CN107545471A - A kind of big data intelligent recommendation method based on Gaussian Mixture - Google Patents

A kind of big data intelligent recommendation method based on Gaussian Mixture Download PDF

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CN107545471A
CN107545471A CN201710844205.1A CN201710844205A CN107545471A CN 107545471 A CN107545471 A CN 107545471A CN 201710844205 A CN201710844205 A CN 201710844205A CN 107545471 A CN107545471 A CN 107545471A
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杨永丽
宁振虎
薛菲
公备
王昱波
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Beijing Linear Overlay Technology Co.,Ltd.
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Beijing University of Technology
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Abstract

The invention discloses a kind of intelligent recommendation method based on Gaussian Mixture, belong to big data intelligent recommendation field；Collaborative Filtering Recommendation Algorithm GMM TCF of the present invention based on gauss hybrid models research and application, the main generation including user and item association probability, maximum likelihood function in big data recommended models how is defined, how the Gaussian mixture parameters in big data recommended models is initialized and is optimized and how linearly to be combined the user interest degree model based on Gaussian Mixture with project-based recommended models.On the one hand some cluster is belonged to the transformation of multiple clusters from initial user, this causes the interest of user to obtain great embodiment；On the other hand, by add items time factor, the similarity between project is improved, so as to establish project-based forecast model so that the recommendation effect of algorithm is more preferable, recommends precision higher.

Description

A kind of big data intelligent recommendation method based on Gaussian Mixture
Technical field
The present invention relates to a kind of intelligent recommendation method based on Gaussian Mixture, belong to big data intelligent recommendation field, be related to The combination and use of big data recommended models and colony intelligence optimized algorithm.
Background technology
The type of merchandize provided with the development of ecommerce, businessman and quantity sharp increase.Use with clear and definite demand Family directly can search the commodity for thinking purchase by searching for.However, user's request generally has uncertain and mould in practice Paste property.Counted according to Amazon, in the client of its site shopping, have clear and definite purchase intention only accounts for 16%.If businessman can The commodity for meeting user's Fuzzy Demand are actively recommended user from the commodity of magnanimity, then are expected to potential demand being converted into reality Border demand, the sales volume of e-commerce website can not only be improved, also contribute to loyalty of the user to website.In this background Under, it can be arisen at the historic moment according to the personalized recommendation system of the targeted Recommendations of user characteristics, and be widely used.Including Many websites including Amazon, eBay, YouTube and Google all deploy various forms of commending systems, and generate Huge commercial profit.According to statistics, commending system in 2006 is the sales volume that Amazon improves 30%.Commending system has weight The application value wanted, not only as one of challenging research topic of computer realm, also attract from mathematics, thing The researcher of the various fields such as reason, cognition, artificial intelligence, management, the marketing.
Therefore data mining and machine learning method how to be effectively utilized and recommends valuable customized information to user As there is the problem of very strong practical significance.Collaborative filtering is a kind of effective technology that can produce personalized recommendation, is pushed away various Recommend in system and be all used widely, its basic task is to match user according to similar preference, may be liked with recommended user Joyous project.Collaborative filtering can be generally divided into based on internal memory and based on model.Wherein, the collaborative filtering based on internal memory is again It can be divided into based on user and based on project.The former is to calculate similarity between user, is obtained similar to targeted customer's interest preference Arest neighbors, recommendation is predicted based on this.The ability that it is not learnt to legacy data, without good extension Property, and cold start-up be present.And project-based recommendation is from the similarity between commodity angle calculation project, pass through project Nearest neighbor search come produce recommend.In general, similarity is more stable than the similarity of user preference between project, offline to the former Calculated, avoid the nearest neighbor search of big order of magnitude user on line, greatly reduce on-line calculation.With based on internal memory Algorithm is different, and the algorithm based on model is not directly to carry out calculating recommendation by the original score data of user-project, but uses machine The method of device study carries out learning model building, then the Habit Preference by model prediction user to non-scoring item to data.It is conventional Model include Bayes, singular value decomposition (Singular ValueDecomposition, SVD), latent semantic analysis (Latent Semantic Analysis, LSA), probability latent semantic analysis (Probabilistic Latent Semantic Analysis, PLSA) etc..
