# Detect User’s Rating Characteristics by Separate Scores for Matrix Factorization Technique

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Methods and Algorithms

#### 3.1. Constructing the Model

#### 3.1.1. Real Score and Bias Score

#### 3.1.2. User Preferences and Item Features

#### 3.1.3. User Bias Features and Item Bias Weights

#### 3.1.4. The Unified Model

#### 3.2. The Solution of Our Method

- (1)
- keep $U$ and $P$, update $V$ and $Q$;
- (2)
- keep $V$ and $Q$, update $U$ and $P$;

#### 3.2.1. The Updating Rules for $V$ and $Q$

#### 3.2.2. The Updating Rules for $U$ and $P$

#### 3.2.3. Algorithm Overview

Algorithm 1. Algorithm of Proposed Model |

Input: User-item rating matrix $R$ Parameters $n$, $m$, $a$, $b$, $k$, $\lambda $ Output: Matrix $P$, $Q$, $U$ and $V$ 1. Randomly initialize $P$, $Q$, $U$ and $V$; 2. repeat 3. Compute $biasR$ and $realR$ based on Equations (4) and (6); 4. for $i=1$ to $n$ do 5. Update ${V}_{j}$ according to Equation (15); 6. Update ${Q}_{j}$ according to Equation (16); 7. end for 8. Go to step 3; 9. for $j=1$ to $m$ do 10. Update ${U}_{i}$ according to Equation (21); 11. Update ${P}_{i}$ according to Equation (22); 12. end for 13. until convergence |

## 4. Experimental Evaluation

#### 4.1. Data Description

#### 4.2. Evaluation Measures

#### 4.3. Compared Methods

#### 4.4. Experimental Results

- The experimental results show that the proposed method has the lowest MAE value in all rounds of tests, which means that our method has a higher prediction accuracy. Therefore, it is verified that considering the user’s rating characteristics can indeed improve the performance of the recommendation system.
- Although our algorithm has achieved the best results in all three datasets, the degree of improvement is different. By comparing with the best results of other algorithms, we reduced the MAE value by about 0.03 in MovieLens-100K, by nearly 0.04 in MovieLens-1M and by 0.02 in Epinions. By observing the statistics of the three datasets from Table 1, we believe that the reason for this difference may be due to the number of ratings per user. Because on the MovieLens-1M dataset, the average number of users’ rating times is the largest, reached about 165 times, which is very useful to get accurate user’s rating characteristics, while in Epinions, the average number of users rating times is only about 23, which brings a certain degree of difficulty to accurately get the user’s rating characteristics.
- We set different values for the parameter $a$ on the three datasets, which means that the more user rating times, the more complex the user’s rating characteristics we can get; thus, we need to use a higher dimensional vector to express bias features.

#### 4.5. Experimental Results

#### 4.5.1. Impact of $a$

#### 4.5.2. Impact of $b$

#### 4.5.3. Impact of $\lambda $ and $k$

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**The framework of the proposed method, in which the user-item rating matrix is divided into a real rating matrix and a bias rating matrix. We then learn the relevant features from these two matrices and use them to predict the user’s rating score.

**Figure 2.**The impact of parameters $a$, $b$, $k$ and $\lambda $. In the experiment on each parameter, we fix three parameters and change the remaining one. The framework of the proposed method divides the user-item rating matrix into a real rating matrix and a bias rating matrix, and then we learn the relevant features from these two matrices and use them to predict the user’s rating score.

MovieLens-100K | MovieLens-1M | Epinions | |
---|---|---|---|

# of users | 943 | 6040 | 15,687 |

# of items | 1682 | 3952 | 11,657 |

# of ratings | 100,000 | 1,000,209 | 354,857 |

# of ratings per user | 106.4 | 165.60 | 22.62 |

# of ratings per item | 59.45 | 253.09 | 30.44 |

Rating Sparsity | 93.70% | 95.81% | 99.81% |

IB | SVD | PMF | MCoC | DsRec | PMMMF | Hern | SCC | TyCo | Our | |
---|---|---|---|---|---|---|---|---|---|---|

1 | 0.7325 | 0.7412 | 0.7248 | 0.7024 | 0.7105 | 0.7221 | 0.7068 | 0.7589 | 0.7356 | 0.6820 |

