Online Spectral Clustering on Network Streams

Graph is an extremely useful representation of a wide variety of practical systems in data analysis. Recently, with the fast accumulation of stream data from various type of networks, significant research interests have arisen on spectral clustering for network streams (or evolving networks). Compared with the general spectral clustering problem, the data analysis of this new type of problems may have additional requirements, such as short processing time, scalability in distributed computing environments, and temporal variation tracking. However, to design a spectral clustering method to satisfy these requirements certainly presents non-trivial efforts. There are three major challenges for the new algorithm design. The first challenge is online clustering computation. Most of the existing spectral methods on evolving networks are off-line methods, using standard eigensystem solvers such as the Lanczos method. It needs to recompute solutions from scratch at each time point. The second challenge is the parallelization of algorithms. To parallelize such algorithms is non-trivial since standard eigen solvers are iterative algorithms and the number of iterations can not be predetermined. The third challenge is the very limited existing work. In addition, there exists multiple limitations in the existing method, such as computational inefficiency on large similarity changes, the lack of sound theoretical basis, and the lack of effective way to handle accumulated approximate errors and large data variations over time. In this thesis, we proposed a new online spectral graph clustering approach with a family of three novel spectrum approximation algorithms. Our algorithms incrementally update the eigenpairs in an online manner to improve the computational performance. Our approaches outperformed the existing method in computational efficiency and scalability while retaining competitive or even better clustering accuracy. We derived our spectrum approximation techniques GEPT and EEPT through formal theoretical analysis. The well established matrix perturbation theory forms a solid theoretic foundation for our online clustering method. We facilitated our clustering method with a new metric to track accumulated approximation errors and measure the short-term temporal variation. The metric not only provides a balance between computational efficiency and clustering accuracy, but also offers a useful tool to adapt the online algorithm to the condition of unexpected drastic noise. In addition, we discussed our preliminary work on approximate graph mining with evolutionary process, non-stationary Bayesian Network structure learning from non-stationary time series data, and Bayesian Network structure learning with text priors imposed by non-parametric hierarchical topic modeling

A framework for dynamic heterogeneous information networks change discovery based on knowledge engineering and data mining methods

Information Networks are collections of data structures that are used to model interactions in social and living phenomena. They can be either homogeneous or heterogeneous and static or dynamic depending upon the type and nature of relations between the network entities. Static, homogeneous and heterogenous networks have been widely studied in data mining but recently, there has been renewed interest in dynamic heterogeneous information networks (DHIN) analysis because the rich temporal, structural and semantic information is hidden in this kind of network. The heterogeneity and dynamicity of the real-time networks offer plenty of prospects as well as a lot of challenges for data mining. There has been substantial research undertaken on the exploration of entities and their link identification in heterogeneous networks. However, the work on the formal construction and change mining of heterogeneous information networks is still infant due to its complex structure and rich semantics. Researchers have used clusters-based methods and frequent pattern-mining techniques in the past for change discovery in dynamic heterogeneous networks. These methods only work on small datasets, only provide the structural change discovery and fail to consider the quick and parallel process on big data. The problem with these methods is also that cluster-based approaches provide the structural changes while the pattern-mining provide semantic characteristics of changes in a dynamic network. Another interesting but challenging problem that has not been considered by past studies is to extract knowledge from these semantically richer networks based on the user-specific constraint.This study aims to develop a new change mining system ChaMining to investigate dynamic heterogeneous network data, using knowledge engineering with semantic web technologies and data mining to overcome the problems of previous techniques, this system and approach are important in academia as well as real-life applications to support decision-making based on temporal network data patterns. This research has designed a novel framework “ChaMining” (i) to find relational patterns in dynamic networks locally and globally by employing domain ontologies (ii) extract knowledge from these semantically richer networks based on the user-specific (meta-paths) constraints (iii) Cluster the relational data patterns based on structural properties of nodes in the dynamic network (iv) Develop a hybrid approach using knowledge engineering, temporal rule mining and clustering to detect changes in the dynamic heterogeneous networks.The evidence is presented in this research shows that the proposed framework and methods work very efficiently on the benchmark big dynamic heterogeneous datasets. The empirical results can contribute to a better understanding of the rich semantics of DHIN and how to mine them using the proposed hybrid approach. The proposed framework has been evaluated with the previous six dynamic change detection algorithms or frameworks and it performs very well to detect microscopic as well as macroscopic human-understandable changes. The number of change patterns extracted in this approach was higher than the previous approaches which help to reduce the information loss

Analyzing Granger causality in climate data with time series classification methods

Attribution studies in climate science aim for scientifically ascertaining the influence of climatic variations on natural or anthropogenic factors. Many of those studies adopt the concept of Granger causality to infer statistical cause-effect relationships, while utilizing traditional autoregressive models. In this article, we investigate the potential of state-of-the-art time series classification techniques to enhance causal inference in climate science. We conduct a comparative experimental study of different types of algorithms on a large test suite that comprises a unique collection of datasets from the area of climate-vegetation dynamics. The results indicate that specialized time series classification methods are able to improve existing inference procedures. Substantial differences are observed among the methods that were tested