The development of network technology has brought about the phenomenon of information overload. The collaborative filtering recommendation system proactively provides a list of resources that may interest users based on the historical evaluation information of certain resources. The existing collaborative filtering recommendation system equally treats historical information occurring at different moments and lacks quantitative timeliness analysis . Some research results use linear or nonlinear decay functions to quantify the changes in aging over time. Some scholars use linear functions as the basis for the quantification of timeliness. Some scholars use the kernel function to calculate the decay of aging with time. Some scholars pointed out that the quantification of timeliness is a process of gradual decline over time. Although the above model satisfies the basic characteristics of aging decline over time to a certain extent, it does not consider the variability of the aging decline of resources. In the recommendation system, user interest drift is ubiquitous, which leads to dynamic changes in the degree of time-dependent decline. It shows that popular resources have a slower decay rate. Therefore, how to explore the decay characteristics of timeliness over time according to user interests is the main way to improve the practical value of timeliness quantification in the recommendation system.
Based on this, we propose a collaborative filtering recommendation model (FC-CFRM) using forgetting curves. This model reveals the differentiation law of the forgetting rate of resources from user interest drift. A multi-stage aging quantification method and a time unit mapping function are used to calculate the aging value of historical information with memory characteristics . This provides a basis for rationally quantifying the timeliness of historical information and improving recommendation effects.
FC-CFRM can be defined as 6-tuple <
The specific implementation process of FC-CFRM is divided into two stages: similarity calculation and evaluation prediction.
According to user resource historical evaluation information, similarity calculation is used to determine the degree of similarity between different resources . This provides a basis for subsequent evaluation and prediction. Common similarity calculation methods include the Euclidean distance method, conditional probability method, and Pearson method.
We regard resources as points in the subspace of user evaluation manifolds. The distance between points determines the degree of similarity between resources. The greater the distance between points, the lower the similarity. If let
We regard the degree of resource similarity as the probability
Pearson's method uses the idea of mathematical statistics. We regard resource evaluation as the sampling result of repeated experiments in the same sample space. If
According to the similarity calculation result, the evaluation value aggregation operation is performed on all resources similar to the unknown evaluation resource
The German psychologist Ebbinghaus used nonsense syllables as materials and used the method of relearning to reveal the characteristics of memory aging in the forgetting process over time (Figure 1). The evaluation information of the designated resource in the recommendation system reflects the user's subjective recognition of the resource. This degree of subjective acceptance will inevitably decay over time, similar to the forgetting process. Different memory sources have different levels of forgetting attenuation, and memory materials that users are interested in are more likely to be remembered . This is the same as the requirement that different resources in the recommendation system have differences in time decay. Based on this, we use the forgetting curve describing memory characteristics as the basis for measuring the time-effect change of resources.
We regard the current aging body as an information storage room. The initial timeliness is used as the input of the room, and the retention of timeliness based on the historical evaluation information of the forgetting feature resources is a function
Solve the original function
The forgetting curve indicated by
The forgetting rate
In this section, the method of determining control parameters is understood as the adjustment process of the forgetting curve in multiple stages based on the phenomenon of memory enhancement in memory psychology.
Memory enhancement refers to the memory step (recovery of complete memory) after learning and a new forgetting process with a lower forgetting rate. If let
Figure 2 can be regarded as a dynamic adjustment process of forgetting rate caused by changes in user interest. If
We need to further determine
The rate of forgetting on the curve is adjusted based on user feedback. If
The numerical relationship between
In the recommendation system,
The adjustment process of the forgetting rate presents a recursive relationship. If the initial forgetting rate is
According to formula (16), the time unit mapping function of the single-stage aging quantification method can be expressed as
2) We substitute the forgetting rate
We recommend the classic data set MovieLens in the system for simulation analysis. MovieLens comprises more than 10,000,000 evaluations made by 71567 users on 10681 different movies on the entire network. Each evaluation record includes user identification, movie identification, evaluation value, and time stamp. We take the first 10,000 time-adjacent resource historical evaluation information as the initial simulation data set in the original data set. The initial experimental data set is divided into training and test sets by cross-validation, and the percentage is divided. The training set is used to obtain the forgetting rate of resource historical evaluation information. The test set will be evaluated and predicted based on the time-effect analysis results obtained from the training.