However, the algorithm based on model is necessary to consider following problem：First, the height that user scores project is by a variety of Factor influences, including user is accustomed to the interest level of item subject/content, the scoring of user, the quality of project in itself etc.. Second, single latent variable is difficult to embody user and user simultaneously, project and project, the relation between user and project, it is necessary to User is clustered according to similar interest and preference, by project according to similar theme and content clustering.3rd, common " hard " Cluster mode, i.e., each user or project are pertaining only to a single class, it is difficult to describe same user may have it is a variety of emerging A variety of different attributes of interest and same project.It is " soft " cluster to compare rational way, and each user or project are according to probability category In multiple classes, user's size of probable value in certain class reflects user's preference a kind of to this, and project is as the same.
Based on above-mentioned thinking, the present invention proposes a kind of new collaborative filtering GMM- based on gauss hybrid models TCF (Gaussian Mixture Model-Time Collaborative Filtering) is recommended, and it, which is combined, is based on Gauss model and improved project-based collaborative filtering.The former draws the concept of more community of interests by latent variable, Learnt to obtain the probability that user belongs to each community of interest to user model, and colony is to the interest preference of project.Separately On the one hand, project-based recommendation is being calculated, it is contemplated that two project time of occurrences are more close, then the phase between article Can be higher like degree, therefore the calculating to similarity introduces an item similarity time factor.Meanwhile algorithm uses CFPSO (Compression Factor Particle Swarm Optimization) algorithm enters to the parameter in gauss hybrid models Row optimization, and will effectively be combined based on user interest and project-based recommendation by way of linear weighted function, so as to It compensate for, based on community of interest limitation caused by the recommendation of user interest degree model, solving the problems, such as the cold start-up of commending system The limitation recommended with single interest, it is effectively improved the accuracy of recommendation.In addition, algorithm is using user interest and project Joint probability carries out model construction.Meanwhile reasonable selection is carried out for how the parameter in gauss hybrid models carries out initialization, And when EM (Expectation Maximization) its parameter of Algorithm for Solving is used in gauss hybrid models, how to use Suitable likelihood function.
Above-mentioned this gauss hybrid models Collaborative Filtering Recommendation Algorithm GMM-TCF main recommendation mechanisms are：Recommending In the selection of algorithm, not only selection is recommended by similarity between user for user, in combination with similar between project Degree is recommended user.This way of recommendation not only compensate for the limitation of single cluster belonging to user, while utilize project Between time factor improve calculating formula of similarity, so as to be effectively improved the recommendation precision of algorithm.
The content of the invention
The invention mainly includes the research of the Collaborative Filtering Recommendation Algorithm GMM-TCF based on gauss hybrid models and answer With, the main generation including user and item association probability, how to define maximum likelihood function in big data recommended models, such as What is initialized to the Gaussian mixture parameters in big data recommended models and optimized and how by based on Gaussian Mixture User interest degree model is linearly combined with project-based recommended models.Its technical scheme used for：1) utilization is passed through User is carried out soft cluster by gauss hybrid models, so as to propose the similarity forecast model based on user interest, calculates the model Prediction scoring；2) by introducing the PROJECT TIME factor, so as to improve calculating formula of similarity, calculate based on the pre- of project model Test and appraisal point；3) the prediction scoring of above-mentioned two model is linearly combined, scored as final project forecast, so as to recommend Targeted customer.
The technical solution adopted by the present invention is a kind of big data intelligent recommendation method based on Gaussian Mixture, the reality of this method Existing step is as follows：
(1) the similarity forecast model based on user interest.First, PLSA model constructions user and the joint of project are passed through Probability, based on this Probability Forms, build suitable likelihood function i.e. big data intelligent recommendation model.Then, CFPSO algorithms are passed through Optimize EM algorithms so as to solve the parameter in big data intelligent recommendation model.Finally, with big data intelligent recommendation model solution Prediction scoring of the targeted customer to project.
