In this paper, we propose a new approach for recommender systems based on target tracking by Kalman filtering. We assume that users and their seen resources are vectors in the multidimensional space of the categories of the resources. Knowing this space, we propose an algorithm based on a Kalman filter to track users and to predict the best prediction of their future position in the recommendation space.
In Web-based services of dynamic content, recommender systems face the difficulty of identifying new pertinent items and providing pertinent and personalized recommendations for users.
Personalized recommendation has become a mandatory feature of Web sites to improve customer satisfaction and customer retention. Recommendation involves a process of gathering information about site visitors, managing the content assets, analyzing current and past user interactive behaviour, and, based on the analysis, delivering the right content to each visitor.
Recommendation methods can be distinguished into two main approaches: content based filtering (M Pazzani, D. Billsus, 2007) and collaborative filtering (D. Goldberg and al 1992). Collaborative filtering (CF) is one of the most successful and widely used technology to design recommender systems. CF analyzes users ratings to recognize similarities between users on the basis of their past ratings, and then generates new recommendations based on like-minded users’ preferences. This approach suffers from several drawbacks, such as cold start, latency, sparsity (M. Grcar, D. and al 2006), even if it gives interesting results.
The main idea of this paper is to propose an alternative way for recommender systems. Our work is based on the following assumption: we consider Users and Web resources as a dynamic system described in a state space. This dynamic system can be modelled by techniques coming from control system methods. The obtained state space is defined by state variables that are related to the users. We consider that the states of the users (by states, we understand « what are the resources they want to see in the next step ») are measured by the grades given to one resource by the users.
In this paper, we are going to present the effectiveness of Kalman filtering based approach for recommendation. We will detail the backgrounds of this approach i.e. state space description and Kalman filter. Then, we expose the applied methodology. Our conclusion will give some guidelines for future works.
In this part, we are going to describe the main principles of our approach, from the main hypothesis to the theoretical backgrounds.
In this work, we assume that a user is a target moving in a specific space. The space will be defined by the main categories describing the viewed resources. This space called recommendation space will have as many dimensions as categories. Figure 1 shows what this trajectory looks like:
The basic task of the Kalman Filter is to estimate as accurately as possible the position and the velocity of a moving object. In our case, the moving object will be a user described in the new space of the categories of the resources.
First, we have to define the state vector of a user. Because our assumption (the user will a point in the space of the categories). This state vector at time k will be as follows: x will give us more details concerning the properties of the trajectories in the recommender space. Then, we can formulate the problem of target tracking by the following state space representation: (3)
T can be seen as the mean time interval between two positions in the “cyberspace” (Gibson, W.). T comes from the equation which links positions to speed and acceleration. Because it represents the time spent between to position (i.e. choices in the movies database), we put it equal to 1 (simulations have shown that its value does not influence the computations).
In the state space formulation given in equations (2.a) and (2.b), we have: Measurement matrix H has the following structure:
Knowing that we can derive the equations of the Kalman predictor. This predictor will be able to predict the future state on the trajectory. These equations are the following (for further details, concerning how to obtain these equations, see (Gevers, M. and Vandendorpe)):
The computed prediction is given by:
The gain of the filter is:
The evolution of the uncertainty on the state estimation is given by:
Where:
is the prediction of the state; it is the optimal estimation of the state of the model
is the state prediction at time k+1 knowing states from time 0 to time k
Using this algorithm, we are going to consider our target as described in figure 2: Using Kalman filtering, we can obtain the best recommendation (predicted index of satisfaction) knowing all the past index seen as coordinates on the recommendation space.
This experiment is based on TV consumption. The dataset is the TV consumption of 6423 english households over a period of 6 months (from 1st September 2008 to 1st March 2009) (Broadcaster Audience Research Board), (Senot, C. and al, 2010). This dataset contains information about the user, the household and about television program. Each TV program is labelled by one or several genres. In the experiment, a user profile build for each person. The user profile is the set of genres associated to the value of interest of user for each genre. This u
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