# Science Navigation Map: An Interactive Data Mining Tool for Literature Analysis

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3 (a) Title V (1) (b) Abstract V (2) (c) Author V (3) (d)citation V (4) (e) Cocitation V (5) (f) Coreference V (6) Figure 1: The similarity matrices calculated from six perspectives: the title, the abstract, the author, the cited papers, the co-cited papers, and the papers co-referencing them W is an m n matrix where m is the number of papers; n is the total number of citing papers that may belong to any journal besides PLoS biology. (f) The sixth view represents the co-reference information. V (6) (i, j) is the cosine similarity of the vectors i and j from reference paper-paper matrix W where each element is computed as: 1 if paper i refer to paper j W(i, j)= (6) W is a m n matrix where m is the number of papers; n is the total number of reference papers that may belong to any journal besides PLoS biology. 2.2 Multi-view NMF The relations between papers are represented as high dimensional matrices, non-negative matrix factorization (NMF) can be used to extract essential features and then give good low-rank approximations [7]. In contrast to principal component analysis (PCA) methods, NMF can achieve more intuitive physical interpretation of feature vectors by allowing only additive combinations of the non-negative basis vectors and sparse representation. Given a non-negative data matrix V R m n and a positive integer k (m,n), NMF problems is to approximate V by computing a pair W R m k and H R k n to minimize the reconstruction error between V and WH. The objective can be mathematically formulated as the follows. min W 0,H 0 V WH 2 F (7) Where basis vector matrix W and coefficient matrix H are all nonnegative. Each column of matrix W contains a basis vector while each column of H contains the weights needed to approximate the corresponding column in V using the basis from W. That is, each data vector v i is approximated by a linear combination of the columns of W, weighted by the entries of i-th column of H, h i.the greatest coefficient in h i indicates the cluster this sample belongs to. Therefore, the clusters can be directly derived from the nonnegative coefficient matrix H depending on a natural parts-based representation of NMF. However, standard NMF just exploits an individual relationship at a time. It cannot deal with complicated multi-wise relationships in papers. Therefore, we propose a novel multi-view NMF, which exploits individual relationships in addition to integrating all link types to find interesting relationship. It regards different link types as different views to observe papers, which can integrate information from multiple views and take advantage of the latent information among different views. The above six relations between papers can be regarded as six views used to observe the papers which are represented by six similarity matrices as shown in Figure 1: V (1), V (2), V (3), V (4), V (5), V (6). Then all the matrices are processed by NMF at the same time with some constraints. The objective function of multi-view NMF is as follows. n min ( λ (i) V (i) W (i) H (i) 2 n W (i),h (i) F + λ (i) λ ( j) H (i) H ( j) 2 F ) i i j s.t. i [1,n],W (i) 0,H (i) 0,λ (i) n [0,1], λ (i) = 1 i (8) Where n is the number of views, here it is six. W (i) R m k and H (i) R k n are the corresponding basis matrix and coefficient matrix for i-th view. λ (i) is the weight of i-th view, which means the 593