A. the joint probability of user and project is built.For each three-dimensional vector ＜ u, i, v ＞, wherein u, i, v difference For the scoring of user u, project i and user u to project i.Introduce latent variable Z={ z1,z2,…,zk, wherein zi(1≤i≤ K) it is different cluster colonies, with P (zk| u) represent that user u belongs to zkThe probability of colony andP(v|i,zk) table Show colony zkTo project i scorings v probability.Then the joint probability of user and project is：
B. it is big data intelligent recommendation model to build likelihood function.The v conditional probability P (v it is assumed that colony z scores project i | i, z) meet Gaussian Profile, there are P (v | i, z)=N (μi,z,σi,z)=P (v；μi,z,σi,z), wherein μi,z,σi,zRespectively colony Z To the average and variance of project i scorings, then the joint probability of user and project is a probabilistic model for meeting Gaussian Mixture：Then obtaining log-likelihood function is：
C. parameter initialization selects.For parameter P (z | u), μi,z,Parameter is carried out using K-means clustering algorithms Initialization.Meanwhile the parameter after initialization is optimized with CFPSO algorithms.The number of population is set as n, any grain Sub- i positional representation is Xi=(x1,x2,…xn), (1) formula is selected as fitness function.Then based on CFPSO optimization EM algorithms The step of it is as follows：
The first step：Initialize particle populations.The number of given population is simultaneously to the initial bit of each particle in population Put and initialized with speed, position and speed formula are as follows:
Wherein,Speed of i-th of particle in t+1 moment d dimension spaces is represented, k is compressibility factor, and ω is inertia weight, c1, c2For aceleration pulse, r1And r2For random number,WithIndividuals of the particle i in t d dimension spaces is represented respectively Optimal and global optimum,Represent i-th of particle in the position of t+1 moment d dimension spaces.
Second step：Calculate the fitness value of each particle in population, and the current individual optimal location of more new particle pbestWith the colony optimal location g of populationbest。
3rd step：To the g of populationbestIt is updated according to EM algorithms.Compare the front and rear fitness value of renewal, such as G after fruit renewalbestValue causes fitness function value to become big, then Population Regeneration optimal location gbestInformation, otherwise not update.
4th step：To the population optimal value g after renewalbestVerified, if it meets to require, terminate CFPSO calculations Method, and obtain gbestInitial parameter of the attribute information of value as EM algorithms；Otherwise the 5th step is gone to.
5th step：According to the speed of particle individual and location parameter in formula (2) and (3) renewal population and go to second Step continues executing with.Wherein, the execution step of EM algorithms is as follows：
E is walked：According to each scoring vectorial ＜ u, i, v ＞, each potential variable z ∈ Z posterior probability P is calculated (z | u, v, i), it is as follows：
M is walked：The posterior probability being calculated according to E steps, and combine Lagrange optimization extreme value and inclined is asked to likelihood function Lead and can obtain P (z | u), μi,z,Value, respectively it is as follows：
Optimize the initiation parameter of EM algorithms according to CFPSO, be alternately performed E steps and M steps, until convergence, try to achieve parameter P (z | u), μi,z,Parameter set as big data recommended models.
D. user interest similarity model prediction scoring.Parameter set in being walked by M, construct the user based on Gaussian Mixture Interest Similarity model, so as to calculate prediction scorings of the user u to project i, specific formula is as follows：
(2) project-based forecast model.More according to the user to be given a mark to project, then the similarity between project is got over It is high.Simultaneously as the time that ware occurs is more close, then the similarity between each article is higher, therefore during introducing project Between the factor, be defined as follows：
Wherein, tiAnd tjThe time occurred for project i and project j.Definition project i and j similarity are sim (i, j)：
Wherein, U (i) and U (j) is that the user of project i and j scoring is gathered respectively, ru,iAnd ru,jRepresent user u to project I and project j scoring,WithAverage score of all users to project i and project j is represented, θ is nonnegative number.Then define user Prediction scoring to project is as follows：
Wherein, the field that S (i) is project i is gathered, and selects whether project adds the mode of neighborhood to judge two projects here Similarity whether be more than certain threshold value, the comparative sorting between the mode reduction project of such calculating, when saving computing Between.
(3) linear weighted function is predicted.User interest comparability prediction model and project-based forecast model are added with linear The prediction scoring of the two is combined by the mode of power, so as to calculate final prediction scoring of the user to project, its formula meter Calculate as follows：
rateu,i=α × rate_uHMMu,i+β×rate_Itemu,i, 0 ＜ α ＜ 1, alpha+beta=1 (12)
To sum up, to user in collaborative filtering to project prediction scoring be improved, respectively by Gaussian Mixture, CFPSO, EM algorithm are established and are based on user interest similarity forecast model, and project forecast mould is based on by adding time factor foundation Type, so as to which the prediction of the two scoring linearly be combined, as final prediction scoring of the user to project.
