# Personalized Scholar Recommendation Based on Multi-Dimensional Features
## 4 The Mul-RSR Approach
### Data Collection and Processing
#### 4.2.1 Textual Similarity Calculation  
In this step, we use the Doc2 Vec model to calculate the similarity of published papers between scholars and construct a textual similarity matrix \(M_{\text{TS}}^{\text{tr}\times\text{tr}}\).  
The Doc2 Vec text depth representation model is an unsupervised paragraph vector algorithm. It is able to learn a fixed-length feature vector from a variable-length text fragment. A sentence, paragraph or document can therefore be represented as a vector.  
Figure 1: Mul-RSR overview.  
The basic idea of Doc2 Vec is: the probability of the central word \(w_{t}\) vector is predicted as the output by the averaging or concatenating function on the hidden layer of the Doc2 Vec neural network model, given the paragraph vector and the context words \(w_{t-k},\ldots,w_{t+k}\) as the input. In addition, the context words \(w_{t-k},\ldots,w_{t+k}\) are generated from text paragraphs by using the sliding window. The paragraph vectors are shared in the context of paragraphs other than between paragraphs [24,25].  
The process of using Doc2 Vec to calculate the textual similarity can be shown in Figure 2. We first need to pre-train the Doc2 Vec model. We add an external WIKI corpus (the details can be found in Section 5.1) in order to improve the feature representation ability of Doc2 Vec. The cleaned text data is appended to the English WIKI dataset as a whole corpus to train and optimize Doc2 Vec. In the Doc2 Vec model, the parameter \(dm\) is used to define the algorithm used for model training. When \(dm=1\), the PV-DM algorithm (Distributed Memory Model of Paragraph Vectors) is used, which treats the text paragraph as a word and considers the concatenation between the paragraph vector and the word vector in the training process. It can remember the current missing content in the context or paragraph text, which is the standard mode of Doc2 Vec. When \(dm=0\), the PV-DBOW algorithm (Distributed Bag of Words Version of Paragraph Vector) is used, which ignores the input contextual words and trains a neural network to predict the probability distribution of randomly selected words in the paragraph. The objective function of Doc2 Vec is to maximize the following average logarithmic probability.  
\[P=\frac{1}{T}\sum_{t=k}^{T-k}\log p(W_{t}|W_{t-k},\ldots,W_{t+k}) \tag{2}\]  
where \(T\) is the length of the training text sequence, \(k\) is the size of the background window and \(p\) is the probability of the success in predicting the central word \(W_{t}\).  
The trained Doc2 Vec model is then employed to convert all the papers of each scholar into a space vector. The space vector is utilized as the text feature representation of each scholar. The cosine value between the angles of two vectors is used to represent the similarity between the papers of the scholars, after obtaining the text feature vector of each scholar. The cosine similarity calculation formula is represented as follows.  
\[\cos\theta=\frac{A\cdot B}{|A|\cdot|B|} \tag{3}\]  
where \(A\) and \(B\) are the vector representations of two scholars. When the cosine value approaches 1, it indicates that the two vectors are more similar.