Improved Generalized Cross-Validation and Unbiased Predictive Risk Estimator Methods Using the RGSVD: Application to Inversion of Potential Field Data

The inversion of potential field data has widely utilized the generalized cross-validation (GCV) and the unbiased predictive risk estimator (UPRE) methods to determine the regularization parameter. However, these two methods are time-consuming and it is difficult for them to determine the optimal linear search range including the optimal regularization. To solve these problems, this article improves the GCV and UPRE methods using the RGSVD (randomized generalized singular value decomposition) algorithm. The improved methods first use the randomized algorithm to compute an approximate generalized singular value decomposition (GSVD) with less computational time. Then, the optimal linear search range is determined based on the generalized singular values. Finally, the GCV and the UPRE functions are efficiently computed on the basis of the results from the RGSVD algorithm. In this way, the GCV and UPRE methods using the RGSVD algorithm are able to determine the optimal regularization parameter fast and effectively. One comparative test shows the effectiveness and efficiency of the GCV and the UPRE methods using the RGSVD algorithm.

Joint 2D SSA with GSVD and binary linear programming based image super-resolution

This paper proposes a joint two dimensional (2D) singular spectrum analysis (SSA) with the generalized singular value decomposition (GSVD) and the binary linear programming based method for performing the super-resolution. For a given low resolution image, first both the upsampling operation and a lowpass filtering are applied on each column of the image to obtain an enlarged image. Second, apply the 2D Hankelization to both the low resolution image and the enlarged image to obtain their corresponding trajectory matrices. Third, both the GSVD and the 2D de-Hankelization are applied to these two trajectory matrices to obtain their corresponding sets of the de-Hankelized 2D SSA components. Here, it is proved that the exact perfect reconstruction is achieved. In order to enhance the high frequency contents of the enlarged image, the selection of the de-Hankelized 2D SSA components is formulated as a binary linear programming problem. Computer numerical simulation results show that the proposed method outperforms the state of art methods.

Implicit Hari–Zimmermann algorithm for the generalized SVD on the GPUs

A parallel, blocked, one-sided Hari–Zimmermann algorithm for the generalized singular value decomposition (GSVD) of a real or a complex matrix pair [Formula: see text] is here proposed, where F and G have the same number of columns, and are both of the full column rank. The algorithm targets either a single graphics processing unit (GPU), or a cluster of those, performs all non-trivial computation exclusively on the GPUs, requires the minimal amount of memory to be reasonably expected, scales acceptably with the increase of the number of GPUs available, and guarantees the reproducible, bitwise identical output of the runs repeated over the same input and with the same number of GPUs.

Design and optimization for UAV-enabled two-way relaying system with SWIPT

In this paper, we investigate the resource allocation scheme for an unmanned-aerial-vehicle-enable (UAV-enabled) two-way relaying system with simultaneous wireless information and power transfer (SWIPT), where two user equipment exchange information with the help of UAV relay and harvest energy through power splitting (PS) scheme. Under the transmission power constraints at UEs and UAV relay, a non-convex intractable optimization problem is formulated which maximizes the sum retained energy of two UEs while satisfying the minimum signal-to-noise ratio requirement. We decouple the complicated beamforming and PS factor optimization problem into three solvable subproblems and propose an efficient alternating optimization scheme. Subsequently, in order to reduce the complexity, a robust scheme based on generalized singular value decomposition (GSVD) is designed. Finally, numerical results verify the robustness and effectiveness of the two proposed schemes.

Latent Evolutionary Signatures: A General Framework for Analyzing Music and Cultural Evolution

Cultural processes of change bear many resemblances to biological evolution. Identifying underlying units of evolution, however, has remained elusive in non-biological domains, especially in music, where music evolution is often considered to be a loose metaphor. Here we introduce a general framework to jointly identify underlying units and their associated evolutionary processes using a latent modeling approach. Musical styles and principles of organization in dimensions such as harmony, melody and rhythm can be modeled as partly following an evolutionary process. Furthermore, we propose that such processes can be identified by extracting latent evolutionary signatures from musical corpora, analogous to the analysis of mutational signatures in evolutionary genomics, particularly in cancer. These latent signatures provide a generative code for each song, which allows us to identify broad trends and associations between songs and genres. To provide a test case, we analyze songs from the McGill Billboard dataset, in order to find popular chord transitions (k-mers), associate them with music genres and identify latent evolutionary signatures related to these transitions. First, we use a generalized singular value decomposition to identify associations between songs, motifs and genres, and then we use a deep generative model based on a Variational Autoencoder (VAE) framework to extract a latent code for each song. We tie these latent representations together across the dataset by incorporating an energy-based prior, which encourages songs close in evolutionary space to share similar codes. Using this framework, we are able to identify broad trends and genre-specific features of the dataset. Further, our evolutionary model outperforms non-evolutionary models in tasks such as period and genre prediction. To our knowledge, ours is the first computational approach to identify and quantify patterns of music evolution de novo.