CN103136694A - Collaborative filtering recommendation method based on search behavior perception - Google Patents

Abstract

The invention discloses a collaborative filtering recommendation method based on search behavior perception. The method includes the following steps: (1) analyzing inquiry behaviors and search behaviors of a user on an e-commerce website; (2) constructing user-product keyword tensor based on search behavior context; (3) constructing a training dataset of a factor machine model and mapping tensor data into vector data; (4) establishing a recommendation method frame based on the factor machine model and utilizing an improved alternate least squares algorithm to carry out parameter estimation; and (5) evaluating the recommendation method based on the factor machine model through an experiment. The collaborative filtering recommendation method based on the search behavior perception utilizes context information ignored by a traditional collaborative filtering recommendation method, solves the problem that a traditional individuation recommendation method cannot provide a recommended result which expresses the intent of the user on a business to business e-commerce website, and is better than a traditional method in accuracy and timeliness of the recommended result.

Description

Collaborative filtering recommendation method based on search behavior perception

technical field

The invention relates to the field of Internet personalized recommendation, in particular to a collaborative filtering recommendation method based on search behavior perception.

Background technique

In recent years, the successful application of personalized recommendation systems on the Internet has created new opportunities for Internet companies, especially e-commerce websites. 30% of the purchase business on B2C e-commerce websites in specific fields comes from personalized recommendation systems. However, recommender systems are not widely used on B2B e-commerce websites. B2B e-commerce websites play an intermediary role in business activities, and buyers look for suppliers of target products through B2B e-commerce websites. In this process, the buyer first enters the search keywords related to the target product, and the e-commerce website returns a large number of products of the same type from different suppliers. Its suppliers make inquiries. The recommendation system on a B2B e-commerce website aims to provide users with suitable product candidates and help users complete the above business activities more effectively, thereby improving user satisfaction and dependence on the website.

Collaborative filtering recommendation algorithm is the most commonly used recommendation algorithm in personalized recommendation system. The collaborative filtering algorithm analyzes the user's interests, finds similar users of the target user in the user group, and synthesizes the evaluation of a certain item by these similar users, and finally forms a prediction of the target user's preference for a specific item. The two main collaborative filtering methods are the method based on the neighbor model and the method based on the latent factor model. The method based on the neighbor model uses the user's historical behavior data to calculate the similarity of the user (item) by using methods such as Pearson correlation and angle cosine, and obtains the set of neighbors of the user (item), and then uses these The neighbor-related behavior data calculates the target user's rating for a specific item to make recommendations. The core idea of the method based on the latent semantic model is to link user interests and items through latent factors. It decomposes the user rating matrix into a low-rank user matrix and item matrix through algorithms such as Matrix Factorization. According to The inner product of the user feature vector and the item feature vector is used to obtain the predicted value of the user's rating for the item. Methods based on latent semantic models are widely used in recommender systems.

On B2B e-commerce websites, synergistic relationships can be used to filter products according to user preferences, but recommendations based entirely on synergy may not reflect user intentions. Context-aware collaborative filtering algorithms provide a solution to this problem. Context-aware collaborative filtering methods can be divided into three types: 1) contextual pre-filtering methods, which drive data selection or data construction through context; 2) contextual post-filtering methods, which pass Contextual filtering recommendation results; 3) contextual modeling (contextual modeling) method, which integrates context into the model. In the research of context-aware recommendation methods, the context modeling method has been paid attention rapidly because of its superior performance over traditional methods. In practical applications, if keywords are used to represent user's search behavior, then the model for perceiving user's search behavior includes users, products, keywords and the relationship between the three at the same time. The collaborative filtering task is defined as: predicting the value of missing elements in the tensor according to the values of some elements in the tensor composed of users, products and keywords.

Tensor factorization algorithms have high computational complexity, which makes tensor factorization-based methods unsuitable for large-scale recommendation tasks. The Factorization Machine model is currently the best context-aware model. The number of its parameters increases linearly, and each parameter has an analytical solution, which effectively solves the problem of computational complexity and retains the advantages of the context-aware collaborative filtering algorithm. The invention uses a factor-machine model to realize the perception of user search behavior, so as to provide more valuable recommendation services for B2B e-commerce websites.

