A study of multivariate behavior and anomaly patterns : tensor decomposition for multiway big data

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A vast majority of the today’s information haul is through Cyber-Physical Systems (CPS). They represent the confluence of extensive data sets, tight time-constraints, latency issues and heterogeneous components. CPS architectures demand newer Big Data processing approaches. Typical applications span from the Internet-of-Things, across the World Wide Web to Smart Cities and Intelligent machines. A standard heterogeneous CPS installation, the Smart Energy Grid, is observed and the logistics are analyzed. The Smart Grid domain is weighed down by lack of unifying framework and systemic intelligence for autonomic management. Preliminary studies of the field under investigation shows how processing of Real-Time data, communication and control signaling is vital. Purely autonomic system governance is proven to be different from the contemporary definition. It takes the form of Interoperability (achieved through automation) instead of elemental Integration. That means autonomic (smart) management requires all elements to have fully controllable behavior. This dissertation teste the hypothesis of applying Tensor decompositions and Factorizations - a momentum-gaining arithmetic tool - to this problem. The aim is to validate the prospects of higher order Anomaly Pattern Processing to capture intelligence along multiple modes of data flow. Tensorial Data representation captures information flows in Big Data, while Multivariate Anomaly Detection performs tracking of the time-series behavioral changes. Together, they implement Autonomic management in CPS super-systems. Uniqueness of this approach is highlighted by the novel multi-modal data flow imaging and models. Requirements of traditional anomalous event definition and cataloging in Data streams are removed. Tensor algebra is then studied for the scope of implementation concerning features, significance, and interpretation in terms of multi-modal data. Standard Decomposition rules and their derivatives, literature analysis on contemporary applications of Tensor algebra, and its scope on prominent real-world data processing problems are studied. Finally, the decomposition tool for Multi-way analysis is inferred, and proposed methodology is derived. The Smart Grid Smart City Project commissioned by the Australian government is chosen as the data source investigated. The need for exhaustive examination of such repositories in the CPS Anomaly Detection context is also highlighted. Experimentation is done by applying Tensor Decomposition on the data set after normalization and pre-processing. Details of those phases, as well as the choice of coding platforms, the design of experimental frameworks, timelines estimated, and testing operations, are included in this work. The outcomes are the defined patterns extracted and their analysis-interpretation defended by proofs from actual events of the Project Trial phase.
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