Planning of research and development trends in science and technology centers should be in line with the actual state of things. Such phenomena as organizational frigidity, research diversi cation and propensity for developing IT products are able to signi cantly impair any strategies and development trends. However, feasibility of plans is an important attribute of development able to which signi cantly raise personnels motivation for achieving best results. This is why setting achievable goals is of such importance. There are never enough quantitative tools for appraisal of research and development activities. Formal paperwork reporting on R&D is not suitable for evaluation of researchers involvement and dedication. Instead, small formats of research works such as presentations at scienti c and technical conferences or scienti c articles in peer-reviewed scienti c publications require much more informal approach from researchers. Analysis of a science and technology centers performance based on its publication activity is a common practice. Many studies analyze text corpus of scienti c articles and make conclusions on development trends. Text data noise levels are quite high; even most advanced analysis methods based on word embedding are able to produce accurate predictions only if analyzed are huge text volumes which are seldom available in case of small organizations. Small research organizations su er the most from inaccurate planning of research activities. Authors of this research propose to take advantages of articles (presentations) analysis based on co-authorship bipartite graph to extract research trends with the purpose of their further evaluation and planning.
Todays focus on scienti c approaches to managerial decisions becomes ever more vital. As data volumes grow analytic tools used by organizations management become less e cient. On the other hand often there is no su cient data volume for sustainable work of advanced algorithms. On the forefront of this trend there is a problem of adaptation and developing new heuristics for solving such classic problems as clustering which are to be used for organizational purposes.
Data clustering based on a static model gained momentum as such
algorithms when PAM [
Algorithms diversity does not make less important the task of their e ciency evaluation. However, given a limited number of data and in order to improve managerial decisions the quality of clustering must to have not only mathematically substantiated but also reliable image components. In other words, it should be comprehensible at a glance and not requiring going deep into formulas. Such are the todays businesses needs.
From a formal point of view we have to solve the problem of unsupervised machine learning for co-authorship graph, attribute clusters to particular subjects and detect variations in clusters over the time.
Clustering of co-authorship graph can be achieved based on various nodes metrics: { Degree centrality { Betweenness centrality { Closeness centrality { Harmonic centrality { Clustering Let us examine the conceptual meaning of the Betweenness centrality metrics applied to the problem of clustering of co-authorship graph in an R&D organization. The Betweenness centrality metrics shows how important is a particular node for the graphs connectivity. Connections in a co-authorship graph re ect research collaboration. Co-authorship graphs are not always connected; usually they consist of several connected components of various sizes.
Connected components are natural clusters. Small connected components re ect primary initiatives researchers rst articles. However the main connected component may contain up to 90% of a co authorship graphs nodes and call for a special approach to clustering.
To extract clusters from a main connected component of a co-authorship graph one may use the method of arti cial removal of the nodes with the topvalue Betweenness centrality metrics. As each of such nodes is removed a graph may break down into several disconnected components. The Figure 2 shows such separation model.
Each of the components resulting from such separation can be analyzed for subjects homogeneity based on articles texts of which each component is formed. Several iterations would result in a set of clusters.
The method proposed by the authors is a heuristic one and requires examination by a particular formal criterion. Conventional criteria for the purposes of clustering are proximity metrics for a cluster components and distances between components in separate clusters.
Convergence of the authors method is ensured through searching a minimum of functional errors in determining k clusters with 1.
Where WSSci within-cluster variation for cluster Ci, mi - centroid of Ci and i 2 [1::k] (2). The total WSS measures the compactness of the clustering and we want it to be as small as possible.
And BSS - weighted inter-cluster separation, measured by the between cluster sum of squares (3).
k W SS = X X x mi jCij mj mi 2 (2) (3) Where jCij - is a cluster size.
Interdisciplinary researches lead to the situation where articles may fall into several subject categories, thus the resulting clusters would be intersecting and non-exclusive. 3
The Gazpromneft R&D Center`s publication activity has been chosen as a research subject. The data has been obtained from the OnePetro open online library of the international Society of Petroleum Engineers (SPE). Upon cleansing 172 articles have been singled out.
