula predictions user bought item:

$P_{u,i}=\stackrel{\‾}{R_u}+\frac{{\mathrm{\Σ}}_{u_k\∈U}sim(u,u_k)(R_{u_k,i}-\stackrel{\‾}{R_{u_k}})}{{\mathrm{\Σ}}_{u_k\∈U}\left(\right|sim(u,u_k)\left|\right)};$

Wherein sim (u, u _k) represent user u and its nearest-neighbors user u _kbetween comprehensive similarity, represent user u _kto the purchase probability of project i, with represent user u, u respectively _kto the average purchase probability of project;

To N _kthe prediction probability of middle element sorts according to order from big to small, gets front p item design and recommends collection I _rec={ i ₁, i ₂..., i _p, recommend targeted customer u.

Adopt said method, even if when user's commodity matrix is sparse especially, also final recommendation results can not be affected, because we adopt is transition matrix, and the decomposition of tensor has been carried out to it, also can well utilize each data.

Above-mentioned embodiment is only concrete case of the present invention; scope of patent protection of the present invention includes but not limited to above-mentioned embodiment; claims of any a kind of collaborative filtering recommending method based on Markov prediction model according to the invention and the those of ordinary skill of any described technical field to its suitable change done or replacement, all should fall into scope of patent protection of the present invention.

Claims (6)

1. based on a collaborative filtering recommending method for Markov prediction model, it is characterized in that, its specific implementation process is,

First Markov prediction model is utilized to obtain user individual transition matrix;

Then use tensor resolution, namely Standard Decomposition processes personalized matrix, analyzes user to the fancy grade of project;

Finally carry out Collaborative Recommendation on this basis, obtain recommended project thus.

2. a kind of collaborative filtering recommending method based on Markov prediction model according to claim 1, is characterized in that, the transition matrix construction process of described user is:

Structure Markov chain, is set to m=1 by the length of chain, tries to achieve user and buys 1 to the transition probability model buying i, then obtain the transition matrix of user.

3. a kind of collaborative filtering recommending method based on Markov prediction model according to claim 1, is characterized in that, the processing procedure of described personalized matrix is:

1) transition matrix obtained carries out tensor resolution;

2) then the formula of tensor resolution is combined with Markov model, obtain new transition matrix, use the similarity between associated similarity calculating user;

3) after calculating similarity, obtain the neighbours of user, thus adopt the method for collaborative filtering to recommend user.

4. a kind of collaborative filtering recommending method based on Markov prediction model according to claim 3, is characterized in that, described step 2) in Similarity measures adopt following formula:

Wherein: C _{u1, u2}represent that user u1 and user u2 has the set of identical transfer item, R _{u1, i, j}and R _{u2, i, j}represent that user's previous step buys the probability of i and next step purchase j respectively, with represent that user buys the average probability of i, j respectively.

5. a kind of collaborative filtering recommending method based on Markov prediction model according to claim 4, it is characterized in that, after using associated similarity to calculate the similarity between two two users, its result is kept in user's similarity matrix R_sim (N, N), this R_sim is N × N square formation, N represents N number of user, and the value of its element is that rotational symmetry distributes with principal diagonal, i.e. sim_ (k, m)=sim_ (m, k).

6. a kind of collaborative filtering recommending method based on Markov prediction model according to claim 5, is characterized in that, described step 3) detailed process be:

What calculate user u does not purchase Item Sets N _k=I-I _k(1≤k≤M), I is Item Sets, I _kfor user, oneself purchases Item Sets;

According to R _simthe nearest-neighbors set U={u of (N, N) select target user u ₁, u ₂..., u _p, make and sim (u, u ₁) maximum, sim (u, u ₂) take second place, by that analogy;

Calculate according to the set U of the nearest-neighbors p of targeted customer u and recommend collection accordingly:

Item Sets N is not purchased for user u _kin each i, utilize the probability of following formula predictions user bought item:

Wherein sim (u, u _k) represent user u and its nearest-neighbors user u _kbetween comprehensive similarity, represent user u _kto the purchase probability of project i, with represent user u, u respectively _kto the average purchase probability of project;

To N _kthe prediction probability of middle element sorts according to order from big to small, gets front p item design and recommends collection I _rec={ i ₁, i ₂..., i _p, recommend targeted customer u.