Analyzing and Predicting Youtube Comments Rating: WWW2010

Citation

Stefan Siersdorfer, Sergiu Chelaru, Wolfgang Nejd, Jose San Pedro, "How useful are your comments?: analyzing and predicting youtube comments and comment ratings", Proceedings of the 17th international conference on World Wide Web WWW2010, 2010

Online version

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Summary

This paper aims at analyzing comments made on videos hosted on Youtube, and predicting the ratings that users give to these comments. The ratings are basically number of people liking (positive rating) or disliking (negative rating) the comments made by other users. The authors refer to comments that have positive rating as accepted comments and those having negative ratings as unaccepted comments. The motivation is basically finding the sentiment of a comment, with the conjecture being that comment with "positive" sentiment tends to have positive rating, whereas one with "negative" sentiment tends to have negative rating. The authors also perform few other experiments to see the correlation between variance of ratings with polarity (more polar a video, more polar are people's opinions about it) of the videos, and the dependency of ratings and sentiment values of comments on videos of different categories. Please see the Youtube comment analysis dataset page for information about dataset.

Reader-Quotation-Topic (ReQuT) model

Each word is given a Reader, a Quotation and a Topic measure. The motivation is that words written by “authoritative” readers, or the ones found in comments which are quoted in other comments, or those that relate to mostly discussed topics, are important than others. So ReQuT scores are given to each word, and the overall importance of that word is judged by a weighted sum of the ReQuT scores.

The Math behind this

Reader Measure

Given the full set of comments to a blog, the authors construct a directed reader graph $G_{R}:=(V_{R},E_{R})$. Each node $r_{a}\epsilon V_{R}$ is a reader, and an edge $e_{R}(r_{b},r_{a})\epsilon E_{R}$ exists if $r_{b}$ mentions $r_{a}$ in one of $r_{b}$’s comments. The weight on an edge, $W_{R}(r_{b},r_{a})$, is the ratio between the number of times $r_{b}$ mentions $r_{a}$ against all times $r_{b}$ mentions other readers (including $r_{a}$). The authors compute reader authority using a ranking algorithm, shown in Equation 1, where $|R|$ denotes the total number of readers of the blog, and d is the damping factor.

$A(r_{a})=d*1/|R|+(1-d)\Sigma W_{R}(r_{b},r_{a})*A(r_{b})............(1)$
$RM(w_{k})=\Sigma tf(w_{k},c_{i})*A(r_{a})...............................(2)$
The reader measure of a word $w_{k}$, denoted by $RM(w_{k})$, is given in Equation 2, where $tf(w_{k},c_{i})$ is the term frequency of word $w_{k}$ in comment $c_{i}$.

Quotation Measure

For the set of comments associated with each blog post, the authors construct a directed acyclic quotation graph $G_{Q}:=(V_{Q},E_{Q})$. Each node $c_{i}\epsilon V_{Q}$ is a comment, and an edge $(c_{j},c_{i})\epsilon E_{Q}$ indicates $c_{j}$ quoted sentences from $c_{i}$. The weight on an edge, $W_{Q}(c_{j},c_{i})$, is 1 over the number of comments that c_j ever quoted. The authors derive the quotation degree $D(c_{i})$ of a comment $c_{i}$ using Equation 3. A comment that is not quoted by any other comment receives a quotation degree of $1/|C|$ where $|C|$ is the number of comments associated with the given post. $D(c_{i})=1/|C|+\Sigma W_{Q}(c_{j},c_{i})*D(c_{j})...........(3)$
$Q_{M}(w_{k})=\Sigma tf(w_{k},c_{i})*D(c_{i})..................(4)$
The quotation measure of a word $w_{k}$, denoted by $QM(w_{k})$, is given in Equation 4. Word $w_{k}$ appears in comment $c_{i}$.

Topic Measure

Given the set of comments associated with each blog post, the authors group these comments into topic clusters using a Single-Pass Incremental Clustering algorithm presented in [1]. The authors conjecture that a hotly discussed topic has a large number of comments all close to the topic cluster centroid. Thus they propose Equation 5 to compute the importance of a topic cluster, where $|c_{i}|$ is the length of comment $c_{i}$ in number of words, $C$ is the set of comments, and $sim(c_{i},t_{u})$ is the cosine similarity between comment $c_{i}$ and the centroid of topic cluster $t_{u}$.

$T(t_{u})=1/\Sigma |c_{j}|*\Sigma |c_{i}|*sim(c_{i},t_{u})......................(5)$
$TM(w_{k})=\Sigma tf(w_{k},c_{i})*T(t_{u})......................................(6)$

Equation 6 defines the topic measure of a word $w_{k}$, denoted by $TM(w_{k})$. Comment $c_{i}$ is clustered into topic cluster $t_{u}$.

Overall Word Representativeness or Importance Score

The representativeness score of a word $Rep(w_{k})$ is the combination of reader-, quotation- and topic- measures in ReQuT model. The three measures are first normalized independently based on their corresponding maximum values and then combined linearly to derive $Rep(w_{k})$ using Equation 7. In this equation $\alpha$, $\beta$ and $\gamma$ are the coefficients (0 ≤ $\alpha$, $\beta$, $\gamma$ ≤ 1.0 and $\alpha$ + $\beta$ + $\gamma$ = 1.0).

$Rep(w_{k})=\alpha *RM(w_{k})+\beta *QM(w_{k})+\gamma *TM(w_{k}).......................(7)$

Sentence Selection Criteria

Density Based Selection: Based on representativeness score of keywords and the distance between two keywords in a sentence. In equation 8, K is the total number of keywords contained in i^th sentence $s_{i}$, $Score(w_{j})$ is the representativeness score of keyword $w_{j}$, and $distance(w_{j},w_{j}+1)$ is the number of non-keywords (including stopwords) between the two adjacent keywords $w_{j}$ and $w_{j}+1$ in $s_{i}$.

$Score(s_{i})=1/K*(K+1)*\Sigma Score(w_{j})*Score(w_{j+1})/distance(w_{j},w_{j+1})^{2}............................(8)$

Summation Based Selection: Based on the number of keywords contained in a sentence. In equation 9, $|s_{i}|$ is the length of sentence $s_{i}$ in number of words (including stopwords), and $tau$ ($tau$ > 0) is a parameter to flexibly control the contribution of a word’s representativeness score.

$Rep(s_{i})=1/|s_{i}|*(\Sigma Rep(w_{k})^{\tau })^{1/\tau }................................(9)$

Results

Two metrics were used: R-Precision and NDCG. NDCG is described in [2].

References

[1] D. Shen, Q. Yang, J.-T. Sun, and Z. Chen. Thread detection in dynamic text message streams. In Proc. of SIGIR ’06, pages 35–42, Seattle, Washington, 2006.
[2] K. Jrvelin and J. Keklinen. IR evaluation methods for retrieving highly relevant documents. In Proc. of SIGIR ’00, pages 41–48, Athens, Greece, 2000.