Chorus translation

Abstract

The traditional recommendation system is mainly inherent to users 、 Modeling long-term preferences , Dynamic user requirements are also very important . Usually , Historical consumption will affect users' demand for their relationship items . for example , Users often buy complementary products at the same time (iPhone and Airpods), Instead of buying alternative products (Powerbeats and Airpods), Although alternatives can still meet user preferences . In order to better simulate the influence of historical sequence , Previous studies have introduced the semantics of item relationships to capture users' recommendation needs . However , We think , The time evolution of the effects caused by different relationships can not be ignored . In the example above , When a user needs a new headset , Users' demand for earphones can be increased after a long time . In order to establish the dynamic meaning model of the project in different sequence environments ,Chorus In this paper, a new method considering project relationship and corresponding time dynamics is proposed . The goal of chorus is to deduce the embedding of target items through a way of knowledge perception and time perception , Each item will get its basic representation and related representation . then , According to whether there are relation items in the historical sequence and the running time , Design Temporal kernel function To dynamically combine these representations . Enhanced target item embedding can flexibly calculate ranking scores and generate recommendations with various algorithms . Based on extensive experiments on three real data sets , Compared with the most advanced baseline method , The chorus has been significantly improved . Besides , The time-dependent parameters are highly interpretable , Can enhance the interpretability of recommendations .

chart 1： The previous relationship consumption is right AirPods Description of the time impact of requirements ：iPhone Current consumption may have a positive impact in the short term , But if the user just bought Powerbeats, The effect is the opposite . The positive effect of complement decays with time , The negative effect of substitutes will turn into positive effect after a period of time .

1. Introduce

With the overload of information on the Internet , Recommendation system is playing a more and more important role in our daily life . It not only provides information that caters to users' tastes , It is also helpful to discover the internal preferences of users . Traditional recommendation methods mainly focus on user preference modeling [11,13,19,33]. for example , Potential factor model [21] Embed users and items into a potential space , The user's embeddedness represents various preferences , It doesn't change at different recommended times .
However , Although user preferences are static most of the time , But the consumer demand of users is actually dynamic 、 Variable . In different environments , The same items have different meanings for the same user . actually , Sequential consumption behavior can be seen as a process to meet the needs of users in different aspects . The consumption of one item may have an impact on other related items , And the impact of this different relationship is also different . Take complementarity and substitution as examples , chart 1 Explains how the effect of purchasing items with different relationships changes over time . Add ： Assume that the user currently purchases iPhone, He / She may buy... In the short term AirPods（ namely iPhone A supplement to ）. But after a while , The positive effect will be reduced ( Users may already have headphones , The recommender system should not continue to provide AirPods). For alternatives ： If he / What she has just consumed is AirPods substitute , Such as Powerbeats, The short-term impact is expected to be mainly negative , Because the user doesn't need another headset immediately . Although the negative impact may turn into positive in the medium term , Because the user may need to buy a new headset , And the newly released AirPods May be attractive . This positive effect will gradually weaken , Users may lose interest in the headset , Or buy another earphone in other ways .
From the example above , We can see that the current consumption of different relationship items has different effects on the target items . what's more , Each relationship has a different time trend . There are also studies that introduce project relationships into recommendation systems [16,40,44,45], But the time dynamics of different relationships are not considered . Although some studies involve long-term and short-term preferences [16], But project relationships are only used to model the transformation of short-term projects , Lack of modeling of the continuous evolution of different relationship effects . Another recent study investigated repeated consumption [41] Time dynamics of . However , Consumption will not only affect the same commodity itself , It will also affect related goods . therefore , The project relationship and the corresponding time dynamics are the key to obtain the dynamic meaning of the project in different contexts .
This paper presents a method of embedding target items based on knowledge and time perception —— Chorus . As far as we know , We are the first to explicitly model the evolution of the effects of different relationships over time , This helps to better capture the meaning of each item in the context of different sequences . Specially ,Chorus The translation based graph embedding method assigns a basic representation and various relational representations to each item . then , These representations are dynamically combined through temporary kernel functions , It depends on how much time has been spent since the relationship was consumed , This is why it was named Chorus Why . The proposed temporal kernel function enables the relational representation to contribute to the final term embedding in different ways . therefore ,Chorus Can dynamically acquire knowledge and time aware project embedding , This can easily be used by various recommended algorithms . Besides , The highly interpretable time-dependent parameters make it possible to interpret the recommendation results in different time periods . The main contributions of this work are summarized as follows ：
$\bullet$ We suggest to consider both the project relationship and the corresponding time dynamics . As far as we know , We are the first to explicitly simulate the duration evolution of the effects of different relationships .
$\bullet$ We designed a novel and flexible method Chorus, When the target item plays different roles in the sequence , Enhance the modeling of target objects by dynamically combining different representations . The final project embedding can easily work with various recommended algorithms .
$\bullet$ Comparative experiments on three real datasets show that Chorus The effectiveness of the , And the high interpretability parameters further help to improve the interpretability of the model .

