On Convergence of Controlled Snowball Sampling for Scientific Abstracts Collection

This paper presents evidences concerned to convergence of controlled snowball sampling iterations applied to collecting seminal papers in a selected domain of research. Iterations start from the seed paper selection, plain snowball sampling and probabilistic topic modelling, then greedy controlled snowball sampling and analysis of the collected citation network are performed in rotation until the list of seminal papers becomes stable. The topic model is built on the base of word-word co-occurrence probability with combination of sparse symmetric nonnegative matrix factorization and principal component approximation. Experiments show that the number of topics in the model is determined in natural way and the Kullback-Leibler (KL) divergence provides the upper bound of the cosine similarity calculated from keywords assigned by publication authors. Several citation networks are collected and analysed. The analysis shows that all networks are “small worlds” and therefore the observed saturation of the controlled snowball sampling can provide the complete set of publications in domains of interest. Experiments with KL-divergence, symmetric KL-divergence and Jensen-Shannon divergence show that KL-divergence produces less connected citation network but provides better convergence of snowball iterations. Multiple runs of the sampling confirm the hypothesis that the set of seminal publications is stable with respect to variations of the seed papers. The modified main path analysis allows to distinguish the seminal papers including new publications following main stream of research. The comparison of different ranking criterion is made. It shows that Search Path Count provides better lists of seminal papers than citation index, PageRank and indegree.