Reverse Nearest Neighbor Heat Maps: A Tool for Influence Exploration

We study the problem of constructing a reverse nearest neighbor (RNN) heat map by finding the RNN set of every point in a two-dimensional space. Based on the RNN set of a point, we obtain a quantitative influence (i.e., heat) for the point. The heat map provides a global view on the influence distribution in the space, and hence supports exploratory analyses in many applications such as marketing and resource management. To construct such a heat map, we first reduce it to a problem called Region Coloring (RC), which divides the space into disjoint regions within which all the points have the same RNN set. We then propose a novel algorithm named CREST that efficiently solves the RC problem by labeling each region with the heat value of its containing points. In CREST, we propose innovative techniques to avoid processing expensive RNN queries and greatly reduce the number of region labeling operations. We perform detailed analyses on the complexity of CREST and lower bounds of the RC problem, and prove that CREST is asymptotically optimal in the worst case. Extensive experiments with both real and synthetic data sets demonstrate that CREST outperforms alternative algorithms by several orders of magnitude.Comment: Accepted to appear in ICDE 201

An adaptive shortest-solution guided decimation approach to sparse high-dimensional linear regression

High-dimensional linear regression model is the most popular statistical model for high-dimensional data, but it is quite a challenging task to achieve a sparse set of regression coefficients. In this paper, we propose a simple heuristic algorithm to construct sparse high-dimensional linear regression models, which is adapted from the shortest solution-guided decimation algorithm and is referred to as ASSD. This algorithm constructs the support of regression coefficients under the guidance of the least-squares solution of the recursively decimated linear equations, and it applies an early-stopping criterion and a second-stage thresholding procedure to refine this support. Our extensive numerical results demonstrate that ASSD outperforms LASSO, vector approximate message passing, and two other representative greedy algorithms in solution accuracy and robustness. ASSD is especially suitable for linear regression problems with highly correlated measurement matrices encountered in real-world applications.Comment: 13 pages, 6 figure

Landau-Zener-Stuckelberg interference in a multi-anticrossing system

We propose a universal analytical method to study the dynamics of a multi-anticrossing system subject to driving by one single large-amplitude triangle pulse, within its time scales smaller than the dephasing time. Our approach can explain the main features of the Landau-Zener-Stuckelberg interference patterns recently observed in a tripartite system [Nature Communications 1:51 (2010)]. In particular, we focus on the effects of the size of anticrossings on interference and compare the calculated interference patterns with numerical simulations. In addition, Fourier transform of the patterns can extract information on the energy level spectrum.Comment: 6 pages, 5 figure

Clustered Federated Learning based on Nonconvex Pairwise Fusion

This study investigates clustered federated learning (FL), one of the formulations of FL with non-i.i.d. data, where the devices are partitioned into clusters and each cluster optimally fits its data with a localized model. We propose a novel clustered FL framework, which applies a nonconvex penalty to pairwise differences of parameters. This framework can automatically identify clusters without a priori knowledge of the number of clusters and the set of devices in each cluster. To implement the proposed framework, we develop a novel clustered FL method called FPFC. Advancing from the standard ADMM, our method is implemented in parallel, updates only a subset of devices at each communication round, and allows each participating device to perform a variable amount of work. This greatly reduces the communication cost while simultaneously preserving privacy, making it practical for FL. We also propose a new warmup strategy for hyperparameter tuning under FL settings and consider the asynchronous variant of FPFC (asyncFPFC). Theoretically, we provide convergence guarantees of FPFC for general nonconvex losses and establish the statistical convergence rate under a linear model with squared loss. Our extensive experiments demonstrate the advantages of FPFC over existing methods.Comment: 46 pages, 9 figure

Denoising of Hyperspectral Images Using Group Low-Rank Representation

Hyperspectral images (HSIs) have been used in a wide range of fields, such as agriculture, food safety, mineralogy and environment monitoring, but being corrupted by various kinds of noise limits its efficacy. Low-rank representation (LRR) has proved its effectiveness in the denoising of HSIs. However, it just employs local information for denoising, which results in ineffectiveness when local noise is heavy. In this paper, we propose an approach of group low-rank representation (GLRR) for the HSI denoising. In our GLRR, a corrupted HSI is divided into overlapping patches, the similar patches are combined into a group, and the group is reconstructed as a whole using LRR. The proposed method enables the exploitation of both the local similarity within a patch and the nonlocal similarity across the patches in a group simultaneously. The additional nonlocallysimilar patches can bring in extra structural information to the corrupted patches, facilitating the detection of noise as outliers. LRR is applied to the group of patches, as the uncorrupted patches enjoy intrinsic low-rank structure. The effectiveness of the proposed GLRR method is demonstrated qualitatively and quantitatively by using both simulated and real-world data in experiments

Hyperspectral and Multispectral Image Fusion using Optimized Twin Dictionaries

Spectral or spatial dictionary has been widely used in fusing low-spatial-resolution hyperspectral (LH) images and high-spatial-resolution multispectral (HM) images. However, only using spectral dictionary is insufficient for preserving spatial information, and vice versa. To address this problem, a new LH and HM image fusion method termed OTD using optimized twin dictionaries is proposed in this paper. The fusion problem of OTD is formulated analytically in the framework of sparse representation, as an optimization of twin spectral-spatial dictionaries and their corresponding sparse coefficients. More specifically, the spectral dictionary representing the generalized spectrums and its spectral sparse coefficients are optimized by utilizing the observed LH and HM images in the spectral domain; and the spatial dictionary representing the spatial information and its spatial sparse coefficients are optimized by modeling the rest of high-frequency information in the spatial domain. In addition, without non-negative constraints, the alternating direction methods of multipliers (ADMM) are employed to implement the above optimization process. Comparison results with the related state-of-the-art fusion methods on various datasets demonstrate that our proposed OTD method achieves a better fusion performance in both spatial and spectral domains

End-point Modification of Recombinant Thrombomodulin with Enhanced Stability and Anticoagulant Activity

Thrombomodulin (TM) is an endothelial cell membrane protein that plays essential roles in controlling vascular haemostatic balance. The 4, 5, 6 EGF-like domain of TM (TM456) has cofactor activity for thrombin binding and subsequently protein C activation. Therefore, recombinant TM456 is a promising anticoagulant candidate but has a very short half-life. Ligation of poly (ethylene glycol) to a bioactive protein (PEGylation) is a practical choice to improve stability, extend circulating life, and reduce immunogenicity of the protein. Site-specific PEGylation is preferred as it could avoid the loss of protein activity resulting from nonspecific modification. We report herein two site-specific PEGylation strategies, enzymatic ligation and copper-free click chemistry (CFCC), for rTM456 modification. Recombinant TM456 with a C-terminal LPETG tag (rTM456-LPETG) was expressed in Escherichia coli for its end-point modification with NH2-diglycine-PEG5000-OMe via Sortase A-mediated ligation (SML). Similarly, an azide functionality was easily introduced at the C-terminus of rTM456-LPETG via SML with NH2-diglycine-PEG3-azide, which facilitates a site-specific PEGylation of rTM456 via CFCC. Both PEGylated rTM456 conjugates retained protein C activation activity as that of rTM456. Also, they were more stable than rTM456 in Trypsin digestion assay. Further, both PEGylated rTM456 conjugates showed a concentration-dependent prolongation of thrombin clotting time (TCT) compared to non-modified protein, which confirms the effectiveness of these two site-specific PEGylation schemes