Let us base our prediction on a co-authorship graph. For this purpose we
build a co-authorship bipartite graph [
The resulting co-authorship graph has 26 connected components of which the strongest one has 556 nodes while the others have maximum eight nodes. Connected components with up to eight nodes represent the researchers rst articles.
Let us examine the strongest connected component (556 nodes). We extract a subgraph from the main co-authorship graph based on the nodes contained in the strongest connected component. The resulting subgraph is shown on the Figure 3 .
Let us compute the Betweenness centrality metrics for the resulting subgraph. The obtained Betweenness centrality values are shown on the Figure 4. Zero values for the Betweenness centrality are not shown.
As we can see on the Figure 4 the values of the Betweenness centrality metrics in the third quartile belong to only 23 nodes which represent less than 5% of the total number of nodes.
Let us apply the algorithm of arti cial removal of the nodes with the highest value of the Betweenness centrality metrics. The Figure 5 shows correlation between the connected components number and the number of arti cially removed nodes.
As the nodes get removed the graph can behave in two following modes: 1. Connectivity constraint (Mode I) 2. Exponential decay (Mode II)
Mode I is characterized by the graphs retaining its connectivity as the nodes with high values of the Betweenness centrality metrics get removed. It means that the removed nodes are not the only connections between clusters.
Mode II is characterized by following the exponential model of a graphs decay when each removed node causes exponential growth in emergence of new connected components.
Let us have a closer look at the second half of the Mode I of the algorithm when the graph has broken down into six connected components. These components sizes are 511, 34, 1, 1, 1, 1. Among them the component with 34 nodes shown on the Figure 6 represents the most pronounced direction of research into Subject 1.
We have examined extraction of one cluster in detail. The complete algorithm of clusters extraction would consist of the following steps: 1. Building a co-authorship bipartite graph: G 2. Finding the Betweenness centrality metrics for the G graph 3. Finding a node with BCmax metrics (Betweenness centrality) 4. Removing the BCmax node (Betweenness centrality) from the G graph 5. Deriving a list of connected components of the G graph 6. Computing a quality metrics W SS and BSS of the retrieved clusters 7. Further the algorithm is iterated for each connected component 8. Algorithm is completed when all connected components represent clusters of acceptable quality.
For the selected co-authorship graph 16 clusters have been extracted. To
compute values and W based on the articles texts we have applied the Vector Space
Model (VSM). Each article is represented as a vector with the BM25 [
For the purposes of comparison of the resulting articles clustering we have performed clustering with the KMeans algorithm which yielded similar results (Figure 8 ).
The articles corpus has been broken down into clusters using the KMeans algorithm. The resulting clusters allowed arranging authors into groups. 4
The authors have proposed a method of extraction of research trends based on the co-authorship graph. Concept-wise the method belongs to the top-down clustering algorithms. The Betweenness centrality metrics has been chosen as a criterion for extracting clusters.
The metrics of cluster components proximity and the metrics of distances between separate clusters based on the subjects of articles in the co-authorship graph have been applied as a clusters quality criterion. This method resulted in an aggregate vision of organizations research trend based on the open data on its researchers publication activities.
The authors method of extraction of research trends based on the co-authorship graph has been tested at the Gazpromneft R&D Center. As a result 16 clusters indicative of the organization activity have been extracted. The following attributes of the authors method of extraction of research trends based on the co authorship graph are signi cant: { Recursive algorithm allows working with graphs of various orders. { Greedy algorithm for clusters quality evaluation allows correcting optimization at any step. { Applying a co-authorship bipartite graph allows analyzing various projections. { Working with the data in public domain gives ample opportunities for application in business intelligence.
The novelty of the method of extraction of research trends based on the coauthorship graph proposed by the authors is in applying the co-authorship bipartite graph and in the dynamic model of clustering using structural metrics for the co-authorship graph and proximity metrics for research articles texts.