In this way, on the one hand some cluster is belonged to the transformation of multiple clusters from initial user, this to use The interest at family has obtained great embodiment；On the other hand, by add items time factor, improve similar between project Degree, so as to establish project-based forecast model so that the recommendation effect of algorithm is more preferable, recommends precision higher.
Brief description of the drawings
Fig. 1：The general frame figure of collaborative filtering based on gauss hybrid models
Fig. 2：User interest degree forecast model flow chart based on gauss hybrid models
Fig. 3：Project-based prediction recommended models flow chart
Fig. 4：MAE figures under different Item-CF neighborhoods
Embodiment
The present invention is explained and illustrated with reference to relevant drawings：
For the purpose of the present invention, technical scheme and feature is more clearly understood, below in conjunction with specific embodiment, and join According to accompanying drawing, further refinement explanation is carried out to the present invention.The general frame of collaborative filtering based on gauss hybrid models Figure is as shown in Figure 1.
Each step is described as follows：
(1) a kind of user interest degree forecast model based on gauss hybrid models is proposed so that the interest of user obtains pole Gross appearance and be not limited among a certain cluster.
(2) a kind of project-based forecast model is proposed, the project of have studied the time factor of priority occurs to recommendation score Influence.
(3) propose that one kind is based on Gaussian Mixture Collaborative Filtering Recommendation Algorithm model, compared to model set forth above, the mould Type recommends precision higher.
Experimental situation is as follows：
The present invention by experimental verification set forth herein the actual effect based on gauss hybrid models collaborative filtering, it is real It is win7 (64) main frame to test environment, 8G internal memories, 1T hard disks, using Netflix data sets, and by way of cross validation come Verify the MAE values recommended.
First, algorithm establishes the user interest degree forecast model based on gauss hybrid models.Dived by using PLSA probability In the interest of semantic analysis user, while more interest that latent variable Z draws user are introduced, so as to calculate the connection of user and project Close probability.On this basis, it is assumed that scoring Gaussian distributeds of the user group Z to project, so as to construct maximum likelihood function, And logarithm is sought it, and then solve the general solution of parameter.For the initialization of parameter, the model uses K-mean clustering algorithms Initial value is carried out to it to set, and initial value parameter is constantly optimized by CFPSO algorithms, until CFPSO algorithms Fitness function is restrained or algorithm reaches the iterations specified, and terminates optimization process, exports the end value of EM algorithm parameters, So as to construct the user interest degree model, scoring rate_uHMM of the prediction user to projectu,i, the model construction flow chart such as 2 It is shown.
Then, algorithm establishes project-based prediction recommended models.By introducing the PROJECT TIME factor, PROJECT TIME is constructed Saturation, so as to improve the Similarity Measure mode based on Project cooperation filtered recommendation, the similitude between raising project.It is logical Cross and construct project-based prediction recommended models, and then scored by predicting that scoring formula calculates prediction of the user to project rate_Itemu,i, the prediction recommended models structure flow chart it is as shown in Figure 3.
Finally, algorithm relies on the user interest degree model based on gauss hybrid models and project-based prediction recommendation mould Type, the collaborative filtering recommending model based on Gaussian Mixture is constructed, i.e. algorithm is directed to the user of two models acquirements to the pre- of project Test and appraisal point, are connected by linear function, improve prediction scoring formula, and then calculate final prediction of the user to project Score rateu,i。
Algorithm model proposed by the present invention is contrasted with other algorithms from Fig. 4, can clearly see set forth herein Algorithm GMM-TCF MAE values are significantly less than other algorithms, and with the increase of item number in project neighborhood, MAE values are in now Drop trend.
Summary is tested, and user is recommended using the collaborative filtering recommending model based on Gaussian Mixture, on the one hand The more interest of user can be effectively utilized, while are optimized in the selection of Gaussian mixture parameters value.On the other hand, project is introduced Time factor not only can be between raising project similitude, and calculation can be effectively reduced by way of threshold calculations neighborhood The run time of method, it is adjusted by way of linear combination that prediction is scored so that scoring of the user to project is more accurate Really, so as to improve the recommendation precision of algorithm and recommend efficiency.

