**Distributed Chebyshev-Accelerated Primal-Dual Algorithm**

We consider a distributed optimization problem over a network of agents aiming to minimize a global objective function that is the sum of local convex and composite cost functions. To this end, we propose a distributed Chebyshev-accelerated primal-dual algorithm to achieve faster ergodic convergence rates. In standard distributed primal-dual algorithms, the speed of convergence towards a global optimum (i.e., a saddle point in the corresponding Lagrangian function) is directly influenced by the eigenvalues of the Laplacian matrix representing the communication graph. In this paper, we use Chebyshev matrix polynomials to generate gossip matrices whose spectral properties result in faster convergence speeds, while allowing for a fully distributed implementation. As a result, the proposed algorithm requires fewer gradient updates at the cost of additional rounds of communications between agents. We illustrate the performance of the proposed algorithm in a distributed signal recovery problem. Our simulations show how the use of Chebyshev matrix polynomials can be used to improve the convergence speed of a primal-dual algorithm over communication networks, especially in networks with poor spectral properties, by trading local computation by communication rounds. … **Time Series Data Compression and Abstraction (TSDCA)**

In the era of big data, practical applications in various domains continually generate large-scale time-series data. Among them, some data show significant or potential periodicity characteristics, such as meteorological and financial data. It is critical to efficiently identify the potential periodic patterns from massive time-series data and provide accurate predictions. In this paper, a Periodicity-based Parallel Time Series Prediction (PPTSP) algorithm for large-scale time-series data is proposed and implemented in the Apache Spark cloud computing environment. To effectively handle the massive historical datasets, a Time Series Data Compression and Abstraction (TSDCA) algorithm is presented, which can reduce the data scale as well as accurately extracting the characteristics. Based on this, we propose a Multi-layer Time Series Periodic Pattern Recognition (MTSPPR) algorithm using the Fourier Spectrum Analysis (FSA) method. In addition, a Periodicity-based Time Series Prediction (PTSP) algorithm is proposed. Data in the subsequent period are predicted based on all previous period models, in which a time attenuation factor is introduced to control the impact of different periods on the prediction results. Moreover, to improve the performance of the proposed algorithms, we propose a parallel solution on the Apache Spark platform, using the Streaming real-time computing module. To efficiently process the large-scale time-series datasets in distributed computing environments, Distributed Streams (DStreams) and Resilient Distributed Datasets (RDDs) are used to store and calculate these datasets. Extensive experimental results show that our PPTSP algorithm has significant advantages compared with other algorithms in terms of prediction accuracy and performance. … **Ensemble Empirical Mode Decomposition (EEMD)**

This approach consists of sifting an ensemble of white noise-added signal (data) and treats the mean as the final true result. Finite, not infinitesimal, amplitude white noise is necessary to force the ensemble to exhaust all possible solutions in the sifting process, thus making the different scale signals to collate in the proper intrinsic mode functions (IMF) dictated by the dyadic filter banks. As EEMD is a time-space analysis method, the added white noise is averaged out with sufficient number of trials; the only persistent part that survives the averaging process is the component of the signal (original data), which is then treated as the true and more physical meaningful answer. The effect of the added white noise is to provide a uniform reference frame in the time-frequency space; therefore, the added noise collates the portion of the signal of comparable scale in one IMF. With this ensemble mean, one can separate scales naturally without any a priori subjective criterion selection as in the intermittence test for the original EMD algorithm. This new approach utilizes the full advantage of the statistical characteristics of white noise to perturb the signal in its true solution neighborhood, and to cancel itself out after serving its purpose; therefore, it represents a substantial improvement over the original EMD and is a truly noise-assisted data analysis (NADA) method. … **Faceted Classification**

A Faceted classification is a classification scheme used in organizing knowledge into a systematic order. A faceted classification uses semantic categories, either general or subject-specific, that are combined to create the full classification entry. Many library classification systems use a combination of a fixed, enumerative taxonomy of concepts with subordinate facets that further refine the topic. There are two primary types of classification used for information organization: enumerative and faceted. An enumerative classification contains a full set of entries for all concepts. A faceted classification system uses a set of semantically cohesive categories that are combined as needed to create an expression of a concept. In this way, the faceted classification is not limited to already defined concepts. While this makes the classification quite flexible, it also makes the resulting expression of topics complex. To the extent possible, facets represent ‘clearly defined, mutually exclusive, and collectively exhaustive aspects of a subject. The premise is that any subject or class can be analyzed into its component parts (i.e., its aspects, properties, or characteristics).’ Some commonly used general-purpose facets are time, place, and form. …

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