Discovering Periodic Patterns in Time Series from Twitter Data Set

The important class of regularities that exist in a time series is nothing but the Partial periodic patterns. These patterns have key properties such as starting, stopping, and restartinganywhere− within a series. Partial periodic patterns areclassifiedinto two types: (i) regular patterns− exhibiting periodic behavior throughout a series with some exceptions and( ii) periodic patterns exhibiting periodic behavior only for particular time intervals within a series. We have focused primarily on finding regular patterns during past studies on partial periodic search. The knowledge pertaining to periodic patterns cannot be ignored. This is because useful information pertaining to seasonal or time-based associations between events is provided bythem. Because of the foll o wi n g two main reasons, finding periodic patterns is a non-trivial task. (i) Each periodic pattern is associated with time-based information pertaining to its durations of periodic appearances in a series. Since the information can vary within and across patterns, obtaining this information ischallenging. (ii) As they do not satisfy the anti-monotonic property, finding all periodic patterns is a computationally expensive process. In this paper, periodic pattern model is proposed by addressing the above issues. Periodic Pattern growth algorithm along with an efficient pruning technique is also proposed to discover these patterns. The results through Experimentation have shown that Periodic patterns canbe really useful and it has also proven that our algorithm isnoteworthy.

Expansion of Generalized Hukuhara Differentiable Interval Valued Function

In this paper, the concept of [Formula: see text]-monotonic property of interval valued function in higher dimension is introduced. Expansion of interval valued function in higher dimension is developed using this property. Generalized Hukuhara differentiability is used to derive the theoretical results. Several examples are provided to justify the theoretical developments.

Estimation accuracy of covariance matrices when their eigenvalues are almost duplicated

The covariance matrix of signals is one of the most essential information in multivariate analysis and other signal processing techniques. The estimation accuracy of a covariance matrix is degraded when some eigenvalues of the matrix are almost duplicated. Although the degradation is theoretically analyzed in the asymptotic case of infinite variables and observations, the degradation in finite cases are still open. This paper tackles the problem using the Bayesian approach, where the learning coefficient represents the generalization error. The learning coefficient is derived in a special case, i.e., the covariance matrix is spiked (all eigenvalues take the same value except one) and a shrinkage estimation method is employed. Our theoretical analysis shows a non-monotonic property that the learning coefficient increases as the difference of eigenvalues increases until a critical point and then decreases from the point and converged to the distinct case. The result is validated by numerical experiments.

Bifurcation Analysis of a Predator–Prey System with Ratio-Dependent Functional Response

In this paper, we are concerned with the structural stability of a density dependent predator–prey system with ratio-dependent functional response. Starting with the geometrical analysis of hyperbolic curves, we obtain that the system has one or two positive equilibria under various conditions. Inspired by the S-procedure and semi-definite programming, we use the sum of squares decomposition based method to ensure the global asymptotic stability of the positive equilibrium through the associated polynomial Lyapunov functions. By exploring the monotonic property of the trace of the Jacobian matrix with respect to [Formula: see text] under the given different conditions, we analytically verify that there is a corresponding unique [Formula: see text] such that the trace is equal to zero and prove the existence of Hopf bifurcation, respectively.

H ∞ and Passivity Control via Static and Integral Output Feedback for Systems With Input Delay

This paper addresses a new approach on H∞ and passivity control via static and integral output feedback controllers of continuous-time linear systems with input delay. By combining an augmentation approach and the delay partitioning technique, criteria for static and integral output feedback H∞/passivity stabilizability are proposed for the closed-loop system in terms of matrix inequalities. These new characterizations possess a special monotonic property, which underpin the convergence of a linearized iterative computational algorithm. The effectiveness and merits of the proposed approach are illustrated through numerical examples.

Robust Fuzzy Clustering Based on Similarity between Data

We present a robust fuzzy clustering method that utilizes a sequential cluster extraction scheme. In contrast to heuristic sequential methods, our algorithm is derived from an optimization problem and is an iterative solution to it. Our method is non-parametric and includes no heuristic parameter, and can deal with asymmetric similarity data. The determination of the number of clusters is simple and is based on a monotonic property of extracted cluster volumes. Our method can extract arbitrarily shaped clusters by extending the measure of distance between data to a shortest path length. The performance of the method is demonstrated for clustering of an image database and the segmentation of images.