4 Table 1: The information of each view View(k) Description Non-zero i j V (k) (i, j) View Weight 1 Title Similarity /32 2 Abstract Similarity /32 3 Author Similarity /32 4 Citation from PLoS Biology /32 5 CoCitation from all papers /32 6 CoReference /32 degree of influence on the model. To ensure the consensus clustering structure of all the H (i), all the views share the same reduced dimension k and extra constraint terms n i j λ (i) λ ( j) H (i) H ( j) 2 F are imported. Equation (8) is not convex in W (i) and H (i) together. We refer to an algorithm of standard NMF for computation, that is, coordinate descent method [5]. It is to fix one variable while updating another variable alternately. According to coordinate descent method, we first update each element of W (e) to minimize the objective function while fixing all the matrices except W (e). For each element W (e) (r,t) of W (e), the update rules are formulated as the follows. W (e) (r,t) max(0,w (e) (r,t) (W (e) H (e) H (e)t V (e) H (e)t )(r,t) H (e) H (e)t ) (r,t) (9) Then, we can update each element of H (e) in the same way. The update rules for each element H (e) (r,t) of H (e) are as the follows. H (e) (r,t) max(0,h (e) (r,t) (W (e)t W (e) H (e) W (e)t V (e) )(r,t)+ n i e λ (i) (H (e) (r,t) H (i) (r,t)) W (e)t W (e) (r,t)+ n i e λ (i) ) (10) The matrices can be updated alternately following equations (9) and (10) until the model converges. Then serials of H (i) are obtained, which have the capacity of clustering papers according to s- tandard NMF. In addition, because of the consistent clustering constraints imported in the model, all the H (i) have the same clustering structure. Therefore, all the H (i) can be combined to one clustering matrix as shown in equation (11): H ( final) n = λ (i) H (i) (11) i=1 Where λ (i) is the corresponding weight of i-th view as in equation (8). H ( final) can be used to cluster the papers as standard NMF. From equations (8) and (11), we can find that if only one λ is set to 1 and other λs are set to 0, the multi-view NMF degenerates into standard NMF. It means that multi-view NMF can not only exploit the individual relation but also integrate all or even part of link types to find internal structure of papers by giving different sets. Its flexibility makes it a suitable tool for interactive data mining. Therefore, we exploit it in SNM. 3. EXPERIMENTS 3.1 Data Collection We collected all the papers published in the journal of PloS Biology during 2003 to 2012 and obtained 2973 papers. The content of papers and the information of citation and social citation counts are collected from the online repository of PLoS biology, and the open API provided by Public Library of Science (PLoS), respectively Then we extract the collected data and calculate six similarity matrices between 2973 papers of PLoS biology as shown in Figure 1, where both x-axis and y-axis represent papers and they are sorted according to the order of publication dates. Each matrix displays the result of one similarity measure. If the paper i is connected to paper j,thenv (i, j) is non-zero and there will be a blue dot to represent this relationship. The statistic of similarity matrices are also listed in Table 1. Here Non-zero denotes the ratio of non-zero elements against total elements in each matrix; The Sum column is the sum of all non-zero elements. Here title similarity is denser than abstract similarity although abstracts include more words than titles. The reason is as follows. In abstract similarity matrix, only scores greater than 0.2 (chosen heuristically as [3]) are retained so that the number of non-zero elements are reduced. Reducing small elements makes representation of abstract similarity more effective. On the contrary, titles include few words originally, so the title similarity matrix is not reduced in order to preserve more information. 3.2 Data Mining via SNM By using our propose multi-view NMF, we can achieve comprehensive relationships individually or simultaneously. Papers and relations with other paper can be showed in the SNM. SNM visualize the papers and provide a graphical article level metric as shown in Figure 2, where each paper is represented by a block, where size of the block denotes the paper impact (citation count) and color of the block denotes paper popularity (social citation count). When the cursor moves over the block, the corresponding paper information will show over the top of SNM. When a paper is selected, its related paper will also show on the SNM. Different link types can be specified. The advantage of visual data exploration is that the user is directly involved in the data mining process, and then unifies the human intuition and cognition ability with advanced machine learning techniques to accelerate the discovery of new knowledge. SNM can facilitate interactivity in order to explore the latten research patterns and trends of data mining techniques within vast quantities of literature. First, the graphical article level metrics help to easily select high quality papers that interests them. Additionally, multiview NMF is employed to find internal structure of the selected papers based on the paper relation matrices by giving view weights as shown in Table 1. Furthermore, the clusters of papers and top words in each cluster can be shown so that some hot research topics can be identified. New interesting topics may inspire the user to select other papers to analyze. Depending on such an iterative data mining process, the user can have a better understanding of the inherent structure involving a given set of papers and underlying interesting research topics. The relations between papers are represented as high dimensional matrices, multi-view NMF can be used to extract essential fea- 594

5 Figure 2: The 10 most popular papers of every year during Figure 3: The cluster results: paper distribution with 2-dimensional view. tures and then give good low-rank approximations. In contrast to P- CA methods, multi-view NMF can achieve more intuitive physical interpretation of feature vectors by allowing only additive combinations of the non-negative basis vectors and sparse representation. The user can select concerned papers in SNM, and specify the number of clusters and link type for clusters, and then click the cluster button. The papers will be clustered depending on the multiview NMF. The sparse representation of NMF can find good features in order to benefit cluster accuracy. However because of the sparse structure, all data points are near to coordinate axis, which is very suitable to computer handling rather than human observation. For easy graphical view of cluster results, PCA is employed to reveal paper distributions by reducing data to two dimensions. As shown in Figure 3, a bubble denotes a research paper whose color indicates the class it belong to and the size are proportionate to citation count. When the cursor moves on the bubble, the information of corresponding paper is shown on the top the SNM such as, title and publication year, impact(citation count), and popularity (social citation count). When the bubble is click, the papers and the other member papers belong to the same class are listed on the right of the SNM. When the cursor moves on the legend of a classes, the top keywords that appear in the abstracts of all papers of corresponding class are listed in decrease order of word frequency. Therefore, SNM helps researchers soon grasp important papers and hot topic in each cluster using multi-view NMF. In a word, SNM provides intuitive and informative navigation and browsing, filtering, and knowledge discovery mechanisms for papers, papers relationships, and papers collection structure respectively. The user can analyze bibliometric data in a variety of interactive ways, so the flexibility, creativity, and general knowledge of the human combines with computational power of computers that facilitates and accelerates the discovery of new knowledge. 3.3 Discussion Science Navigation Map (SNM) can be accessed through link All paper information, c- itations and social citations supporting SNM are from Public Library of Science (PLoS) which is the first publisher to provide an open application programming interface (API). This API allows developers to access article level metric data, such as usage statistics, 595

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