Claims (1)

  1. A kind of 1. big data intelligent recommendation method based on Gaussian Mixture, it is characterised in that：This method realizes that step is as follows,
    (1) the similarity forecast model based on user interest；First, the joint by PLSA model constructions user and project is general Rate, based on this Probability Forms, build suitable likelihood function i.e. big data intelligent recommendation model；Then, it is excellent by CFPSO algorithms Change EM algorithms so as to solve the parameter in big data intelligent recommendation model；Finally, with big data intelligent recommendation model solution mesh Mark prediction scoring of the user to project；
    A. the joint probability of user and project is built；For each three-dimensional vector ＜ u, i, v ＞, wherein u, i, v is respectively to use The scoring of family u, project i and user u to project i；Introduce latent variable Z={ z1,z2,…,zk, wherein zi(1≤i≤k) is Different cluster colony, with P (zk| u) represent that user u belongs to zkThe probability of colony andP(v|i,zk) represent Colony zkTo project i scorings v probability；Then the joint probability of user and project is：
    B. it is big data intelligent recommendation model to build likelihood function；It is assumed that colony z to project i score v conditional probability P (v | i, Z) meet Gaussian Profile, there are P (v | i, z)=N (μi,z,σi,z)=P (v；μi,z,σi,z), wherein μi,z,σi,zRespectively Z pairs of colony The average and variance of project i scorings, then the joint probability of user and project is a probabilistic model for meeting Gaussian Mixture：Then obtaining log-likelihood function is：
    <mrow> <mi>R</mi> <mrow> <mo>(</mo> <msup> <mi>&amp;theta;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> <mo>=</mo> <mo>-</mo> <munder> <mo>&amp;Sigma;</mo> <mrow> <mo>&lt;</mo> <mi>u</mi> <mo>,</mo> <mi>i</mi> <mo>,</mo> <mi>v</mi> <mo>&gt;</mo> </mrow> </munder> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>z</mi> <mo>&amp;Element;</mo> <mi>Z</mi> </mrow> </munder> <mi>P</mi> <mrow> <mo>(</mo> <mi>z</mi> <mo>|</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo>,</mo> <mi>i</mi> <mo>;</mo> <msup> <mi>&amp;theta;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> <mo>&amp;lsqb;</mo> <mi>log</mi> <mi> </mi> <mi>P</mi> <mrow> <mo>(</mo> <mi>v</mi> <mo>,</mo> <mi>i</mi> <mo>|</mo> <mi>z</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>log</mi> <mi> </mi> <mi>P</mi> <mrow> <mo>(</mo> <mi>z</mi> <mo>|</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
    C. parameter initialization selects；For parameter P (z | u), μi,z,Parameter is carried out using K-means clustering algorithms initial Change；Meanwhile the parameter after initialization is optimized with CFPSO algorithms；The number of population is set as n, Arbitrary Particles i's Positional representation is Xi=(x1,x2,…xn), (1) formula is selected as fitness function；Then based on CFPSO optimization EM algorithms the step of It is as follows：
    The first step：Initialize particle populations；The number of given population simultaneously to the initial position of each particle in population with Speed is initialized, and position and speed formula are as follows:
    <mrow> <msubsup> <mi>v</mi> <mrow> <mi>i</mi> <mi>d</mi> </mrow> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <mi>k</mi> <mo>&amp;lsqb;</mo> <msubsup> <mi>&amp;omega;v</mi> <mrow> <mi>i</mi> <mi>d</mi> </mrow> <mi>t</mi> </msubsup> <mo>+</mo> <msub> <mi>c</mi> <mn>1</mn> </msub> <msub> <mi>r</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <msubsup> <mi>pbest</mi> <mrow> <mi>i</mi> <mi>d</mi> </mrow> <mi>t</mi> </msubsup> <mo>-</mo> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mi>d</mi> </mrow> <mi>t</mi> </msubsup> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>c</mi> <mn>2</mn> </msub> <msub> <mi>r</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <msubsup> <mi>gbest</mi> <mrow> <mi>i</mi> <mi>d</mi> </mrow> <mi>t</mi> </msubsup> <mo>-</mo> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mi>d</mi> </mrow> <mi>t</mi> </msubsup> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mi>d</mi> </mrow> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>x</mi> <mrow> <mi>i</mi> <mi>d</mi> </mrow> <mi>t</mi> </msubsup> <mo>+</mo> <msubsup> <mi>v</mi> <mrow> <mi>i</mi> <mi>d</mi> </mrow> <mrow> <mi>t</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
