## 1 Introduction  
Recommender technologies have been applied to a variety of Internet-based systems, such as online multimedia services, online shopping, and online social networking. Collaborative filtering (CF) recommendation is one of the most important techniques for recommender systems [1, 2]. The main techniques of CF recommendation include the neighborhood method and latent factor model [3]. The neighborhood method aims at improving predictive accuracy by similarities of relations, such as [4, 5, 6, 7]. The latent factor model uses historical rating data to discover latent features in users' behaviors and explain user ratings in conjunction with explicit evidence, such as [8; 9; 10; 11; 12], including baseline estimation model and latent factor model as in Equation (1):  
\[\hat{r}_{ui}=(b_{u}+b_{i}+\mu)+f\Big{(}q_{i}^{T}p_{u}\Big{)}. \tag{1}\]  
The formalized function \(f\big{(}q_{i}^{T}p_{u}\big{)}\) decomposes the user-item rating matrix \(R\) into users' latent factor matrix \(P\) and items' latent factor matrix \(Q\), where \(P\) reflects the weight of users' preference on each latent factor, and \(Q\) reflects the weight of items' characteristics. Parameters \(q_{i}\) and \(p_{u}\) are related factors of \(Q\) and \(P\). Most researchers have focused on algorithms of \(f\big{(}q_{i}^{T}p_{u}\big{)}\) to obtain more accurate predictive accuracy by personalization methods, such as [8; 9; 10; 11; 12; 13; 14]. In this paper, we focus on the first part in Equation (1), called baseline estimation [8; 5; 14], where \(b_{u}\) and \(b_{i}\) denote the observed global deviations of user \(u\) and item \(i\), respectively. The related equation is:  
\[\hat{r}_{ui}=b_{u}+b_{i}+\mu, \tag{2}\]  
where \(\hat{r}_{ui}\) denotes the baseline prediction for an unknown item \(i\) by \(u\), and \(\mu\) denotes the global average rating of the system. Baseline estimation evaluates the global deviations of users' personalized ratings on items against global average ratings and the deviations of items' received ratings to the overall average [5]. Usually, \(b_{u}\) and \(b_{i}\) can be observed from the user-item rating matrix by calculating the related row average rating and column average rating, denoted by \(\widetilde{r}_{u}\) and \(\widetilde{r}_{i}\), respectively, and \(b_{u}=(\widetilde{r}_{u}-\mu)\) and \(b_{i}=(\widetilde{r}_{i}-\mu)\). Our main motivation comes from the limitation of the baseline estimation, which is firstly mentioned by [PERSON] in [8; 5]. The main problem of baseline estimation in (2) is that system cannot differentiate users' personalized rating range from the system's rating range. Factually, different users usually have different rating criteria on the same items. Some have relatively higher ratings for items than others, while some have very strict rating criteria for the same item. As a result, users' actual rating range may differ from the system's rating range, and the baseline estimation may result in an irrational predictive value. We believe that the main limitation of classical baseline estimation is the lack of local personalization consideration. From observations on real recommendation datasets, we found that users in all datasets can be classified into four kinds according to their real rating ranges: Normal, strict, lenient, and middle. The normal users gave ratings within the system's range, but the strict users' rating range's supremum was less than that of the system's range, while the lenient users' rating range's infimum was larger than that of the system's, and the middle users' rating scale did not cover both the supremum and infimum of the system's rating range. The observation proves that users' real rating range is influenced by users' personalized rating criteria, and baseline estimation should not only consider global deviation from the system's rating range but also consider the local deviation from users' personalized rating ranges. We discuss this problem in Section 3 in detail.