2. Related work

2.1 Timing recommendations

Different from the traditional recommendation method , Sequence recommendation is based on Markov chains , Use sequence data to predict users' next consumption , Markov chain assumes that the next action depends on the previous action sequence [34,37].Rendleet al.[34] Combined with matrix decomposition [21] And Markov decomposition chain , Give the next basket of recommendations for the previous basket . lately , There is a lot of work using recurrent neural networks (RNN)[36] Encode interaction history into hidden vectors [6,12,23,27,32,38].Hidasi wait forsomeone [12] First of all, will RNN Introduced into the sequence recommendation , And achieved impressive performance gains .Loyolaet al.[27] and Peiet al.[32] Will pay attention to the mechanism [39] be applied to RNN, To get more effective recommendations . Besides , Many follow-up studies have focused on extending the RNN The ability of the model .
Although based on RNN The sequential recommendation method has strong expression ability , But due to the lack of external knowledge , They are still not good at simulating complex user requirements , And there are serious interpretability problems [26]. The difference is , Our approach clearly addresses project relationships and the corresponding temporal dynamics , To better capture user needs .

2.2 Project relationship modeling

In a real application , Items with specific semantics usually have multiple relationships . Some recent studies have focused on how to introduce project relationships into recommendation systems [16,28,30,40,44,45], Most of them use knowledge maps (KG)[42] To represent the project relationship .CFKG[45] The user and product relationship diagram is introduced as an entity , Think of buying as another relationship , And then use TransE[3] Represent heterogeneous information networks and make recommendations .Xin wait forsomeone [44] A general recommendation task is proposed , This task contains multiple relationships between projects , And integrate relational data into collaborative filtering (CF)[35] in .Ma wait forsomeone [28] A joint learning framework is proposed , It integrates the induction of interpretable rules from the knowledge graph .
However , All these methods assume that the impact of relational item consumption is static , And it has nothing to do with time information , under these circumstances , Even if the user does not need a complement , It may also continue to recommend complements after a long period of time .

2.3 Time dynamics modeling

Considering the time information , There are two main types of work . One side , Some work aims to use temporal information as a contextual feature .TimeSVD++[20] Divide time into slots , And design parameters related to time .TransMF utilize FM Use timestamp as an additional context feature [31]. Tensor decomposition is also a major method [2,17], Where time is regarded as the user - The third dimension of the object interaction cube . On the other hand , Some work focuses on simulating the time decay effect of historical interactions . In this line ,Hawkes Process (HP)[8] It is always used to model the mutual excitation characteristics of user consumption sequence [7,22,24,41].Du wait forsomeone [7] First of all, will Hawkes The process should be used for time sensitive recommendations .SLRC[41] Combined with the Hawkes Process and collaborative filtering to simulate the time dynamics of repeated consumption .
However , These methods do not take into account the temporal dynamics of different relationships . therefore , To better model dynamic user requirements , We creatively considered the project relationship and the corresponding time evolution .

