Optimization of Recommender Systems Using Particle Swarms

Introduction

Recommender systems constitute the basis for building technologies oriented towards improving user experience. Their use is part of our daily lives, given the popular use of applications such as Amazon, YouTube, and Google, whose recommender systems require a large volume of training information in order to provide effective suggestions ¹.

To achieve the necessary volume of data, applications record user actions on platforms, with the aim to profile users. Nowadays, it is natural to record the time, the number of clicks, and the reactions of users while interacting with a specifc content ². Additionally, it is important to gather content characteristics and quantify in order them to provide high-quality suggestions.

After training with the aforementioned data, a vector of hyperparameters is generated for each user, which works as an input to calculate the suggestions resulting from the multiplication of the vector by the content characteristics. However, calculating each hyperparameter vector is rarely easy, since finding the function that reduces the difference between the values expected by the user and the values obtained by the model depends on iterative methods that are computationally expensive ³.

In light of the above, it is common to find novelties in the techniques for the optimization of recommender systems, such as those described below:

In ⁴, a model capable of generating effective recommendations using collaborative models is presented. This memory-based model introduces a hybrid recommendation strategy that uses particle swarm optimization (PSO) to efficiently learn the weights of the parameters for each user. In addition, it uses fuzzy sets to naturally represent user ratings.

In ⁵, the PSO algorithm is implemented in order to learn about the user’s personal preferences. From this study, it is concluded that the use of this type of model specializes individual results for each user, thus generating greater precision in model predictions. On the other hand, in ⁶, low-rank matrices are implemented which introduce pairs of vectors and, via vector products, generalize user preferences towards one or more types of content. In conclusion, generalizing user preferences is possible, although the accuracy of the results is affected.

As opposed to the proposal made in this work, optimization using algorithm genetics is not performed in ⁷. The authors present a coevolutionary algorithm named cooperative coevolutionary invasive weed optimization (CCIWO), which optimizes functions with either local optima or Nash equilibria searches. The results show that implementing these algorithms optimizes the precision of the models and reduces their computational means.3

The authors of ⁸⁾ combine a semi-supervised optimization algorithm using a particle swarm with the clustering process from the recommender systems. They manage to overcome the expectations of the traditional recommender systems’ algorithms, thus reducing the time spent, as well as its corresponding computational resources.3

The work by ⁹ presents the Cognitive Information Filtering System (CIFS), which applies an evolutionary model while learning from user feedback. A CIFS filters emails based on user ratings and behavior monitoring.

Other techniques can be utilized to this effect, as is the case of the work presented in ¹⁰. This research demonstrates the use of networks based on the Bayesian Beliefs Network, which are also known as Bayesian Networks, allow reasoning under uncertainty, and combine the advantages of visual representation for decision-making. This work is crucial, as it allows for an approach towards creating a collaborative filter for recommender systems.33

On the other hand, bio-inspired algorithms consist of a set of problem-solving strategies based on Darwin’s natural selection theories, the functioning of neural networks, and bee swarms ¹¹. These algorithms can represent an optimization problem as a function to be maximized or minimized according to a set of constraints. This type of problem is usually studied by operations research and techniques such as linear programming, which are generally employed to obtain a solution. However, it is not always possible to find a solution by analytical or mathematical means. Thus, iterative methods must sometimes be used.

Considering the importance of recommender systems, as well as their broad implementation, an optimization technique is herein suggested that utilizes all the advantages of genetic algorithms, which can solve optimization problems whenever iterative methods must be used. Thus, it is a model capable of recommending based on user preferences and particle swarm optimization. To test the algorithm, a movie database was used as an example. The algorithm succeded in consolidating a parameterizable and adaptive model according to data characteristics.33

Materials and methods

Approach to the issue of optimization

Recommender systems base their operations on two aspects:

1. User attributes correspond to user metadata and actions recorded within the platform, aiming to classify users into a group that allows profiling their preferences into a categorical group.

2. Element attributes: These correspond to element metadata and allow grouping elements by categories, groups, currents, authors, etc

Figure 1: Movement of the particles in the function

The issue regarding the optimization of recommender systems consists of predicting a user’s rating of an element based on user and element attributes. Mathematically, this can be represented as follows:

1. nu: number of users

2. nm: number of elements.

3. r^{(i, j)} = 1: whether the user j has rated the element i

4. y ^(i,j): the rating given by the user j to the element i (defined only if r ^{(i, j)} = 1)

5. x ⁽ⁱ⁾ : characteristics of the element

6. i θ ^(j): a vector of parameters for the user j

Based on the above, the algorithm should try to predict y ^(i,j) for the values r (i, j) = 0 and recommend an element based on the result. Thus, for each user j, a parameter θ ^(j) must be learned, and the rating of user j to the element i must be predicted with I ^(i). Finally,

the objective function for user j is constructed using the mean squared error:

simplifying

the parameter λ is employed as a regularization parameter for the objective function.

