Recently, nested and coprime arrays have attracted considerable interest due to their capability of providing increased array aperture, enhanced degrees of freedom (DOFs), and reduced mutual coupling effect compared to uniform linear arrays (ULAs). These features are critical to improving the performance of direction-of-arrival estimation and adaptive beamforming.
Graph-based representations play a key role in machine learning. The fundamental step in these representations is the association of a graph structure to a dataset. In this paper, we propose a method that finds a block sparse representation of the data by associating a graph, whose Laplacian matrix admits the sparsifying dictionary as its eigenvectors.
The state-of-the-art graph wavelet decomposition was constructed by maximum spanning tree (MST)-based downsampling and two-channel graph wavelet filter banks. In this work, we first show that: 1) the existing MST-based downsampling could become unbalanced, i.e., the sampling rate is far from 1/2, which eventually leads to low representation efficiency of the wavelet decomposition; and 2) not only low-pass components, but also some high-pass ones can be decomposed to potentially achieve better decomposition performance.
The optimal mean-reverting portfolio (MRP) design problem is an important task for statistical arbitrage, also known as pairs trading, in the financial markets. The target of the problem is to construct a portfolio of the underlying assets (possibly with an asset selection target) that can exhibit a satisfactory mean reversion property and a desirable variance property.
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