    Wherein,Represent speed of i-th of particle in t+1 moment d dimension spaces, k is compressibility factor, and ω is inertia weight, c1, c2 For aceleration pulse, r1And r2For random number,WithRepresent particle i in the individual optimal of t d dimension spaces respectively And global optimum,Represent i-th of particle in the position of t+1 moment d dimension spaces；
    Second step：Calculate the fitness value of each particle in population, and the current individual optimal location p of more new particlebestAnd grain The colony optimal location g of subgroupbest；
    3rd step：To the g of populationbestIt is updated according to EM algorithms；Compare the front and rear fitness value of renewal, if more G after newbestValue causes fitness function value to become big, then Population Regeneration optimal location gbestInformation, otherwise not update；
    4th step：To the population optimal value g after renewalbestVerified, if it meets to require, terminate CFPSO algorithms, and Obtain gbestInitial parameter of the attribute information of value as EM algorithms；Otherwise the 5th step is gone to；
    5th step：According to formula (2) and (3) renewal population in particle individual speed and location parameter and go to second step after It is continuous to perform；Wherein, the execution step of EM algorithms is as follows：
    E is walked：According to each scoring vectorial ＜ u, i, v ＞, be calculated each potential variable z ∈ Z posterior probability P (z | U, v, i), it is as follows：
    <mrow> <mi>P</mi> <mrow> <mo>(</mo> <mi>z</mi> <mo>|</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo>,</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>P</mi> <mrow> <mo>(</mo> <mi>v</mi> <mo>;</mo> <msub> <mi>&amp;mu;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>z</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;sigma;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>z</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>P</mi> <mrow> <mo>(</mo> <mi>z</mi> <mo>|</mo> <mi>u</mi> <mo>)</mo> </mrow> </mrow> <mrow> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>z</mi> <mo>&amp;Element;</mo> <mi>Z</mi> </mrow> </munder> <mi>P</mi> <mrow> <mo>(</mo> <mi>v</mi> <mo>;</mo> <msub> <mi>&amp;mu;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>z</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;sigma;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>z</mi> </mrow> </msub> <mo>)</mo> </mrow> <mi>P</mi> <mrow> <mo>(</mo> <mi>z</mi> <mo>|</mo> <mi>u</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
    M is walked：The posterior probability being calculated according to E steps, and combine Lagrange optimization extreme value and ask local derviation can likelihood function Obtain P (z | u), μi,z,Value, respectively it is as follows：
    <mrow> <mi>P</mi> <mrow> <mo>(</mo> <mi>z</mi> <mo>|</mo> <mi>u</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msub> <mi>&amp;Sigma;</mi> <mrow> <mo>{</mo> <msup> <mi>u</mi> <mo>&amp;prime;</mo> </msup> <mo>,</mo> <mi>v</mi> <mo>,</mo> <mi>i</mi> <mo>}</mo> <mo>:</mo> <msup> <mi>u</mi> <mo>&amp;prime;</mo> </msup> <mo>=</mo> <mi>u</mi> </mrow> </msub> <mi>P</mi> <mrow> <mo>(</mo> <mi>z</mi> <mo>|</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo>,</mo> <mi>i</mi> <mo>)</mo> </mrow> </mrow> <mrow> <munder> <mi>&amp;Sigma;</mi> <mrow> <msup> <mi>z</mi> <mo>&amp;prime;</mo> </msup> <mo>&amp;Element;</mo> <mi>Z</mi> </mrow> </munder> <msub> <mi>&amp;Sigma;</mi> <mrow> <mo>{</mo> <msup> <mi>u</mi> <mo>&amp;prime;</mo> </msup> <mo>,</mo> <mi>v</mi> <mo>,</mo> <mi>i</mi> <mo>}</mo> <mo>:</mo> <msup> <mi>u</mi> <mo>&amp;prime;</mo> </msup> <mo>=</mo> <mi>u</mi> </mrow> </msub> <mi>P</mi> <mrow> <mo>(</mo> <msup> <mi>z</mi> <mo>&amp;prime;</mo> </msup> <mo>|</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo>,</mo> <mi>i</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mi>&amp;mu;