A privacy preserving association rule mining algorithm was introducedThis algorithm preserved privacy of individual values by computing scalar productMeanwhile the algorithm of computing scalar product was given and the security was analyzed

Privacy preserving association rule mining in vertically partitioned data

A survey of distributed optimization

Broad Learning System (BLS) are widely used in many fields because of its strong feature extraction ability and high computational efficiency. However, the BLS is mainly used in supervised learning, which greatly limits the applicability of the BLS. And the obtained data is less labeled data, but is a large number of unlabeled data. Therefore, the BLS is extended based on the semi-supervised learning of manifold regularization framework to propose a semi-supervised broad learning system (SS-BLS). Firstly, the features are extracted from labeled and unlabeled data by building feature nodes and enhancement nodes. Then the manifold regularization framework is used to construct Laplacian matrix. Next, the feature nodes, enhancement nodes and Laplacian matrix are combined to construct the objective function, which is effectively solved by ridge regression in order to obtain the output coefficients. Finally, the validity of the SS-BLS is verified by three different complex data of G50C, MNIST, and NORB, respectively. The experiment result show that the SS-BLS can achieve higher classification accuracy for different complex data, takes on fast operation speed and strong generalization ability.

Semi-Supervised Broad Learning System Based on Manifold Regularization and Broad Network

A large number of intelligent algorithms based on social intelligent behavior have been extensively researched in the past few decades, through the study of natural creatures, and applied to various optimization fields. The learning-based intelligent optimization algorithm (LIOA) refers to an intelligent optimization algorithm with a certain learning ability. This is how the traditional intelligent optimization algorithm combines learning operators or specific learning mechanisms to give itself some learning ability, thereby achieving better optimization behavior. We conduct a comprehensive survey of LIOAs in this paper. The research includes the following sections: Statistical analysis about LIOAs, classification of LIOA learning method, application of LIOAs in complex optimization scenarios, and LIOAs in engineering applications. The future insights and development direction of LIOAs are also discussed.

A Survey of Learning-Based Intelligent Optimization Algorithms

In this study, by using a characterisation of functions having a fractional derivative, the authors propose a rigorous fractional Lyapunov function candidate method to analyse the stability of fractional-order nonlinear systems. First, they prove an inequality concerning the fractional derivatives of convex Lyapunov functions without the assumption of the existence of the derivative of pseudo-states. Second, they establish fractional Lyapunov functions to fractional-order systems without the assumption of the global existence of solutions. Their theorems fill the gaps and strengthen results in some existing papers.

Stability of fractional-order nonlinear systems by Lyapunov direct method

This study presents an inequality which can be used to analyse the stability of fractional order systems by constructing Lyapunov functions. By using the presented inequality, it is shown that the fractional order system is Mittag-Leffler stable if there is a convex
 and positive definite function such that its fractional order derivative is negative definite. This result generalises the existing works and gives a useful method to construct the Lyapunov function for the stability analysis of the fractional order systems. Finally, the authors illustrate the advantages of the proposed method by two examples and their numerical simulation.

Convex Lyapunov functions for stability analysis of fractional order systems

A distributed algorithm is presented in this article under directed communication networks, which is used to solve the economic dispatch problem in fixed time in smart grid systems. A new globally fixed-time stability theory (Lemma 3 ) is first given in this article, which contains a new upper bound for the estimation of the settling time. Moreover, the fixed-time convergence for the proposed algorithm is rigorously proved with the aid of convex optimization theory, the new lemma, and Lyapunov stability theory under the strongly connected and weight-balanced network topology. Finally, numerical simulations show the effectiveness and advantages of the distributed fixed-time optimization algorithm.

Distributed Fixed-Time Optimization in Economic Dispatch Over Directed Networks

Exponential synchronization of complex dynamical networks with time-varying inner coupling via event-triggered communication

Three new power law inequalities for fractional derivative are proposed in this paper. We generalize the original useful power law inequality, which plays an important role in the stability analysis of pseudo state of fractional order systems. Moreover, three stability theorems of fractional order systems are given in this paper. The stability problem of fractional order linear systems can be converted into the stability problem of the corresponding integer order systems. For the fractional order nonlinear systems, a sufficient condition is obtained to guarantee the stability of the true state. The stability relation between pseudo state and true state is given in the last theorem by the final value theorem of Laplace transform. Finally, two examples and numerical simulations are presented to demonstrate the validity and feasibility of the proposed theorems.

New power law inequalities for fractional derivative and stability analysis of fractional order systems

This paper focuses on the exponential synchronization problem of complex dynamical networks (CDNs) with time-varying inner coupling via distributed event-triggered transmission strategy. Information update is driven by properly defined event, which depends on the measurement error. Each node is described as a second-order nonlinear dynamic system and only exchanges information with its neighboring nodes over a directed network. Suppose that the network communication topology contains a directed spanning tree. A sufficient condition for achieving exponential synchronization of second-order nonlinear systems in CDNs with time-varying inner coupling is derived. Detailed theoretical analysis on exponential synchronization is performed by the virtues of algebraic graph theory, distributed event-triggered transmission strategy, matrix inequality and the special Lyapunov stability analysis method. Moreover, the Zeno behavior is excluded as well by the strictly positive sampling intervals based on the upper right-hand Dini derivative. It is noted that the amount of communication among network nodes and network congestion have been significantly reduced so as to avoid the waste of network resources. Finally, a simulation example is given to show the effectiveness of the proposed exponential synchronization criteria.

Exponential synchronization for second-order nonlinear systems in complex dynamical networks with time-varying inner coupling via distributed event-triggered transmission strategy

Hao Dai

Papers

Convex Lyapunov functions for stability analysis of fractional order systems

Distributed Fixed-Time Optimization in Economic Dispatch Over Directed Networks

Exponential synchronization of complex dynamical networks with time-varying inner coupling via event-triggered communication

New power law inequalities for fractional derivative and stability analysis of fractional order systems

Exponential synchronization for second-order nonlinear systems in complex dynamical networks with time-varying inner coupling via distributed event-triggered transmission strategy