Complex Networks and Symmetry I: A Review

In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs, the analysis of more general symmetries in real complex networks is far less developed. We argue that real networks, as any entity characterized by imperfections or errors, necessarily require a stochastic notion of invariance. We therefore propose a definition of stochastic symmetry based on graph ensembles and use it to review the main results of network theory from an unusual perspective. The results discussed here and in a companion paper show that stochastic symmetry highlights the most informative topological properties of real networks, even in noisy situations unaccessible to exact techniques.Comment: Final accepted versio

A CLUE for CLUster Ensembles

Cluster ensembles are collections of individual solutions to a given clustering problem which are useful or necessary to consider in a wide range of applications. The R package clue provides an extensible computational environment for creating and analyzing cluster ensembles, with basic data structures for representing partitions and hierarchies, and facilities for computing on these, including methods for measuring proximity and obtaining consensus and "secondary" clusterings.

NEXT LEVEL: A COURSE RECOMMENDER SYSTEM BASED ON CAREER INTERESTS

Skills-based hiring is a talent management approach that empowers employers to align recruitment around business results, rather than around credentials and title. It starts with employers identifying the particular skills required for a role, and then screening and evaluating candidates’ competencies against those requirements. With the recent rise in employers adopting skills-based hiring practices, it has become integral for students to take courses that improve their marketability and support their long-term career success. A 2017 survey of over 32,000 students at 43 randomly selected institutions found that only 34% of students believe they will graduate with the skills and knowledge required to be successful in the job market. Furthermore, the study found that while 96% of chief academic officers believe that their institutions are very or somewhat effective at preparing students for the workforce, only 11% of business leaders strongly agree [11]. An implication of the misalignment is that college graduates lack the skills that companies need and value. Fortunately, the rise of skills-based hiring provides an opportunity for universities and students to establish and follow clearer classroom-to-career pathways. To this end, this paper presents a course recommender system that aims to improve students’ career readiness by suggesting relevant skills and courses based on their unique career interests

Ultra-Scalable Spectral Clustering and Ensemble Clustering

This paper focuses on scalability and robustness of spectral clustering for extremely large-scale datasets with limited resources. Two novel algorithms are proposed, namely, ultra-scalable spectral clustering (U-SPEC) and ultra-scalable ensemble clustering (U-SENC). In U-SPEC, a hybrid representative selection strategy and a fast approximation method for K-nearest representatives are proposed for the construction of a sparse affinity sub-matrix. By interpreting the sparse sub-matrix as a bipartite graph, the transfer cut is then utilized to efficiently partition the graph and obtain the clustering result. In U-SENC, multiple U-SPEC clusterers are further integrated into an ensemble clustering framework to enhance the robustness of U-SPEC while maintaining high efficiency. Based on the ensemble generation via multiple U-SEPC's, a new bipartite graph is constructed between objects and base clusters and then efficiently partitioned to achieve the consensus clustering result. It is noteworthy that both U-SPEC and U-SENC have nearly linear time and space complexity, and are capable of robustly and efficiently partitioning ten-million-level nonlinearly-separable datasets on a PC with 64GB memory. Experiments on various large-scale datasets have demonstrated the scalability and robustness of our algorithms. The MATLAB code and experimental data are available at https://www.researchgate.net/publication/330760669.Comment: To appear in IEEE Transactions on Knowledge and Data Engineering, 201