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Graph Embedding, a learning paradigm that represents graph vertices, edges, and other semantic information about a graph into low-dimensional vectors, has found wide applications in different machine learning tasks. In the past few years, we have had a plethora of methods centered on graph embedding using different techniques, such as spectral classification, matrix factorization and learning. In this context, choosing the appropriate dimension of the obtained embedding remains a fundamental issue. In this paper, we propose a compact representation of a node's neighborhood, including attributes and structure, that can be used as an additional dimension to enrich node embedding, to ensure accuracy. This compact representation ensures that both semantic and structural properties of a node's neighboring-hood are properly captured in a single dimension. Consequently, we improve the learned embedding from state-of-the-art models by introducing the neighborhood compact representation for each node as an additional layer of dimensionality. We leverage on this neighborhood encoding technique and compare with embedding from state-of-the-art models on two learning tasks: node classification and link prediction. The performance evaluation shows that our approach gives a better prediction and classification accuracy in both tasks. [ABSTRACT FROM AUTHOR]

In this paper, a novel robust adaptive fuzzy control is presented for a quite general class of multivariable nonlinear systems with actuators' nonlinearities (saturation with dead zone) and uncertain dynamics. The backstepping concept in combination with the variable-structure control framework and Lyapunov approach is used to design this adaptive fuzzy control. The fuzzy systems are incorporated in the controller for approximating online the unknown system dynamics. In the controller design and stability analysis, the control gain matrices, which are not necessarily symmetric and definite, are decomposed via the so-called SDU matrix decomposition lemma into a product of three main useful matrices, namely a symmetric definite-positive matrix, a diagonal constant matrix with + 1 or − 1 in its main diagonal and a unity upper triangular matrix. It is shown that the proposed adaptive fuzzy control is able to ensure the uniform ultimate boundedness of all solutions of the closed-loop system, as well as the convergence of the underlying tracking errors. Finally, in a numerical simulation framework, the effectiveness of the presented controller is illustrated on two practical examples. [ABSTRACT FROM AUTHOR]