3 Preprocessing

3.1 Task definition

Definition 3.1( Problem definition )： Whereas the user $u\in U$ And interaction history $S_u=(i_1,t_1),(i_2,t_2)...(i_{N_u},t_{N_u})\in S$, In time $t_n<t_{n\prime }$ For arbitrary $n<n\prime <N_u$ Of $N_u$ Secondary interaction , The recommended tasks are ： Consider the target time t( Write it down as $S_u^t$) Previous interaction sequence , Generate a sequence table , This includes the user in t May be interested in k A project .
Besides , set up R A collection of all item relationships , Each item relationship $r\in R$ There's a matrix $I_r\in N^{M\times M}$, among M Is the total number of items , If the relationship r Pair item i and j If it is established, then $I_r(i,j)$ = 1, Otherwise 0. Relationship r Can be complementary , And so on .

3.2 Knowledge graph embedding

Information about project relationships can be viewed as a knowledge map , Its components are a set of triples (i,r,j), among i and j Represent different items ,r Represents the relationship type . for example ,(AirPods, is_complementary _o f,iPhone) Express AirPods yes iPhone A supplement to . It should be noted that , Sometimes the opposite of a triple may not hold ( for example iPhone No AirPods A supplement to ), So the graph is directional .
In order to introduce the structure information of the diagram into the recommendation system , It is very important to obtain the embedding with the semantic meaning of project relationship . Among various embedding methods , Translation based model [3,25,43] With its efficiency and effectiveness . Its internal idea is to embed projects and relationships into the same potential space , And find a translation function to minimize the scoring function ：

among D(·) Is a measure function of distance ( Usually $l_2-norm$).Trans(i,r) Is an arbitrary translation function , It can be a simple pan operation , It can also be a specially designed neural network . A lot of work has focused on the ability expansion of translation functions , Such as TransE [3], TransH [43], TransR[25] etc. . about TransE[3], The translation function is Trans(i,r) = i +r, For any triple (i,r,j) application $l_2-norm$ The scoring function is $f(h,r,t)=||h+r-t|{|}_2$.
To learn project and relationship embedding from diagrams , Will be based on marginal losses [45] To minimize the , As shown below ：

For each triplet , The tail term is a random sampling term $j^{\prime }$ Replace , In order to ensure that $(i,r,j^{\prime })$ Not observed in the knowledge map . Similarly , The title item is $i^{\prime }$ Replace , also $(i^{\prime },r,j)$ Don't set up . The purpose of the above objective function is to distinguish between observed triples and corrupted triples , And force embeddedness to maintain relationships between projects .

3.3 Recommend basic methods

The project modeling method proposed in this paper can be flexibly used with various recommended algorithms . Because Bayesian personalized sorting (Bayesian Personalized Ranking, BPR)[33] It is a widely used matrix factorization method , And generalized matrix factorization (Generalized matrix factorization, GMF)[11] It is one of the most advanced methods based on neural network , We chose them as the basic recommendation model to verify the effectiveness of our method .
This paper briefly reviews the two collaborative filtering methods .CF The method assumes that similar users like similar items . stay BPR Under the circumstances , There is one for each user and item k Dimensional potential factor , The ranking score is calculated as follows ：

among $b_u$ and $b_i$ The preferences of each user and project .
stay GMF Under the circumstances , The ranking score is obtained by multilayer neural network , It can be expressed as ：

among ${\varphi }_{out}$ and ${\varphi }_x$ Represents the output layer and the... Respectively X Mapping function of a neural co filtering layer , share X Nerves CF layer . then , According to the predicted score ${\hat{y}}_{ui}$ Rank the candidate projects .
In order to learn the parameters in the recommendation model , You can sort the losses in pairs [33] To optimize :

among ,$\sigma$ by s Type of function , A negative term $j\notin S_u$ Is a random sample of each training instance .

4 Chorus model

4.1 Model overview

Chorus is a two-stage model , It integrates the project relationship and its specific time effect . chart 2 The whole model structure is demonstrated . In the first phase ( Relationship modeling ), Using graph embedding, the structural information of project relationship is encoded into embedding . Here you can flexibly use the 3.2 The various translation based methods described in section . The results of graph embedding will be used to derive the basic and relational representations in our chorus model .

