## 4 Results
### Temporal Models and Recommendation Approaches
#### 4.3.1 Time-Dependent Model  
_Neighborhood:_ Neighborhood models are CF methods that utilized the collaborative power of the ratings provided by similar users to make recommendations [76]. Generally, the neighborhood model can be adapted to model dynamic changes in RS over time, either by integrating time-dependent algorithms [118; 119; 120; 121; 122] or using time-independent algorithms [123; 124; 125; 126]. In this second we present various studies that basically used time-dependent or time-independent algorithms for neighborhood-based RS as shown in Table 5. These include weight or decay functions, window-based methods, among others. The weighting functions penalized the old ratings by applying a decreasing weight to old data and give more weight to recent data. Exponential function, logistic function and damping functions [113] are the weighting functions commonly used to regulate the importance of data over time. One of the advantages of weighting methods is that they do not need to maintain past batch data. Further, instance weighting should lead to an adaptive decision model that balances new knowledge and old knowledge. While the primary challenge of the approach is the selection of an appropriate rate of forgetting so that it corresponds to the actual rate and type of change [114]. With the window-based approach, the ratings which are considered older than a predefined window length are discounted [100; 127]. A simple time-based k-Nearest Neighborhood (k-NN) approach was proposed by [115] which uses only the recent ratings and ignores the ratings that are older than a defined window length. An approach based on the time-biased k-NN graph is also proposed by [126]. They considered a different number of nearest neighbors to make rating predictions with a set of item-based CF algorithms. These algorithms were retrained with the data in the last interval at a fixed one-week interval. Each set is continuously monitored and the algorithm with the lowest error is then considered to generate a recommendation. The downside of this approach is the choice of window size, which is very critical. If the size is too long, the system will be less responsive to changes and become unstable and will be undertrained when the size is too short. Another challenge of windowing is the cost of retraining the model each time the window moves. _Factorization Models_ Several contributions have also been made to address the issues related to temporal dynamics by adapting different time-approaches for factorization models. For such purposes, both matrix and tensor factorizations have been modified as time-dependent and time-independent models [26]. In a time-dependent approach, the time information is not necessarily used in the models, hence the timestamps are not strictly required [127; 128; 129; 130]. Instead, the rating data is approached as an ordered sequence as a time series problem. One of the basic approaches that considered Time-dependent Matrix Factorization (TMF) was proposed by [23]. The study was aimed to find a better way of adapting to preference changes in RS and proposed several weighting strategies to forget the obsolete information. The authors later extended this approach by introducing additional weighting strategies to improves the predictive power of recommendations in a streaming fashion [47]. A different TMF method was introduced by [22] to better learn the time series of user latent vectors for tracking the concept drift of user of preferences at an individual level. Here, the rating matrix is partitioned into uniformly spaced time slices according to the order of ratings. At each time frame, the user preference associated with that time is obtained using the preference vector of previous time with the transition matrix to track the changes of the user latent vector over time. Time-Dependent tensor models were also exploited in the literature where time is not explicitly defined in the model [73; 74; 129; 130; 131].