# Online Discussion Participation Prediction Using Non-Negative Matrix Factorization

Fung, Y.-H., Li, C.-H., & Cheung, W. K. (2007). Online Discussion Participation Prediction Using Non-negative Matrix Factorization. In Proceedings of the 2007 IEEE/WIC/ACM International Conferences on Web Intelligence and Intelligent Agent Technology - Workshops (pp. 284—287). Washington, DC, USA: IEEE Computer Society.

## Introduction

This paper presents an approach for estimating the user participation in discussions taking place in Internet forums, i.e. to estimate whether a particular user will participate in a certain discussion.

## User participation follows Zipf's law:

The authors note that the user participation frequency obeys the Zipf's law, i.e. the posting frequency of a user is inversely proportional to his rank in the "user activity" table. Therefore, active users post significantly more than inactive ones.

## Method

The used method encodes discussions and users in the $$n \times m$$ matrix $$F$$ where $$f_{ij} \in F$$ represents the number of posts posted by the user $$j$$ in the discussion$$i$$. To account for the Zipf's law frequency the following normalization which has been inspired by pf/idf is used:

$$x_{ij} = (pf_{ij}) \times (idf_j) = f_{ij} \times log\frac{n}{n_j}$$

where $$n_j$$ represents the number of discussions in which a user $$j$$ has participated. Furthermore the discussion $$i$$ is normalized to unit Euclidean length by dividing the $$L_2$$ norm corresponding to the pf/idf vector.

Afterwards, Weighted Non-negative Matrix Factorization (WNMF) rather than Singular Value Decomposition (SVD) is used to find the latent factors based on the observed participation frequency, i.e. to estimate the model.

## Evaluation

The evaluation experiments observe user interaction in three different discussion boards and use the mean absolute error (MAE) to describe the method's performance:

$$MAE = \frac{1}{N} \sum_{i,j \in S_{test}} |x_{ij} - y_{iy} |$$

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