# A Hybrid Fuzzy Profiling-Nonnegative Latent Factor Model Considering Consumer Preference at Different Levels

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## Abstract

**:**

## 1. Introduction

- (1)
- Implicit data can aid us in tracking the real behaviors of consumers despite lacking of methods for modeling consumer preference [9,10]. Additionally, consumer preference is complex and existed at different levels, but current research usually characterizes it only in a rough manner and ignores natural noise. Considering these issues and taking the advantages of fuzzy sets for processing vague information, in this paper, we extract consumer preference from implicit feedback information and propose the method of FP to characterize actual behavior data in terms of preference ratings at different preference levels.
- (2)
- In case the recommendation results are directly generated without considering consumer preference for recommended items, the recommendation quality will be unsatisfactory [15,16]. Therefore, according to the understanding of consumer preference, two series of strategies are provided for preference integration and comprehensive utilization in different scenarios. A hybrid FP-NLF model is proposed that can systematically solve the problem mentioned above by providing high quality recommendation that satisfies various consumer preference levels.
- (3)
- To demonstrate our proposal, a case study is conducted using the sub-dataset of The Echo Nest Taste Profile Subset containing 100,000 records. To recommend items of higher preference, we revise the evaluation metrics to a higher requirement. The results show that high quality recommendation satisfying given recommendation level can be achieved compared with other four related models. Sensitivity analysis shows more details to develop strategies that can purposefully serve consumers.

## 2. Related Literature

#### 2.1. Inferring Consumer Preference from Implicit Feedback

#### 2.2. Latent Factor Model

**Definition**

**1.**

**Definition**

**2.**

## 3. Hybrid FP-NLF Model

- (1)
- Data collector: the implicit feedback information is collected and stored mostly in the company database, and it is preprocessed.
- (2)
- (3)
- Strategy: to achieve a higher quality recommendation, the weights of the higher preference level are emphasized. By understanding consumer behavior patterns, two series of strategies are supplied for different intentions, which are used to generate the entire fuzzy preference profiles.
- (4)
- (5)
- Recommender: this stage is the last step of our model, which accomplishes the task of recommendation. The standard is enhanced in that the items are placed into recommendation list only if consumers have medium preference or high preference for them.

#### 3.1. Fuzzy Profiling

**Definition**

**3.**

_{1}= low-preference, l

_{2}= medium-preference, l

_{3}= high-preference$\}$ to describe the various preference levels for each consumer on the item. The fuzzy semantics is illustrated in Figure 3, where ${\mu}_{1},{\mu}_{2},{\mu}_{3},{\mu}_{4}$ are determined in the exact application scenario. The next step is to construct the membership function that maps implicit feedback data $R$ to each linguistically represented label in $l$. Therefore, we build the membership function ${\mu}_{l}(R):R\to [0,1]$ to characterize the relationship between usage frequency and preference rating in each level by expanding the scale of 1–5 [12] to 1-N.

**Remark**

**1.**

#### 3.2. Strategy

**Strategy 1**, denoted as “H-M”: ${w}_{H}>{w}_{M}>{w}_{L}$

**Strategy 2**, denoted as “M-H”: ${w}_{M}>{w}_{H}>{w}_{L}$

#### 3.3. Preference Prediction

#### 3.4. Recommender

#### 3.5. Basic Evaluation Metric

## 4. Experiment

#### 4.1. Data Collector and Pre-Process

#### 4.2. Fuzzy Profiling

#### 4.3. Integration Strategy

#### 4.4. Train Latent Factor Model

#### 4.5. Recommender

## 5. Results and Discussion

#### 5.1. Results and Comparative Analysis

#### 5.2. Sensitivity Analysis

_{RHPL=high}than threshold

_{RHPL=medium}for all weight vectors. Denote the weight difference between ${w}_{M}$ and ${w}_{H}$ as $\Delta w=|{w}_{M}-{w}_{H}|$, and we can discover that the better recommendation results could be generated with proper $\Delta w$. In this experiment of ${w}_{L}=0.2$, the optimal value of $\Delta w$ is 0.4 for Strategy 1.

_{RHPL=high}. However, similarly, it cannot always get good results at threshold

_{RHPL=medium}. When $\Delta w=0.2$, the Strategy 2 can accomplish a brilliant recommendation result.

_{RHPL=medium}. In addition, a specific guidance for setting strategies with ${w}_{L}=0.2$ is derived that we can set $\Delta w=0.4$ for Strategy 1 and $\Delta w=0.2$ for Strategy 2 to obtain optimal recommendation.