Contents of the invention

Purpose of the invention: Aiming at the problem that the collaborative filtering algorithm cannot perceive the user's search behavior, analyze the user's search behavior and inquiry behavior, use the keywords used in the user's search behavior as the context of the user's inquiry behavior, and provide a B2B e-commerce website Collaborative filtering recommendation method based on user search behavior perception.

Technical solution: a collaborative filtering recommendation method based on search behavior perception, including the following steps:

(101) Analyze the inquiry behavior and search behavior of users on e-commerce websites, and unify the identification of users, products and keywords;

(102) Construct a user-product-keyword tensor based on the search behavior context, which uses keywords as the context of the inquiry behavior;

(103) Constructing a factor machine model training data set, establishing a mapping between tensors and vectors, and the mapping converts three-dimensional tensors into one-dimensional vectors;

(104) Establish a recommendation method framework based on the factor machine model, the framework learns the parameters of the factor machine model through the training data set and predicts the user's evaluation value of the product according to the current search behavior as the context;

(105) experimentally evaluate recommendation methods based on factor machine models.

Wherein, step (101) includes:

(101-1) Analyze user identities in log files of e-commerce websites, perform disambiguation operations on user identities, and map user identities to unique user identifiers in the system;

(101-2) Identify the type of behavior in the user behavior records, and extract the behavior sequence; use the inquiry behavior as the end of the behavior sequence, use the search behavior closest to the inquiry behavior as the beginning of the behavior sequence, and combine the two behaviors The click behavior of is used as the middle content of the behavior sequence; among them, if there is no search behavior before the inquiry behavior occurs, the search behavior is considered to be empty;

(101-3) Analyze the products involved in the sequence of actions, and the keywords used in the search action.

In step (104), the recommendation method framework based on the factor machine model is divided into two processes: learning and prediction; in the learning process, the framework obtains the parameters of the factor machine model through learning according to the training data set constructed in step (103). ; During the prediction process, the framework calculates the evaluation value using the learned model parameters according to the given user, product and keywords used by the user. Step (104) uses the improved alternating least squares algorithm to estimate the parameters of the factor machine model, and the method used is to first fix the known quantities that have nothing to do with the solution parameters, and then calculate the analytical solution of the solution parameters; the improved alternating least squares The multiplication algorithm reduces computational complexity by pre-computing known quantities.

Step (105) includes preparing a data set; using the root mean square error as an evaluation index; conducting experiments on the data set; and analyzing the experimental results.

The present invention adopts the above technical solution, and has the following beneficial effects: the present invention uses the search behavior on the B2B e-commerce website as the context of its inquiry behavior, so that the recommendation system has the ability to perceive the specific needs of users. The number of parameters of the factor machine model increases linearly, and each parameter has an analytical solution, which makes the optimization algorithm have a lower time complexity. The invention adopts the context-aware collaborative filtering algorithm based on the factor machine model, which effectively improves the accuracy and timeliness of the recommendation results of the B2B e-commerce website, thereby improving user satisfaction and dependence on the e-commerce website.

Description of drawings

Fig. 1 is the method flowchart of the embodiment of the present invention;

FIG. 2 is a tensor schematic diagram of a search behavior context according to an embodiment of the present invention;

Fig. 3 is the schematic diagram that the tensor data of the embodiment of the present invention is converted into vector data;

Fig. 4 is a schematic diagram of the experimental results of the embodiment of the present invention on the MovieLens scoring data set;

Fig. 5 is a schematic diagram of the experimental results of the embodiment of the present invention on the MovieLens implicit feedback data set.

Detailed ways

Below in conjunction with specific embodiment, further illustrate the present invention, should be understood that these embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention, after having read the present invention, those skilled in the art will understand various equivalent forms of the present invention All modifications fall within the scope defined by the appended claims of the present application.