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>z</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>&amp;Sigma;</mi> <mrow> <mo>{</mo> <msup> <mi>u</mi> <mo>&amp;prime;</mo> </msup> <mo>,</mo> <mi>v</mi> <mo>,</mo> <mi>i</mi> <mo>}</mo> <mo>:</mo> <msup> <mi>i</mi> <mo>&amp;prime;</mo> </msup> <mo>=</mo> <mi>i</mi> </mrow> </msub> <mi>v</mi> <mi>P</mi> <mrow> <mo>(</mo> <mi>z</mi> <mo>|</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo>,</mo> <mi>i</mi> <mo>)</mo> </mrow> </mrow> <mrow> <munder> <mi>&amp;Sigma;</mi> <mrow> <msup> <mi>z</mi> <mo>&amp;prime;</mo> </msup> <mo>&amp;Element;</mo> <mi>Z</mi> </mrow> </munder> <msub> <mi>&amp;Sigma;</mi> <mrow> <mo>{</mo> <msup> <mi>u</mi> <mo>&amp;prime;</mo> </msup> <mo>,</mo> <mi>v</mi> <mo>,</mo> <mi>i</mi> <mo>}</mo> <mo>:</mo> <msup> <mi>i</mi> <mo>&amp;prime;</mo> </msup> <mo>=</mo> <mi>i</mi> </mrow> </msub> <mi>P</mi> <mrow> <mo>(</mo> <mi>z</mi> <mo>|</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo>,</mo> <mi>i</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msubsup> <mi>&amp;sigma;</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>z</mi> </mrow> <mn>2</mn> </msubsup> <mo>=</mo> <mfrac> <mrow> <msub> <mi>&amp;Sigma;</mi> <mrow> <mo>{</mo> <msup> <mi>u</mi> <mo>&amp;prime;</mo> </msup> <mo>,</mo> <mi>v</mi> <mo>,</mo> <mi>i</mi> <mo>}</mo> <mo>:</mo> <mi>i</mi> <mo>=</mo> <msup> <mi>i</mi> <mo>&amp;prime;</mo> </msup> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mi>v</mi> <mo>-</mo> <msub> <mi>u</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>z</mi> </mrow> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mi>P</mi> <mrow> <mo>(</mo> <mi>z</mi> <mo>|</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo>,</mo> <mi>i</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>&amp;Sigma;</mi> <mrow> <mo>{</mo> <msup> <mi>u</mi> <mo>&amp;prime;</mo> </msup> <mo>,</mo> <mi>v</mi> <mo>,</mo> <mi>i</mi> <mo>}</mo> <mo>:</mo> <mi>i</mi> <mo>=</mo> <msup> <mi>i</mi> <mo>&amp;prime;</mo> </msup> </mrow> </msub> <mi>P</mi> <mrow> <mo>(</mo> <mi>z</mi> <mo>|</mo> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo>,</mo> <mi>i</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
    Optimize the initiation parameter of EM algorithms according to CFPSO, be alternately performed E steps and M steps, until convergence, try to achieve parameter P (z | u), μi,z,Parameter set as big data recommended models；
    D. user interest similarity model prediction scoring；Parameter set in being walked by M, construct the user interest based on Gaussian Mixture Similarity model, so as to calculate prediction scorings of the user u to project i, specific formula is as follows：
    <mrow> <mi>r</mi> <mi>a</mi> <mi>t</mi> <mi>e</mi> <mo>_</mo> <msub> <mi>uHMM</mi> <mrow> <mi>u</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mi>E</mi> <mrow> <mo>(</mo> <mi>P</mi> <mo>(</mo> <mrow> <mi>v</mi> <mo>|</mo> <mi>u</mi> <mo>,</mo> <mi>i</mi> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <mo>=</mo> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>z</mi> <mo>&amp;Element;</mo> <mi>Z</mi> </mrow> </munder> <mi>P</mi> <mrow> <mo>(</mo> <mi>z</mi> <mo>|</mo> <mi>u</mi> <mo>)</mo> </mrow> <msub> <mi>u</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>z</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
    (2) project-based forecast model；More according to the user to be given a mark to project, then the similarity between project is higher；Together When, due to ware occur time it is more close, then the similarity between each article is higher, thus introduce PROJECT TIME because Son, it is defined as follows：
    <mrow> <msub> <mi>facT</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>=</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mo>|</mo> <msub> <mi>t</mi> <mi>i</mi> </msub> <mo>-</mo> <msub> <mi>t</mi> <mi>j</mi> </msub> <mo>|</mo> </mrow> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, tiAnd tjThe time occurred for project i and project j；Definition project i and j similarity are sim (i, j)：