In the second phase (Dynamic Item Representation) in , There are two key modules ：(1) Dynamic integration ,(2) Design of temporal kernel function . First , In addition to the basic relationship representation based on the translation function , Each entry will get $|R|$ Relationship means , The translation function represents the representation of the target item when it plays different roles in the context . then , According to whether there is corresponding relationship consumption and running time in the historical sequence , Dynamically integrate these representations . To combine the temporal dynamics of each relationship , We propose a time kernel function with a specific relationship to control the polarity and intensity of the effect . therefore , Relational representations have different contributions to final item embedding in different contexts , Thus, the dynamic items of knowledge perception are embedded . Last , Many algorithms can use enhanced item embedding to calculate ranking scores and make recommendations . In the rest of this section , We will elaborate on the key modules of chorus in the second stage .

4.2 Dynamic integration

First , According to the results embedded in the diagram , Define the basic representation of each item ( Write it down as $i_b$) And relationship means ( Write it down as $i_r$ Represents the relationship $r\in R$). The basic representation encodes the inherent characteristics of the item , Use the item embedding learned in the first stage to initialize $i_b$, Then we use the translation function to get the relation representation ：

among $e_r$ yes $r\in R$ The relationship is embedded in , such , Relational representation integrates the semantic information corresponding to each relationship .
After obtaining the basic and relational item representations , Here we focus on how to dynamically combine them according to different contexts , This is ours Chorus The core idea of the model . Be careful , Relational representation is knowledge aware , But it is still static . Our goal is to derive a context aware coefficient for each relational representation $f_r$, To reflect the actual level of influence in the current context . Finally, context and knowledge aware items are embedded $i_{Chorus}$ Put forward the following expression ：

It consists of two parts ： Basic item representation and scaled relational item representation , Where context ( Historical sequence $S_t^u$, Time t And target projects i) As a coefficient $f_r$ The input of . Next, we focus on how to get reasonable from a given context $f_r$.
Intuitively speaking , Some relationships indicate that in some cases there may be no impact , Even negative effects . chart 3 Some examples are given , Explain how these representations contribute to the final embedding in different contexts . The three corners of the triangle represent different representations of the target item . When there is no relation to consumption ( Context A) when , The final embedding is just the basic item representation , The other two relationships have no effect . When Powerbeats or iPhone When I first bought ( Context B and C), The corresponding relationship indicates that there should be negative and positive effects respectively . And if the substitute was purchased a long time ago ( Context D), The characterization of alternatives may have a positive impact on the final embedding . Besides , When there are many different relational terms in the sequence , All three representations will work in varying degrees .

To integrate the temporal dynamics of different relationships , We creatively designed a time kernel function for each relationship , It is a continuous function of the lag time between consumption . The purpose of temporal kernel function is to control the influence degree of consumption of each previous relationship . The polarity of the function value indicates the polarity of the effect . Suppose we have obtained the time kernel function ${\kappa }_r^i(∆t)$, In terms of i And relationship r Index ( The specific design and related discussion are left in the next section ), We suggest defining the relationship coefficient $f_r$ as follows ：

among $I_r$ Is a relational matrix . Every previous consumption and target project $i$ The relationship between $r$ The coefficient will be $f_r$ There is a superposition effect , By kernel function $k_r^i(\cdot )$ control . such , Different from the previous research on static project embedding , The correlation coefficient makes different representations have different contributions to the final embedding . Because of the existence of time kernel function , Relational representations may be too long apart to work , In some cases, it may even have a negative impact . therefore , Choral embedding can better capture the meaning of items in different contexts , So as to better simulate the change of user requirements over time .
Besides , For simplicity and efficiency , We can only consider the latest relational terms in the historical sequence , under these circumstances ,Equ.(7) It can be expressed directly as ：

In style ,$∆t_r$ Indicates the elapsed time since the last consumption , With the current item $r$ relevant . If there is no relation item in the history sequence of a relation , We assume that there is a relation term with a positive infinite time interval ($∆t_r=+\infty$). Suppose that the temporal kernel function approaches zero with time , Then the corresponding relationship embedding is not affected .