The invention analyzes the user's search behavior, inquiry behavior and click behavior on the B2B e-commerce website, uses keywords generated by the search behavior as the context of the inquiry behavior, and constructs a user-product-keyword three-dimensional tensor. Furthermore, by establishing the mapping from tensor data to vector data, the training data of the factor machine model is constructed. Then the parameter estimation method of the factor machine model is given, which is the improved alternating least squares method. Finally, comparisons are made with baseline algorithms on standard datasets. As shown in Figure 1, the method of the embodiment of the present invention includes the following steps:

Step 101: Analyze the search behavior, click behavior and inquiry behavior of users on the e-commerce website, identify user identities and generate user sets, identify products and generate product sets, identify search keywords and generate keyword sets. All elements in the set have globally unique identifiers. Specifically include:

(101-1) Analyze user identities in log files of B2B e-commerce websites, perform disambiguation operations on user identities, map user identities to unique user identifiers in the system, and generate user set U. The behavior sequence of each user in a session period is recorded as a user behavior record, where a session period refers to the period from when the user logs in to the website and starts to operate to when he leaves the website and no longer operates.

(101-2) Identify the type of behavior in user behavior records, and extract the behavior sequence. The inquiry behavior is regarded as the end of the behavior sequence, the search behavior closest to the inquiry behavior is regarded as the beginning of the behavior sequence, and the click behavior between the two behaviors is regarded as the middle content of the behavior sequence. Wherein, if there is no search behavior before the inquiry behavior occurs, the search behavior is considered to be empty.

(101-3) Analyze the products involved in the sequence of actions, and the keywords used in the search action. Correspond the product to the unique product identifier in the system and generate product set I. The keywords are subjected to standardization processing such as stemming and synonym merging, corresponding to the unique keyword identifier in the system and generating a keyword set Q.

，则f(u,i,q)＝r表示张量中某个元素的值。分析步骤101得到的行为序列，当用户u在使用了关键词q进行搜索之后，对产品i进行了询盘，则定义f(q,u,i)＝1；当u在使用了关键词q进行搜索后，对产品i进行了点击，但没有进行询盘，则定义f(q,u,i)＝0；否则f(q,u,i)的值缺失。Step 102: Construct a user-product-keyword tensor T≡U×I×Q based on the search behavior context, as shown in FIG. 2 . Among them, keywords serve as the context of user-product behavior. define function

, then f(u,i,q)=r represents the value of an element in the tensor. Analyze the behavior sequence obtained in step 101, when user u makes an inquiry about product i after using the keyword q to search, then define f(q,u,i)=1; when u uses the keyword q After searching, product i is clicked but no inquiry is made, then define f(q,u,i)=0; otherwise, the value of f(q,u,i) is missing.

Step 103: Construct the factor machine model training data set, and establish the mapping between tensor and vector. The mapping process projects the three dimensions of each element of the tensor to different components of the vector, that is, T _uiq → x ^(uiq) , where T _uiq represents an element of the tensor, and x ^(uiq) represents a one-dimensional vector.

The specific operation of mapping a tensor to a vector is as follows:

Use the function φ(u)=x ^(u) to transform the value u into a vector x ^(u) , where

Use the function φ(i)=x ⁽ⁱ⁾ to convert the value i into a vector x ⁽ⁱ⁾ , where

Use the function φ(q)=x ^(q) to convert the value q into a vector x ^(q) , where

将三个部分连接成一个向量，其中

表示两个向量的连接操作。Concatenate operations via vectors

Concatenate the three parts into one vector, where

Represents the join operation of two vectors.

具有以下三种形式：where the conversion function φ(·):

Has the following three forms:

(1) Category domain: The category variable C can be mapped to a real-valued vector for each category through an indexer. As shown in Figure 3, there are only three situations for keywords, so if user u ₁ uses keyword q ₂ to search and inquire about product i ₁ , then the vector φ(q ₂ )=(0,1,0), if the key The word is q ₃ , then the vector φ(q ₃ )=(0,0,1).

(2) Category set domain: The category variable set C can be mapped to a real-valued vector for each context through an exponent, and all non-zero elements have the same value, and the sum is 1. For example, user u ₁ uses keywords {q ₂ , q ₃ } to search and inquire about product i ₁ , then the vector φ({q ₂ ,q ₃ })=(0,0.5,0.5).