## 6. Conclusions and Future Work

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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Literature | Objective | Feedback Type | Data Type |
---|---|---|---|

Wang et al. (2020) [19] | Explore the hotel selection differences among four types of travelers by analyzing their preferences for selected key factors | Explicit feedback | Multi-ratings; Text reviews |

Yang et al. (2018) [18] | Assist patients seeking satisfactory doctors based on their preferences | Explicit feedback | Multi-ratings |

Zhang et al. (2018) [5] | Recommend a personalized restaurant to the consumer with consideration of group correlations and customer preferences | Explicit feedback | Multi-ratings; Text reviews |

Choi et al. (2012) [22] | Characterize consumer preference by deriving implicit ratings from online transaction data and further predict a target product | Implicit feedback | Purchase frequency |

Lee et al. (2010) [25] | Recommend music for consumers after analyzing their taste according to listening behavior | Implicit feedback | Listening behavior |

UserId | ItemId | PlayCount | |
---|---|---|---|

1 | b8034…dca9e | SOA…0A9 | 1 |

2 | 3887c…c601e | SOB…CF5 | 2 |

3 | b8034…dca9e | SOD…F7E | 5 |

4 | e2147…477e5 | SOI…F96 | 1 |

... | ... | ... | ... |

99,998 | f3e52…ce9f9 | SOZ…1C6 | 5 |

99,999 | 3887c…1c601e | SOZ…17F | 4 |

100,000 | 21f4ac…35f59 | SOS…26F | 18 |

${\mathit{w}}_{\mathit{L}}$ | ${\mathit{w}}_{\mathit{M}}$ | ${\mathit{w}}_{\mathit{H}}$ | ||
---|---|---|---|---|

Strategy 1 | 1 | 0.25 | 0.35 | 0.4 |

2 | 0.2 | 0.3 | 0.5 | |

3 | 0.1 | 0.4 | 0.5 | |

4 | 0 | 0.4 | 0.6 | |

Strategy 2 | 1 | 0.25 | 0.4 | 0.35 |

2 | 0.2 | 0.5 | 0.3 | |

3 | 0.1 | 0.5 | 0.4 | |

4 | 0 | 0.6 | 0.4 |

MAE | RMSE | ||
---|---|---|---|

Model 1 | 0.2253 | 0.2897 | |

Model 2 | 0.2623 | 0.3410 | |

Model 3 | 0.2467 | 0.2957 | |

The proposed model | Strategy 1-1 | 0.0566 | 0.0886 |

Strategy 1-2 | 0.0597 | 0.0913 | |

Strategy 1-3 | 0.1128 | 0.1378 | |

Strategy 1-4 | 0.1384 | 0.1738 | |

Strategy 2-1 | 0.0686 | 0.0976 | |

Strategy 2-2 | 0.1086 | 0.1357 | |

Strategy 2-3 | 0.1371 | 0.1637 | |

Strategy 2-4 | 0.1892 | 0.2290 |

Threshold_{RHPL=medium} | Threshold_{RHPL=high} | ||
---|---|---|---|

Model 1 | 0.710 | 0.771 | |

Model 2 | 0.679 | 0.785 | |

Model 3 | 0.581 | 0.572 | |

Model 4 | 0.608 | 0.607 | |

The proposed model with Strategy 1 | 1 | 0.743 | 0.896 |

2 | 0.623 | 0.892 | |

3 | 0.850 | 0.852 | |

4 | 0.747 | 0.898 | |

The proposed model with Strategy 2 | 1 | 0.942 | 0.625 |

2 | 0.944 | 0.745 | |

3 | 0.625 | 0.856 | |

4 | 0.745 | 0.853 |

$$({\mathit{w}}_{\mathit{L}},{\mathit{w}}_{\mathit{M}},{\mathit{w}}_{\mathit{H}}{)}_{}$$
| Threshold_{RHPL=medium} | Threshold_{RHPL=high} | |
---|---|---|---|

${w}_{H}>{w}_{M}$ | (0.2, 0.05, 0.75) | 0.864 | 0.991 |

(0.2, 0.1, 0.7) | 0.786 | 0.977 | |

(0.2, 0.15, 0.65) | 0.862 | 0.949 | |

(0.2, 0.2, 0.6) | 0.948 | 0.948 | |

(0.2, 0.25, 0.55) | 0.491 | 0.895 | |

(0.2, 0.3, 0.5) | 0.619 | 0.897 | |

${w}_{M}>{w}_{H}$ | (0.2, 0.75, 0.05) | 0.769 | 0.919 |

(0.2, 0.7, 0.1) | 0.871 | 0.918 | |

(0.2, 0.65, 0.15) | 0.918 | 0.914 | |

(0.2, 0.6, 0.2) | 0.920 | 0.916 | |

(0.2, 0.55, 0.25) | 0.919 | 0.915 | |

(0.2, 0.5, 0.3) | 0.921 | 0.917 |

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## Share and Cite

**MDPI and ACS Style**

Li, Y.; Wang, J.; Wang, J.
A Hybrid Fuzzy Profiling-Nonnegative Latent Factor Model Considering Consumer Preference at Different Levels. *Symmetry* **2020**, *12*, 1399.
https://doi.org/10.3390/sym12091399

**AMA Style**

Li Y, Wang J, Wang J.
A Hybrid Fuzzy Profiling-Nonnegative Latent Factor Model Considering Consumer Preference at Different Levels. *Symmetry*. 2020; 12(9):1399.
https://doi.org/10.3390/sym12091399

**Chicago/Turabian Style**

Li, Yu, Jianqiang Wang, and Jing Wang.
2020. "A Hybrid Fuzzy Profiling-Nonnegative Latent Factor Model Considering Consumer Preference at Different Levels" *Symmetry* 12, no. 9: 1399.
https://doi.org/10.3390/sym12091399