4.3 Design of temporal kernel function

Next , We focused on how to design temporal kernels for each relationship . actually , The concrete form of time kernel function can be regarded as a kind of artificial intervention to the model . One side , We can design functions according to the characteristics of each relationship . for example , Pictured 1 Shown , Complementary relationships have a positive impact in a short time , This effect decays over time . On the other hand , It can be designed according to the subjective requirements of the system . If we want substitutes to appear on the recommended list in the short term , The time-domain kernel function can be designed with a positive initial value , Decay faster . In this paper , We mainly study two kinds of relations ： Complementarity and substitution . As an instance , According to the general cognition and characteristics of these two relations, we design the corresponding time kernel function .
For supplements , In addition to the overall downward trend , The positive effect usually lasts for a period of time , Then it begins to decay in daily life . therefore , We choose the normal distribution with zero mean as its time kernel function , Instead of an intuitive exponential distribution that decays too fast ：

In style $N(∆t|\mu ,\sigma )$ yes ∆t along with $\mu$ Mean and $\sigma$ Normal distribution of standard deviation . Note the parameters here ${\sigma }_c^{z(i)}$ And $z(i)$ of ,$z(i)$ Represents a project i Categories . We do not estimate project specific parameters , Because category is usually a more appropriate level , To simulate the characteristics of a group of projects . Term specific parameters can also be plagued by data sparsity .
For alternatives , We expect that the impact will change from negative to positive , Because we don't need another thing with similar effect in the short term , But hopefully at the end of its life [41] Replace new items when necessary . therefore , We use two opposite normal distributions to simulate such characteristics ：

This is a (1) Short term inhibition ( negative ) and (2) Lifelong promotion ( just ) The superposition . The negative normal distribution is designed as zero mean , Because the effect of retraining is usually the strongest after alternative consumption . In positive numbers , Parameters ${\mu }_s^{z(i)}$ To some extent, it represents the life cycle of this class , That is, the impact will peak at this time .
chart 2 Shows these two temporary kernel functions . Other forms of temporary kernel functions can also be designed to meet different needs . Besides , Chorus is not limited to these two relationships . Many relationships can be merged , Such as the same brand 、 Same manufacturer, etc ,
The only thing to do is to design a corresponding temporal kernel function on the basis of prior knowledge .
ad locum , We get the final knowledge aware dynamic project embedding . Then use various algorithms to recommend , Using our algorithm instead of embedding the original target term . Different from the previous model ,Chorus It also integrates sequence information 、 Project relationship modeling and corresponding time dynamics . Recently proposed CFKG and SLRC Or just focus on commodity relations , Or just focus on the time dynamics in the consumption order . surface 1 The related methods and our Chorus The difference between models . More details on these baselines will be found in section 5.1.3 Section describes .

4.4 Parameter learning

In order to obtain better robust performance , We use a two-stage training process to learn the model parameters ： First , Optimize $L_{rel}$ Get the project and relationship embedding with structural information , In the second stage, the basic item representation and relationship embedding are initialized ; Then minimize $L_{rec}$ To learn all the parameters of the model . In the second phase , We will not freeze what we have learned before . Experiments show that , use $L_{rec}$ Better results can be obtained by optimization . On the other hand , It may also destroy meaningful embeddedness at the beginning of training . therefore , In the second phase , We reduce the learning rate of embedding basic item representation and relationship 0.1. because Adam[18] It has been successful in many recommendation models , So use it as a learning algorithm at every stage .

5. experiment

5.1 Experimental setup

5.1.1 Data sets The experiment was conducted in a public interview Amazon Data sets [9] on . Except for user interaction sequences with time stamps , It also has project metadata , Include also_view,also_buy and category information A list of . Following previous studies [28,29] after , We will also_view As an alternative relationship ,also_buy As a complementary relationship . The difference is , In our work , Relationship means being complementary and replaced . therefore , The original also_view,also_buy The direction of the relationship should be reversed .
We use three representative sub datasets ：Grocery and Gourmet Food (Grocery), phones and Accessories (Cellphones), and Home and Kitchen (Home). surface 2 The statistics of three data sets are summarized . Be careful , stay Home Data set , The proportion of test cases related to historical items is very low , And the relational data is relatively sparse .