(3) Real-valued domain: If C is a real number, then use the real value as the feature, that is, φ(C)=C.

Step 104: Establish a recommendation method framework based on the factor machine model, the framework is divided into two processes of learning and prediction. During the learning process, the framework obtains the parameters of the factor machine model through learning according to the training data set constructed in step 103 . In the prediction process, the framework uses the learned model parameters to calculate evaluation values based on the given user, product, and keywords used by the user. The specific implementation method is:

(104-1) Model Representation. The factor machine model measures the relationship between the components of the vector by factoring the interaction parameters, and its model is shown in formula (1):

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&equiv;</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="w"\; filenames="HDA00002943473800021.png,HDA00002943473800022.png"\; state="\{\{state\}\}">w</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

in represents the factorized interaction parameter between the components of the vector,

${\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; \&equiv;</span><span\; class="notranslate">\; \&lang;</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; \&rang;</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; k</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; \&Center\; Dot;</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

建模分量之间的因子化互作用关系。其中x表示训练样本，表示预测评价值。Among them, the model parameters Θ that need to be estimated are: w ₀ ∈ R, w ∈ R ⁿ , V ∈ R ^n×k . From formula (1), it can be seen that w ₀ is the global bias, and w _i models the interaction relationship between the i-th component and the evaluation value,

Models factorized interaction relationships between components. where x represents the training samples, Indicates the predicted evaluation value.

(104-2) Optimization objectives. Define the loss function as:

$\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; ,</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; S</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Where (x, r) represents a training data and its corresponding evaluation value, and S represents a training data set. According to the loss function defined by the formula (3), the optimization goal is obtained, and the optimization goal after adding the regularization item is shown in the formula (4):

$\mathrm{<span\; class="notranslate">\; RLS</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; OPT</span>}<span\; class="notranslate">\; =</span>\underset{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; S</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; \&Theta;</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

是正则化项，λ_(θ)是参数θ对应的正则化因子。in

Is the regularization term, λ _(θ) is the regularization factor corresponding to the parameter θ.

(104-3) Estimate the parameters of the factorial machine model, namely w ₀ ∈ R, w ∈ R ⁿ , V ∈ R ^n×k , using alternating least squares. In the calculation process, the model parameters are represented by θ, and the joint optimization method is adopted for all parameters θ∈Θ, that is, the optimal value of each parameter is alternately calculated until the termination condition is met.

The computational complexity of the alternating least squares algorithm is usually relatively high, but the computational complexity can be effectively reduced by the pre-computation method when the analytical solution can be obtained. When using the alternating least squares algorithm to estimate the parameters of the factor machine model, it can be seen that the factor machine model is a linear model when the parameters irrelevant to the solution parameters are fixed, and the model can be divided into a constant part that is not related to the solution parameters and a part that is related to the solution parameters In the first-order function part, the analytical solution of the parameters can be quickly obtained through the invariant of the pre-computation model. Theorem 1 and Theorem 2 give the proof of the linear model of the factor machine model and the process of solving the parameter analytical solution for the optimization objective respectively.

Theorem 1: For each model parameter θ∈Θ, its factor machine is a linear model, namely:

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; g</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

The form of the function g, h is related to θ, but the specific value has nothing to do with θ.

The proof process is as follows:

The specific forms of parameters w ₀ , w _l , v _l,f can be obtained from formulas (1) and (2), as follows:

w ₀ :

w _l :

v _{l, f} :

It can be seen from the above formula that for each parameter θ∈Θ, its factor machine model can be described as two relatively independent parts: the constant part g _(θ) (x) and the linear function part θh _(θ) related to θ (x), so that the factor machine model can be formally described as a linear function expression:

Theorem 2: For each parameter θ in the optimization objective, its analytical solution can be obtained,

$\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; g</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; S</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 6</span>}<span\; class="notranslate">\; )</span>$

The proof process is as follows:

$\mathrm{<span\; class="notranslate">\; RLS</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; OPT</span>}<span\; class="notranslate">\; =</span>\underset{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; S</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; \&Theta;</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$