2.2. Solution to the optimization problem using a particle swarm

Based on the study conducted by (14), it was concluded that particle swarms algorithms are useful when it comes to finding solutions faster than other bio-inspired algorithms such as evolutionary and genetic algorithms, which is why they were selected to solve this problem. Within this algorithm, each one of the particles moves across the surface of possible solutions according to three coefficients:

1. Inertia coefficient (W): it indicates the state of rest or motion of the particle.

2. Cognitive acceleration coefficient (C1): it indicates the speed of movement of the individual particle.

3. Social acceleration coefficient (C2): ): it indicates the speed of movement of the particle in a social way.

Therefore, the motion xi of the particle pi at an instant of time t is given by:

and its velocity Vi at an instant of time t is

where Pi is the best value obtained by the particle, and g is the best value obtained by a group of particles.

Thus, the particle moves in a vector parallel to the best individual value, the best global value, and its inertia at an instant of time t. Based on the above, each of the particles p corresponds to a solution θ^(j) , and the result obtained after executing the algorithm is employed as the optimal solution

Proposed algorithm

To develop the algorithm, the traditional model for training of recommender systems was considered, and its steps were adapted for the implementation of PSO. In general, these steps are as follows:

1. Data cleaning: Deletion or correction of the data outside the average or standardized data.

2. Profiling and definition of object features: The feature vector for each object x⁽ⁱ⁾ is defined. Additionally, the user is asked to rate some random objects, capturing r (i, j) = 1 and y^(i,j) .

3. Training: Initializing the particles pi to a random value within the feature domain X.

4. Subsequently, a number of maximum iterations and a minimum expected error are determined. The vectors [W Vi(t), C1(Pi(t) − xi(t)), C2(g(t) − xi(t))] are calculated, and the particle is displaced based on the equation for V_i until the stopping condition is reached. The convergence position of the particles will be taken as θ^(j) . Suggestions made to users based on the result of θX, taking the result as the probability that a user likes the content, with 1 being the most likely. Fig. 2 depicts these steps.

Figure 2: Description of the algorithm used to perform the training process

Results

To test the algorithm, a set of metadata was used which comprised 45.000 films that were released on July 2017 or before MovieLens. The metadata includes the cast, crew, plot keywords, budget, revenue, posters, release dates, languages, production companies, countries, and The Movie Database (TMDB) vote counts and averages. These are available in the Movies Dataset from Kaggle. We used two groups of regularization parameters for the particle swarm in order to generate two variations of the algorithm:

1. In the first variation, the Cognitive Acceleration Coefficient (C1) was prioritized with the values of W =1, C1 =3, and C2 =1,5, hereafter referred to as the school of fish (CP).

2. In the second variation, the Social Acceleration Coefficient (C2) was prioritized with the values of W =1, C1 =1,5, and C2 =3, hereafter referred to as the swarm of particles (SP).

Each of the algorithm’s variations was tested on a dataset that increased in volume by 50 records after each run. The Python programming language was used to develop the algorithm. Fig. 3 shows the execution of the algorithm on the terminal device. For the execution, a computer with an Intel Core i5 4 GHz 4-core processor and 16 Gb RAM memory were used.

Figure 3: Example of the algorithm’s execution

The results were recorded in Table I, which provides evidence that the CP model requires less time than the EP one. However, more iterations are needed

Table I: Comparison of training results for the proposed models

Let us recall that a good recommender system must be able to answer as quickly as possible, and, although the CP model demands more iterations, it meets the requirements for recommender systems training.

1. As part of the training process, the data were divided into three groups: 60 % used for data training

2. 20 % used for model testing

3. 20 % used for model validation

Table II shows the errors obtained when testing the model. It can be seen that the error rate decreases and converges as the data increase. Thereupon, the conclusion is that the model correctly generalizes each of the data groups presented in the previous model.

Table II: Comparison of validation mistakes for the different data sizes using a particle swarm

Finally, the algorithm was compared to the traditional recommender systems training method via the descending gradient. Table III shows the training results and validation errors for the different datasets. According to the results, it can be seen that the error obtained is greater and requires a higher number of iterations in comparison with the particle swarm algorithm.

Table III: Comparison of validation errors for different data sizes using the descending gradient

Conclusions

Based on these results, the following conclusions were reached:

Through bio-inspired algorithms, specifically particle swarms, it is possible to solve the problem regarding the optimization of recommender systems. Moreover, its implementation was demonstrated using a case study.

1. It was found that it is possible to generate a wide range of solutions by varying the parameters with which particle swarm algorithms are executed. However, their assessment will depend on the defined metrics.

2. The training of recommender systems using particle swarms allows for the implementation of parallelization strategies different from the traditional training employed.

Future works should experiment with other types of bio-inspired algorithms and variations of particle swarms.