Multiple Graphs and Low-Rank Embedding for Multi-Source Heterogeneous Domain Adaptation

Multi-source domain adaptation is a challenging topic in transfer learning, especially when the data of each domain are represented by different kinds of features, i.e., Multi-source Heterogeneous Domain Adaptation (MHDA). It is important to take advantage of the knowledge extracted from multiple sources as well as bridge the heterogeneous spaces for handling the MHDA paradigm. This article proposes a novel method named Multiple Graphs and Low-rank Embedding (MGLE), which models the local structure information of multiple domains using multiple graphs and learns the low-rank embedding of the target domain. Then, MGLE augments the learned embedding with the original target data. Specifically, we introduce the modules of both domain discrepancy and domain relevance into the multiple graphs and low-rank embedding learning procedure. Subsequently, we develop an iterative optimization algorithm to solve the resulting problem. We evaluate the effectiveness of the proposed method on several real-world datasets. Promising results show that the performance of MGLE is better than that of the baseline methods in terms of several metrics, such as AUC, MAE, accuracy, precision, F1 score, and MCC, demonstrating the effectiveness of the proposed method.

A Compact High-Dimensional Yield Analysis Method using Low-Rank Tensor Approximation

“Curse of dimensionality” has become the major challenge for existing high-sigma yield analysis methods. In this article, we develop a meta-model using Low-Rank Tensor Approximation (LRTA) to substitute expensive SPICE simulation. The polynomial degree of our LRTA model grows linearly with the circuit dimension. This makes it especially promising for high-dimensional circuit problems. Our LRTA meta-model is solved efficiently with a robust greedy algorithm and calibrated iteratively with a bootstrap-assisted adaptive sampling method. We also develop a novel global sensitivity analysis approach to generate a reduced LRTA meta-model which is more compact. It further accelerates the procedure of model calibration and yield estimation. Experiments on memory and analog circuits validate that the proposed LRTA method outperforms other state-of-the-art approaches in terms of accuracy and efficiency.

Effective diffraction separation using the improved optimal rank-reduction method

Seismic diffractions encoding subsurface small-scale geologic structures have great potential for high-resolution imaging of subwavelength information. Diffraction separation from the dominant reflected wavefields still plays a vital role because of the weak energy characteristics of the diffractions. Traditional rank-reduction methods based on the low-rank assumption of reflection events have been commonly used for diffraction separation. However, these methods using truncated singular-value decomposition (TSVD) suffer from the problem of reflection-rank selection by singular-value spectrum analysis, especially for complicated seismic data. In addition, the separation problem for the tangent wavefields of reflections and diffractions is challenging. To alleviate these limitations, we propose an effective diffraction separation strategy using an improved optimal rank-reduction method to remove the dependence on the reflection rank and improve the quality of separation results. The improved rank-reduction method adaptively determines the optimal singular values from the input signals by directly solving an optimization problem that minimizes the Frobenius-norm difference between the estimated and exact reflections instead of the TSVD operation. This improved method can effectively overcome the problem of reflection-rank estimation in the global and local rank-reduction methods and adjusts to the diversity and complexity of seismic data. The adaptive data-driven algorithms show good performance in terms of the trade-off between high-quality diffraction separation and reflection suppression for the optimal rank-reduction operation. Applications of the proposed strategy to synthetic and field examples demonstrate the superiority of diffraction separation in detecting and revealing subsurface small-scale geologic discontinuities and inhomogeneities.