Taking partial derivatives of its parameters, we can get:

$\frac{<span\; class="notranslate">\; \&PartialD;</span>}{<span\; class="notranslate">\; \&PartialD;</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}}\mathrm{<span\; class="notranslate">\; RLS</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; OPT</span>}<span\; class="notranslate">\; =</span>\underset{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; S</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}$

Then let the derivative be 0, and the formula can be obtained as follows:

$\underset{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; S</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}$

Substituting formula (5) into it, the following equation can be obtained:

$\underset{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; S</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; g</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}$

Expand to get the following equation:

$\underset{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; S</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; g</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\underset{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; S</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; \&theta;</span>}{\mathrm{<span\; class="notranslate">\; h</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}$

Simplification can be obtained:

$\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; S</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; g</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; h</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Element;</span>\mathrm{<span\; class="notranslate">\; S</span>}}{\mathrm{<span\; class="notranslate">\; h</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}_{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; )</span>}}$

It can be seen from the above formula (6) that in the factor machine model, an analytical solution can be calculated for each parameter θ, so the improved alternating least squares algorithm can be used to calculate the parameters.

Improved Alternating Least Squares Algorithm:

In this embodiment, first iteratively calculates parameters with small interaction, and then calculates parameters with relatively large interaction, that is, iteratively calculates w ₀ , w _l , v _l,f sequentially. It can be seen from the calculation formula (6) of θ that the calculation of the optimal value of θ mainly depends on the calculation of the two function values of g and h. It can be seen from Theorem 1 that the functions g and h have nothing to do with the parameter θ, so the value of the functions g and h can be pre-calculated to avoid repeated calculations in the iterative process, thereby reducing the computational complexity.

则有g_(θ)(x)＝e(x,r|Θ)-θh_(θ)θ。首先计算

当参数θ变成θ^*时候，再更新e，更新公式如下:For the function g, define:

Then there is g _(θ) (x)=e(x,r|Θ)-θh _(θ) θ. calculate first

When the parameter θ becomes θ ^* , update e again, and the update formula is as follows:

e(x,r|Θ ^* )=e(x,r|Θ)+(θ ^* -θ)h _(θ) (x) (7)

则有：For the function h, define:

Then there are:

${\mathrm{<span\; class="notranslate">\; h</span>}}_{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; \&NotEqual;</span>\mathrm{<span\; class="notranslate">\; l</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; f</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}$

$<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; f</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; f</span>}}$

$<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; \&Theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; f</span>}}$

包含一个循环，此时可以采用预先计算已知量的方式在常数时间复杂度完成参数的计算。通过观察

可以看出q与l是相互独立的，因此可以提前计算q，当参数v_l,f变成

时更新q，更新公式如下：Since for the parameters w ₀ and w _l , the corresponding h _(θ) (x) can be calculated in constant time, and for the parameters v _i,f , the corresponding parameters

Contains a loop, at this time, the calculation of parameters can be completed in constant time complexity by pre-computing known quantities. By observing

It can be seen that q and l are independent of each other, so q can be calculated in advance, when the parameters v _{l, f} become

When updating q, the update formula is as follows:

$\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; \&Theta;</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; |</span>\mathrm{<span\; class="notranslate">\; \&Theta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; f</span>}}^{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; v</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$

The pseudocode of the above improved alternating least squares algorithm is as follows:

Step 105: Experimentally evaluate the recommendation method based on the factor machine model, specifically including:

(105-1) preparing data sets;

a. Use the MovieLens1M (http://www.grouplens.org/node/73) data set as the experimental data set in this embodiment. The MovieLens1M dataset contains 6,040 users and 3,900 movies, with a total of 1,000,209 user evaluation data (value range 1-5). Each movie corresponds to several keywords to indicate the theme of the movie. In this embodiment, movies are used to simulate products in e-commerce, and movie themes are used to simulate search keywords.

b. Analyze the evaluation data of MovieLens1M, take user behaviors with evaluation values greater than 3 to simulate inquiry behaviors, and use user behaviors with evaluation values less than 3 to simulate click behaviors. Each movie is associated with one or more topics, and the topics are used to simulate the keywords of the search behavior, so that each user behavior has a corresponding context.

c. Randomly select 80% of all behavioral data in the MovieLens1M dataset as the training dataset, and the rest as the test dataset.