2 | 0.7290 | 0.7335 | 0.7213 | 0.7210 | 0.7098 | 0.7104 | 0.7087 | 0.7546 | 0.7247 | 0.6713 |

3 | 0.7329 | 0.7401 | 0.7205 | 0.7138 | 0.7122 | 0.7156 | 0.7080 | 0.7574 | 0.7289 | 0.6753 |

4 | 0.7432 | 0.7388 | 0.7280 | 0.7189 | 0.7201 | 0.7166 | 0.7133 | 0.7621 | 0.7301 | 0.6894 |

5 | 0.7405 | 0.7342 | 0.7235 | 0.7242 | 0.7164 | 0.7190 | 0.7064 | 0.7608 | 0.7298 | 0.6818 |

avg | 0.7356 | 0.7376 | 0.7236 | 0.7197 | 0.7138 | 0.7167 | 0.7086 | 0.7588 | 0.7298 | 0.6800 |

IB | SVD | PMF | MCoC | DsRec | PMMMF | Hern | SCC | TyCo | Our | |
---|---|---|---|---|---|---|---|---|---|---|

1 | 0.7012 | 0.6956 | 0.6923 | 0.6824 | 0.6795 | 0.6745 | 0.6689 | 0.6913 | 0.6643 | 0.6247 |

2 | 0.6946 | 0.6915 | 0.6886 | 0.6836 | 0.6823 | 0.6757 | 0.6675 | 0.6874 | 0.6613 | 0.6231 |

3 | 0.7088 | 0.7013 | 0.6894 | 0.6876 | 0.6804 | 0.6742 | 0.6681 | 0.6902 | 0.6620 | 0.6221 |

4 | 0.6985 | 0.6950 | 0.6902 | 0.6824 | 0.6794 | 0.6750 | 0.6692 | 0.6895 | 0.6637 | 0.6222 |

5 | 0.7023 | 0.6968 | 0.6911 | 0.6853 | 0.6811 | 0.6762 | 0.6684 | 0.6908 | 0.6640 | 0.6264 |

avg | 0.7011 | 0.6960 | 0.6903 | 0.6843 | 0.6805 | 0.6751 | 0.6684 | 0.6898 | 0.6631 | 0.6237 |

IB | SVD | PMF | MCoC | DsRec | PMMMF | Hern | SCC | TyCo | Our | |
---|---|---|---|---|---|---|---|---|---|---|

1 | 0.8622 | 0.8594 | 0.8574 | 0.8489 | 0.8122 | 0.8019 | 0.7984 | 0.8067 | 0.8011 | 0.7748 |

2 | 0.8678 | 0.8612 | 0.8591 | 0.8502 | 0.8094 | 0.8024 | 0.8012 | 0.8071 | 0.8042 | 0.7789 |

3 | 0.8712 | 0.8577 | 0.8563 | 0.8491 | 0.8130 | 0.8003 | 0.7990 | 0.8058 | 0.8037 | 0.7801 |

4 | 0.8638 | 0.8584 | 0.8575 | 0.8480 | 0.8105 | 0.8047 | 0.8005 | 0.8074 | 0.8020 | 0.7764 |

5 | 0.8694 | 0.8569 | 0.8579 | 0.8496 | 0.8117 | 0.8033 | 0.7991 | 0.8062 | 0.8041 | 0.7813 |

avg | 0.8669 | 0.8578 | 0.8576 | 0.8492 | 0.8114 | 0.8025 | 0.7996 | 0.8066 | 0.8030 | 0.7783 |

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**MDPI and ACS Style**

Zhao, J.; Sun, G.
Detect User’s Rating Characteristics by Separate Scores for Matrix Factorization Technique. *Symmetry* **2018**, *10*, 616.
https://doi.org/10.3390/sym10110616

**AMA Style**

Zhao J, Sun G.
Detect User’s Rating Characteristics by Separate Scores for Matrix Factorization Technique. *Symmetry*. 2018; 10(11):616.
https://doi.org/10.3390/sym10110616

**Chicago/Turabian Style**

Zhao, Jia, and Gang Sun.
2018. "Detect User’s Rating Characteristics by Separate Scores for Matrix Factorization Technique" *Symmetry* 10, no. 11: 616.
https://doi.org/10.3390/sym10110616