5.1.2 Evaluation protocol We use the leave one method to evaluate , This method has been widely used in the literature [4,10,15]. For each consumption sequence $S_u\in S$, We use each user's recent interaction to test , Verify with the second most recent entry , Use the remaining items to train . Considering that when the data set is large , Some methods of sorting all items are time-consuming , We randomly selected 99 Projects that the target user has not interacted with , take ground-truth Projects with these negative Items are sorted together . This method is also widely used [11,41,44].
In order to evaluate the recommended quality , We use hit rate (HR) And normalized discounted cumulative gain (NDCG)[14] As an evaluation indicator [email protected] It's evaluation “ground-truth” Whether it is in the top of the recommended rankings k Bit of website ,[email protected] It's evaluation “ground-truth” Whether it is in the top of the recommended rankings k Bit of website . We repeated each experiment with different random seeds 5 Time , And report the average score .
5.1.3 Baseline approach We will Chorus Model and 7 The two baseline methods are compared in different aspects , Including traditional collaborative filtering 、 Sequential recommendations and methods that include project relationships or temporal dynamics ：
•BPR[33]: This method proposes a matrix decomposition model with pairwise ordering loss optimization .
•GMF[11]: This is an advanced collaborative filtering method , Using multilayer neural network .
•Tensor[17]: This method divides time into multiple containers , And decompose a three-dimensional tensor ( user - project - Time ).
•GRU4Rec[12]: This is a sequential recommendation model , application GRU[5] Get the ranking score .
•NARM[27]: The model uses GRU And attention mechanism to improve the performance of sequential recommendation , This is a session based approach .
•CFKG[45]: This method considers various commodity relationships , And regard purchase as another relationship between users and commodities . then , utilize TransE Learn graph embedding and make suggestions .
•SLRC Of [41]:SLRC combination Hawkes and CF To simulate the time dynamics of repeated consumption . Considering that the Amazon data set has removed repeated consumption , We extend this setting to the impact of relational items , Name it SLRC '. But it still lacks semantic modeling of project relationships .
5.1.4 Implementation details We are PyTorch All models are implemented in . The implementation code has been released . For comparison , The embedded dimensions of all models are set to 64. All the super parameters are tuned to get the best results in the validation data set . about CFKG, We have considered also_view and also_buy The relationship is consistent with ours . about SLRC ' and Chorus, We find that there are few interactions between two or more relational terms in the historical sequence . therefore , For simplicity and efficiency , We do this without sacrificing versatility and performance , Consider the latest relational interactions in the sequence . Besides , It is also used in chorus TransE As a translation function . For numerical stability , All time related parameters are initialized to 1, Other parameters are usually initialized to 0 Mean and 0.01 Standard deviation .

5.2 Overall performance

surface 3 Shows all baselines and our Chorus The model is used in BPR and GMF Performance when calculating ranking scores , Expressed as $Choru{s}_{BPR},Choru{s}_{GMF}$.
First , Different types of baselines show significant performance gaps . For collaborative filtering methods ( for example BPR and GMF), They serve as benchmarks , Because the only information they have is the user - Project interaction . The tensor method is superior to the basic method by considering the time dynamics CF Method . Sequential recommendation method ( Such as GRU4Rec and NARM) Further better performance , This illustrates the importance of the dynamic user needs for the delivery of recently consumed items .CFKG Got a fair result , It has become the best baseline on some indicators , This shows that the project relationship does help recommend . about SLRC’, Because of its explicit modeling of the mutual incentive characteristics of the consumption sequence , Generally, the best results are obtained in the baseline .
secondly , our Chorus The model performed better than other baselines in all data sets , This benefits from dealing with project relationships and their temporal dynamics . This shows that the proposed model can better capture the dynamic needs of users and the meaning of items in different contexts . And CFKG comparison , Chorus not only considers the relationship between objects , It also integrates time dynamics between items . And SLRC comparison , Chorus can simulate the semantic and category specific temporal effects of each relationship . stay SLRC in ,Hawkes The basic form of may be more concerned with the impact of relationship projects , therefore , In the absence of a prior relationship , It usually affects performance consumption ( See chapter for more discussion 5.4). The difference is ,Chorus Integrating project relationships into knowledge aware dynamic project representation , This is more effective and flexible .
On the other hand , Please note that , stay Home Data set , The improvement is relatively small . The possible reason is that the relationship information is too sparse and not so reliable . We use CFKG Similar relation graph embedding method , But the performance of this method on this data set is also very poor . Even though TransE Works well in other datasets , however Home Relationships in data sets can be so complex , So much so that TransE Not enough to model accurately . More evidence in 5.3 Section provides .