(105-2) Evaluation indicators;

The root mean square error (RMSE) is used as the evaluation index of this embodiment. After each iteration of the algorithm, calculate the root mean square error of the current model on the test set.

(105-3) Experiment on the data set;

a. Compare the experimental results of the collaborative filtering method based on user search behavior perception and the collaborative filtering method based on SVD. In this embodiment, the stochastic gradient descent algorithm and the improved alternating least squares algorithm are used for training, and the SVD model is trained using the stochastic gradient descent algorithm. Among them, the hidden factor dimension of the factor machine model is set to 20; the learning rate of the stochastic gradient descent algorithm is set to 0.002, and the regularization factor is set to 0.01.

b. Compare the experimental results of context-aware FM and context-free FM. Among them, the hidden factor dimension of the factor machine model is set to 20.

(105-4) Analyze the experimental results;

a. It can be seen from Figure 4 and Figure 5 that under the premise of being context-independent, the collaborative filtering method based on user search behavior perception is superior to the collaborative filtering method based on SVD on both the scoring data set and the implicit feedback data set, thus improving the system correctness.

b. As can be seen from Figure 4, on the scoring data set, the root mean square error after convergence of the context-aware factor machine model and the context-independent factor machine model is similar, but the convergence speed of the context-aware factor machine model is significantly faster than that of the context-free model The factor machine model, thus effectively improving the training speed and system effectiveness.

Claims (5)

1. based on the collaborative filtering recommending method of search behavior perception, it is characterized in that, comprise the steps:

(101) user's inquiry behavior and search behavior on the analytical electron business web site, the sign of unification user, product and keyword;

(102) structure is based on the contextual user-product of search behavior-keyword tensor, and it uses keyword as the context of inquiry behavior;

(103) structure factor machine model training data set, the mapping of setting up tensor and vector, described mapping changes into one-dimensional vector with three-dimensional tensor;

(104) set up recommend method framework based on factor machine model, described framework learns to obtain the parameter of factor machine model by training dataset, and according to the current search behavior as the evaluation of estimate of context-prediction user to product;

(105) experimental evaluation is based on the recommend method of factor machine model.

2. the collaborative filtering recommending method based on the search behavior perception according to claim 1, it is characterized in that: described step (101) comprising:

(101-1) user identity in analytical electron business web site journal file carries out the disambiguation operation to user identity, and user identity is mapped to user ID unique in system;

(101-2) type of behavior in identification user behavior record, extract behavior sequence; With the end of inquiry behavior as behavior sequence, will with the beginning of the nearest search behavior of inquiry behavior as behavior sequence, with the medium content of the click behavior between two kinds of behaviors as behavior sequence; Wherein, if the inquiry behavior does not have search behavior before occuring, think that search behavior is empty;

(101-3) resolve related products in behavior sequence, and the keyword that uses in search behavior.

3. the collaborative filtering recommending method based on the search behavior perception according to claim 1 is characterized in that: in described step (104), described recommend method framework is divided into study and predicts two processes; In learning process, described recommend method framework obtains the parameter of factor machine model according to the training dataset of step (103) structure by study; In forecasting process, the keyword that described framework uses according to given user, product and user uses the model parameter that study obtains to calculate evaluation of estimate.

4. according to claim 1 or 3 described collaborative filtering recommending methods based on the search behavior perception, it is characterized in that: described step (104) adopts improved alternately least-squares algorithm to carry out the parameter estimation of factor machine model, and the mode that adopts is at first to fix and the known quantity of finding the solution cache oblivious, then calculates the analytic solution of finding the solution parameter.

5. the collaborative filtering recommending method based on the search behavior perception according to claim 1, it is characterized in that: described step (105) comprises the preparation data set; Adopt root-mean-square error as evaluation index; Test on data set; Analyze experimental result.

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