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.

## 1. Principles

In this part, we are going to describe the main principles of our approach, from the main hypothesis to the theoretical backgrounds.

## 1.1 Target Tracking In The Cyberspace

In this work, we assume that a user is a 

![0_image_0.png](0_image_0.png)

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:
Using this assumption, we are going to detail what is Kalman filtering, how we can apply it in this case and what are our main assumptions.

## 1.2 Kalman Filter Formulation

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:

(1) k k x x x X  
Where xis the vector containing the position coordinates x is the vector containing the velocity coordinates xis the vector containing the acceleration coordinates In a first step, we are going to use only the position vector x but the knowledge of x and xwill 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:

(2.a) (2.b) Xk 1 AXk wk Zk HXkvk Where: (3) T 1 2 T 2 A 0 T 0 0

T can be seen as the mean time interval between two positions in the "cyberspace" 