5.3 Ablation Experiment

To verify the effect of relationship modeling and time dynamic processing in our model , We compared the chorus with two variants ：
• Chorus \ R. The model assigns a separate project embed for each relationship , And through optimization Lr ec Estimate all parameters . The results of graph embedding are not used to initialize the basic representation and derive the relational representation .
• Chorus \ T. The model does not consider the time dynamic relationship , Suppose that all time kernels ( namely :∆t) All are constants , The value is 1.
chart 4 Shows $choru{s}_{B}PR$ Of [email protected]0 And its variants , as well as SLRC’. We can conclude that , Relationship modeling and time dynamics are very important . The lack of chorus module leads to the loss of performance . Besides , We have the following views ：
First , Project relationships are really helpful . stay Grocery and phones Data set ,Chorus\R The biggest performance loss , This shows the importance of relational structure information modeling , And our translation based approach , Derive relational representations through graph embedding .
secondly , It is very important to build time dynamic models of different relationships . Without time information , Chorus \T Moderate loss of performance in the first two datasets . This does not mean that the temporal dynamics dealt with in our model are unimportant . Literally , The relationship between commodities has a greater impact on users' consumption decisions . therefore , It is reasonable to model project relationships to bring greater improvements than modeling time dynamics . On the other hand , And Chorus\T comparison , The chorus has made consistent improvements , Especially in Home in , This shows the usefulness of moving forward , Take into account the temporal dynamics of the project relationship .
Third , The diagram is embedded in Home Poor performance in data set , among Chorus\T The biggest loss of performance , and Chorus\R Less performance loss . This is another proof that the relational model is inadequate . although TransE Is the natural choice of translation function , And it usually works well on the other two datasets , But we found it in Home Data set scenarios may not be enough , stay Home Data set CFKG Use TransE As its graph embedding method, it also performs badly . chart 4 Show , No relationship modeling , Performance won't degrade much (Chorus\R). But if there is relational modeling and there is no temporal kernel function (Chorus\T), Improper embedding of items and relationships will affect performance . It also shows that , The temporal dynamics handled in our model can help to adaptively avoid the possible bad effects of chaotic relationships , This shows the usefulness and necessity of considering time dynamics .

5.4 Different scene performance

In addition to the improvement of overall performance , We also want to figure out where these improvements come from . Here we study the performance of the model in different scenarios . say concretely , We construct three subsets of the test data set according to whether there is corresponding relationship consumption in the historical sequence . Normal means that there were no related items before . Complement means that the target item is the complement of some items in the historical sequence . Similarly , A substitute is a situation in which previous consumption is used as a substitute . When there were two kinds of relation items before , Test cases may be in both complement and substitution groups . chart 5 It shows different models in the three subsets of the mobile phone data set ( That's ok ) Of [email protected] And the number of cases ( strip ). We can see , Although there are fewer cases in the complement and substitution groups , But models tend to perform better in these situations . They may prove some patterns in essence , In this way, all models can achieve better performance than normal , Even if the project relationship is not explicitly considered BPR So it is with .
Besides , Chorus can combine the advantages of various methods , So as to achieve the best average score . Be careful , about SLRC and CFKG, They all have their own advantages and disadvantages . Even though SLRC Good performance in relationship cases , Especially in Substitute In the group , But it's even better than BPR Worse . This shows that SLRC ' It is easy to over fit the relationship , This, in turn, can damage normal performance . On the other hand , Even though CFKG It performed well in the normal group , But in the relational case , It's not as good as SLRC ' Powerful , because SLRC ' The temporal characteristics of each relationship are explicitly simulated . As for chorus , It captures the temporal dynamics of project relationships and their category specific . It is worth noting that , Under normal circumstances ,Chorus And CFKG similar ; In the supplementary case , Chorus ratio SLRC A little bit better. , Both of these are the best baselines in each scenario . Although singing in alternative groups is not as good as SLRC’ strong , But with CFKG It is obviously improved . result ,Chorus Significantly better average results were obtained , This shows the importance of integrating project relationships and fine-grained temporal dynamics .

