# Citation Oriented AuthorRank for Scientific Publication Ranking
## 3 Methodology  
### Topic Modeling of LLDA  
Labeled Latent Dirichlet Allocation (Labeled-LDA or LLDA) was proposed for training the labeled topic model. It employs a generative probabilistic model in the hierarchical Bayesian framework and assumes the availability of topic labels and the characterization of each topic by a multinomial distribution, \(\beta_{key_{i}}\), overall vocabulary words.  
In Labeled-LDA, W is a set of words, \(w_{i}\), chosen from a document in the training text, \(\text{W}\,=\,\{w_{1},w_{2},\cdots,\,w_{n}\}\). \(n\) is the number of words. The set of documents in this article, as \(\text{P}\,=\,\{p_{1},p_{2},\cdots,\,p_{d}\}\). d is the number of documents. KEY is a set of labels, \(key_{s}\); we used keywords as labels from training text, so \(\text{KEY}\,=\,\{key_{1},key_{2},\cdots,\,key_{m}\}\). \(m\) is the number of labels. Words are chosen in proportion to a label's preference for the word, \(\beta_{key_{i}}\), and the publication's preference for the associated label, \(\theta_{p_{j}}\).  
\[\beta_{key_{i}}=\left(\begin{array}{ccc}\text{P}_{key_{1}}(w_{1})&\cdots& \text{P}_{key_{1}}(w_{n})\\ \vdots&\ddots&\vdots\\ \text{P}_{key_{m}}(w_{1})&\cdots&\text{P}_{key_{m}}(w_{n})\end{array}\right) \tag{1}\]  
\[\theta_{p_{j}}=\left(\begin{array}{ccc}\text{P}_{key_{1}}(p_{1})&\cdots& \text{P}_{key_{m}}(p_{1})\\ \vdots&\ddots&\vdots\\ \text{P}_{key_{1}}(p_{d})&\cdots&\text{P}_{key_{m}}(p_{d})\end{array}\right) \tag{2}\]  
The two matrices can be constructed by \(\text{P}_{key_{s}}(w_{i})\) and \(\text{P}_{key_{s}}(p_{j})\), representing the co-occurrence probability of label (\(key_{s}\)) and word (\(w_{i}\)), and the co-occurrence probability of paper (\(p_{j}\)) and label (\(key_{s}\)), respectively.  
\[\text{P}_{keys}(w_{i})=\frac{\text{P}(w_{i}|key_{s})}{\sum_{t=1}^{|W|}\text{P }(key_{s}|w_{t})} \tag{3}\]  
\[\text{P}_{keys}(p_{j})=\frac{\text{P}(key_{s}|p_{j})}{\sum_{x=1}^{|V|}\text{P }(key_{s}|p_{x})} \tag{4}\]  
Stemming from the LDA method, Labeled-LDA is a supervised topic modeling algorithm, which employs existing topics from scientific metadata. Therefore, in this paper, topic labels were assigned based on author-assigned keywords, and each scientific publication was treated as a mixture of its author-assigned topics (keywords). As a result, both topic labels and topic numbers (the total number of keywords in the metadata repository) are given.  
We can therefore infer a possible topic distribution for each paper by LLDA. Figure 1 is an example of 2 topic distributions; to show it clearly, we randomly sampled 50. The horizontal axis shows the possible topics (keywords authorized by the author), and the vertical axis is the topic probability. Content in the paper includes title, abstract, and full-text or citation context in publications. For different content, the topic probability distribution is diverse, while the sum of all values (topic probabilities) for each paper is equal to 1.  
The blue line is a conference paper, \"Using architectural 'families' to increase FPGA speed and density\", which is about narrowing the speed and density gap between FPGAs and MPGAs. So, the highest topic in this paper is \"FPGA\". The orange line is a paper named \"Rerun: Exploiting Episodes for Lightweight Memory Race Recording\", published in \"the 35 th Annual International Symposium on Computer Architecture\", which mainly focuses on the field of Multiprocessor deterministic replay. So, the highest topic in this paper is \"multi core processor\".  
In this method, the labels are keywords from the sources. These keywords may be author-provided or derived by greedy matching. Greedy matching means loading all possible keywords into memory, and then searching each keyword from the paper title and abstract by using fast matching, with the purpose of expanding the paper topic space.