Obtain the time-sensitive forgetting rate of the resource according to the resource identifier in the test record. Calculate the aging value based on the system time difference to make recommendations. After the recommendation is over, the forgetting rate is adjusted for the resource of the record feedback. At the same time, the test records after evaluation and prediction are moved to the end of the training set. This provides a basis for calculating the similarity between resources in the subsequent recommendation process.
The average absolute error (MAE) is used to measure the recommended effect of FC-CFPM in different experiments, and its calculation method is shown in equation (20).
The specific setting method of the initial critical system time
|Parameter name||Parameter meaning||Value|
||Initial critical system time||6E(ΔT)|
|Initial forgetting rate||1|
The laziness factor
Each curve in Figure 4 represents the 10-time segmented MAE sampling of FC-CFRM under different
The comparative analysis of the recommendation effect measures the recommendation effect of different models on the test set. The classic collaborative filtering recommendation model that lacks consideration of the timeliness of resource historical evaluation information is expressed as (N-CFRM). The collaborative filtering recommendation model with simple index k=1 and time-effect quantification is expressed as (E-CFRM). The collaborative filtering recommendation model based on the quantification of the mechanical forgetting curve is expressed as (F-CFRM). The collaborative filtering recommendation model based on the forgetting curve is expressed as (FC-CFRM). Recommendation effect analysis uses the formula (21) to calculate the degree of MAE difference between other recommendation models *-CFRM and N-CFRM. If the value is negative, the recommendation effect is worse than N-CFRM. On the contrary, if the value is positive and larger, the recommendation effect is better. The experimental results are shown in Figure 5.
Each segment in Figure 5 contains the degree of MAE difference between the three recommended models and N-CFRM. The segment length is 200. In general, the recommendation error of all recommendation models shows a fluctuating state on different segmented data sets. Among them, E-CFRM has 7 positive segments and 3 negative segments. F-CFRM has 8 positive segments and 2 negative segments. FC-CFRM are all positive segments. Table 2 shows the statistical characteristics of MAE for each recommendation model, indicating its specific recommendation effect.
MAE statistical analysis
|Recommended method||Max||Minimum||variance||average value|
The average recommendation effect ranking of each recommended method is E-CFRM<N-CFRM<F-CFRM<FC-CFRM. The order of stability is F-CFRM < E-CFRM < N-CFRM < FC-CFRM
Since E-CFRM adopts an artificial method to set the forgetting rate of the exponential function, it ignores the influence of user interest on the time-dependent quantification of different resources. Therefore, its performance is worse than N-CFRM in terms of recommendation effect and recommendation stability.
From the experimental results of F-CFRM, it can be seen that adopting the forgetting curve can better fit the change of resource aging with time. Its performance is that the average recommendation effect is higher than that of N-CFRM. Still, it ignores the characteristics of the multi-stage forgetting process in the quantification of resource timeliness. The recommendation effect of F-CFRM will fluctuate greatly when user interests change. FC-CFRM can adopt a useful historical information time-sensitive quantitative model to track changes in user interests.
We propose a collaborative filtering recommendation model using forgetting curves based on the temporal characteristics of historical evaluation. The experimental results show that the model reasonably reveals the changing law of forgetting rate with user interest and provides stable and high-quality recommendation effects.
|Parameter name||Parameter meaning||Value|
||Initial critical system time||6E(ΔT)|
|Initial forgetting rate||1|
MAE statistical analysis
|Recommended method||Max||Minimum||variance||average value|
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