5.5 Parameter interpretability

ad locum , We hope to verify whether the time-dependent parameters have interpretable meaning when designing the time kernel function . Be careful , These parameters are indexed by item category , This shows how the impact of previous relationship consumption on this category changes over time . Although the overall trend of a particular relationship tends to converge because of its functional form , But their concrete forms reveal the characteristics of category . chart 6 It shows the temporal kernel functions of some representative categories learned in the mobile phone data set .

The figure on the left corresponds to the complementary relationship between headphones and replacement parts . As shown in the figure , The effect on the earphone decays much faster than the replacement part . One side , After buying a mobile phone , It is reasonable to recommend earphones to users as a supplement . But if the user doesn't use the recommended headphones , He / She may already have a headset or buy one from somewhere else . therefore , The positive effect of complement is expected to fade soon , Otherwise, continuous recommendation of earphones may cause trouble to users . On the other hand , For replacement parts such as backup batteries , The positive effect of supplementary consumption will last for some time . Because users usually buy backup batteries after the original equipment battery runs out for a period of time .
Although the general form consists of two opposite normal distributions , But the time kernel function in the basic case is very different from the other two cases , The component of inhibition effect is almost flat . This shows that when users buy mobile phone cases , Will not have a strong negative impact , Because we often change the case for various reasons , For example, the edge is broken , Or just want to try new styles . For international chargers and mobile phones , Their time-domain kernel functions show obvious negative effects and positive peaks . It's reasonable , Because if we just bought a charger or cell phone , There is usually no need for another charger or mobile phone . Interestingly , The time intervals corresponding to the peaks of the two items are similar , This reflects that changes in mobile phones often lead to changes in matching chargers . Besides , Compared with charger , The curve of the mobile phone is smoother . The reason might be , We can change mobile phones for various reasons , But if the charger works , It is seldom replaced . therefore , New phones can be used after a long time interval .
in summary , our Chorus The time-dependent parameters in the model are highly interpretable , It well reflects the characteristics of different types of projects . These parameters can help the recommendation system to interpret the recommendation results . for example , The user has purchased iPhone, This happens to be the peak value of the time kernel function of the mobile phone , Recommending a new mobile phone can be explained as “ Your mobile phone has been used for a long time , Take a look at some new products ?”

6 Conclusion and future work

In this work , We propose a new approach to choral knowledge and time aware project modeling . As far as we know , We are the first to explicitly model the impact of different relationships over time , And embed this information into the project . We use graph embedding to learn structural information from the project diagram , Then derive different relational representations for each item . Using a specific time kernel function to control the time dynamics of the relationship , And according to the time interval between the target item and the relation item in the historical sequence, the dynamic combination relation is expressed , Get the dynamic term representation of knowledge perception . in addition , The design of temporal kernel function can be regarded as a kind of human intervention to the model , It can be used to meet different requirements for recommended results . because Chorus The flexibility of the , It can easily use a variety of embedding based algorithms to calculate ranking scores and make recommendations . A large number of experimental results show that , Chorus is superior to the most advanced baseline , This shows that project relationships and their time evolution effects are very important . Besides , The time-dependent parameters in chorus are highly interpretable , Help to improve the interpretability of recommendations .
The model still has some limitations , Such as predefined time function and two-stage learning process . Besides , Although the method based on translation works well on the whole , But in some cases , We found its shortcomings , Further research is needed . future , We will study how to adaptively estimate the time evolution effects of different relationships , And try to design a more suitable method , Closely combine project relationship modeling and recommendation .