    <mrow> <mi>s</mi> <mi>i</mi> <mi>m</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>u</mi> <mo>&amp;Element;</mo> <mi>U</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>&amp;cap;</mo> <mi>U</mi> <mrow> <mo>(</mo> <mi>j</mi> <mo>)</mo> </mrow> </mrow> </munder> <mrow> <mo>(</mo> <msub> <mi>r</mi> <mrow> <mi>u</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>-</mo> <mover> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <msub> <mi>r</mi> <mrow> <mi>u</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>-</mo> <mover> <msub> <mi>r</mi> <mi>j</mi> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> </mrow> <mrow> <msqrt> <mrow> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>u</mi> <mo>&amp;Element;</mo> <mi>U</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>&amp;cap;</mo> <mi>U</mi> <mrow> <mo>(</mo> <mi>j</mi> <mo>)</mo> </mrow> </mrow> </munder> <msup> <mrow> <mo>(</mo> <msub> <mi>r</mi> <mrow> <mi>u</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>-</mo> <mover> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </msqrt> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>u</mi> <mo>&amp;Element;</mo> <mi>U</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> <mo>&amp;cap;</mo> <mi>U</mi> <mrow> <mo>(</mo> <mi>j</mi> <mo>)</mo> </mrow> </mrow> </munder> <mrow> <mo>(</mo> <msub> <mi>r</mi> <mrow> <mi>u</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>-</mo> <mover> <msub> <mi>r</mi> <mi>j</mi> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>&amp;times;</mo> <mi>min</mi> <mrow> <mo>(</mo> <msqrt> <mfrac> <mrow> <mi>max</mi> <mrow> <mo>(</mo> <mo>|</mo> <mi>U</mi> <mo>(</mo> <mi>i</mi> <mo>)</mo> <mo>&amp;cap;</mo> <mi>U</mi> <mo>(</mo> <mi>j</mi> <mo>)</mo> <mo>|</mo> <mo>,</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> </mrow> <mi>&amp;theta;</mi> </mfrac> </msqrt> <mo>)</mo> </mrow> <mo>&amp;times;</mo> <msub> <mi>facT</mi> <mrow> <mi>i</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, U (i) and U (j) is that the user of project i and j scoring is gathered respectively, ru,iAnd ru,jRepresent user u to project i and Project j scoring,WithAverage score of all users to project i and project j is represented, θ is nonnegative number；Then define user couple The prediction scoring of project is as follows：
    <mrow> <mi>r</mi> <mi>a</mi> <mi>t</mi> <mi>e</mi> <mo>_</mo> <msub> <mi>Item</mi> <mrow> <mi>u</mi> <mo>,</mo> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mover> <msub> <mi>r</mi> <mi>i</mi> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>+</mo> <mfrac> <mrow> <mi>s</mi> <mi>i</mi> <mi>m</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <msub> <mi>r</mi> <mrow> <mi>u</mi> <mo>,</mo> <mi>j</mi> </mrow> </msub> <mo>-</mo> <mover> <msub> <mi>r</mi> <mi>j</mi> </msub> <mo>&amp;OverBar;</mo> </mover> <mo>)</mo> </mrow> </mrow> <mrow> <munder> <mo>&amp;Sigma;</mo> <mrow> <mi>j</mi> <mo>&amp;Element;</mo> <mi>S</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>)</mo> </mrow> </mrow> </munder> <mi>s</mi> <mi>i</mi> <mi>m</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>
    Wherein, the field that S (i) is project i is gathered, and selects whether project adds the mode of neighborhood to judge the phase of two projects here Whether it is more than certain threshold value like spending, the comparative sorting between the mode reduction project of such calculating, saves operation time；
    (3) linear weighted function is predicted；By user interest comparability prediction model and project-based forecast model with linear weighted function The prediction scoring of the two is combined by mode, and so as to calculate final prediction scoring of the user to project, its formula calculates such as Under：
    rateu,i=α × rate_uHMMu,i+β×rate_Itemu,i, 0 ＜ α ＜ 1, alpha+beta=1 (12)
    To sum up, to user in collaborative filtering to project prediction scoring be improved, respectively by Gaussian Mixture, CFPSO, EM algorithms are established and are based on user interest similarity forecast model, and project forecast model is based on by adding time factor foundation, from And linearly combined the prediction scoring of the two, as final prediction scoring of the user to project.
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