We present a new algorithm for manifold learning and nonlinear dimensionality reduction. Based on a set of unorganized data points sampled with noise from a parameterized manifold, the local geometry of the manifold i...We present a new algorithm for manifold learning and nonlinear dimensionality reduction. Based on a set of unorganized data points sampled with noise from a parameterized manifold, the local geometry of the manifold is learned by constructing an approximation for the tangent space at each point, and those tangent spaces are then aligned to give the global coordinates of the data points with respect to the underlying manifold. We also present an error analysis of our algorithm showing that reconstruction errors can be quite small in some cases. We illustrate our algorithm using curves and surfaces both in 2D/3D Euclidean spaces and higher dimensional Euclidean spaces. We also address several theoretical and algorithmic issues for further research and improvements.展开更多
We present our recent work on both linear and nonlinear data reduction methods and algorithms: for the linear case we discuss results on structure analysis of SVD of columnpartitioned matrices and sparse low-rank appr...We present our recent work on both linear and nonlinear data reduction methods and algorithms: for the linear case we discuss results on structure analysis of SVD of columnpartitioned matrices and sparse low-rank approximation; for the nonlinear case we investigate methods for nonlinear dimensionality reduction and manifold learning. The problems we address have attracted great deal of interest in data mining and machine learning.展开更多
不同工况下的轴向柱塞泵故障数据存在分布差异,现有的基于特征迁移学习的变工况故障诊断方法大多只通过单个传感器信号进行分析,具有一定的局限性和片面性。为了利用多传感器信号提高变工况下轴向柱塞泵故障诊断的性能,该研究提出一种...不同工况下的轴向柱塞泵故障数据存在分布差异,现有的基于特征迁移学习的变工况故障诊断方法大多只通过单个传感器信号进行分析,具有一定的局限性和片面性。为了利用多传感器信号提高变工况下轴向柱塞泵故障诊断的性能,该研究提出一种耦合分类器子空间嵌入分布自适应(Subspace Embedded Distribution Adaptation with Coupled Classifiers,SEDACC)方法。该方法利用多传感器信号的频谱数据构造主要数据集和辅助数据集,通过子空间对齐(Subspace Alignment,SA)方法将源域和目标域的主要数据投影到公共子空间中,并采用加权条件最大均值差异(Weighted Conditional Maximum Mean Discrepancy,WCMMD)作为度量进行特征分布的适配。同时,基于结构风险最小化(Structural Risk Minimization,SRM)准则在源域标签数据上学习主分类器,根据主分类器对于目标域的预测结果在目标域辅助数据上学习辅助分类器。通过交替和迭代策略不断优化分类器参数,最后对二者进行加权融合得到最终的诊断模型。通过轴向柱塞泵变工况故障诊断试验进行验证,结果表明,当以垂直于端盖的z方向振动信号为主要数据并使用声音信号(或以平行于端盖的x方向的振动信号)作为辅助数据时,SEDACC方法在6种迁移任务中的平均准确率为99.88%(99.46%),高于其他方法。此外,所提方法在目标工况样本稀少的情况下仍具有较高的诊断精度,当目标域和源域样本数比值为0.2时,6种迁移任务的平均准确率达到92.66%。研究结果可为更完备与准确的机械故障诊断提供参考。展开更多
The problem of robust alignment of batches of images can be formulated as a low-rank matrix optimization problem, relying on the similarity of well-aligned images. Going further, observing that the images to be aligne...The problem of robust alignment of batches of images can be formulated as a low-rank matrix optimization problem, relying on the similarity of well-aligned images. Going further, observing that the images to be aligned are sampled from a union of low-rank subspaces, we propose a new method based on subspace recovery techniques to provide more robust and accurate alignment. The proposed method seeks a set of domain transformations which are applied to the unaligned images so that the resulting images are made as similar as possible. The resulting optimization problem can be linearized as a series of convex optimization problems which can be solved by alternative sparsity pursuit techniques. Compared to existing methods like robust alignment by sparse and low-rank models, the proposed method can more effectively solve the batch image alignment problem,and extract more similar structures from the misaligned images.展开更多
The interference alignment （IA） algorithm based on FDPM subspace tracking （FDPM-ST IA） is proposed for MIMO cognitive network （CRN） with multiple primary users in this paper. The feasibility conditions of FDPM-S...The interference alignment （IA） algorithm based on FDPM subspace tracking （FDPM-ST IA） is proposed for MIMO cognitive network （CRN） with multiple primary users in this paper. The feasibility conditions of FDPM-ST IA is also got. Futherly, IA scheme of secondary network and IA scheme of primary network are given respectively without assuming a priori knowledge of interference covariance matrices. Moreover, the paper analyses the computational complexity of FDPM-ST IA. Simulation results and theoretical calculations show that the proposed algorithm can achieve higher sum rate with lower computational complexity.展开更多
文摘We present a new algorithm for manifold learning and nonlinear dimensionality reduction. Based on a set of unorganized data points sampled with noise from a parameterized manifold, the local geometry of the manifold is learned by constructing an approximation for the tangent space at each point, and those tangent spaces are then aligned to give the global coordinates of the data points with respect to the underlying manifold. We also present an error analysis of our algorithm showing that reconstruction errors can be quite small in some cases. We illustrate our algorithm using curves and surfaces both in 2D/3D Euclidean spaces and higher dimensional Euclidean spaces. We also address several theoretical and algorithmic issues for further research and improvements.
基金This work was supported in part by the Special Funds for Major State Basic Research Projectsthe National Natural Science Foundation of China(Grants No.60372033 and 9901936)NSF CCR9901986,DMS 0311800.
文摘We present our recent work on both linear and nonlinear data reduction methods and algorithms: for the linear case we discuss results on structure analysis of SVD of columnpartitioned matrices and sparse low-rank approximation; for the nonlinear case we investigate methods for nonlinear dimensionality reduction and manifold learning. The problems we address have attracted great deal of interest in data mining and machine learning.
文摘不同工况下的轴向柱塞泵故障数据存在分布差异,现有的基于特征迁移学习的变工况故障诊断方法大多只通过单个传感器信号进行分析,具有一定的局限性和片面性。为了利用多传感器信号提高变工况下轴向柱塞泵故障诊断的性能,该研究提出一种耦合分类器子空间嵌入分布自适应(Subspace Embedded Distribution Adaptation with Coupled Classifiers,SEDACC)方法。该方法利用多传感器信号的频谱数据构造主要数据集和辅助数据集,通过子空间对齐(Subspace Alignment,SA)方法将源域和目标域的主要数据投影到公共子空间中,并采用加权条件最大均值差异(Weighted Conditional Maximum Mean Discrepancy,WCMMD)作为度量进行特征分布的适配。同时,基于结构风险最小化(Structural Risk Minimization,SRM)准则在源域标签数据上学习主分类器,根据主分类器对于目标域的预测结果在目标域辅助数据上学习辅助分类器。通过交替和迭代策略不断优化分类器参数,最后对二者进行加权融合得到最终的诊断模型。通过轴向柱塞泵变工况故障诊断试验进行验证,结果表明,当以垂直于端盖的z方向振动信号为主要数据并使用声音信号(或以平行于端盖的x方向的振动信号)作为辅助数据时,SEDACC方法在6种迁移任务中的平均准确率为99.88%(99.46%),高于其他方法。此外,所提方法在目标工况样本稀少的情况下仍具有较高的诊断精度,当目标域和源域样本数比值为0.2时,6种迁移任务的平均准确率达到92.66%。研究结果可为更完备与准确的机械故障诊断提供参考。
基金supported by the National Natural Science Foundation of China (Grant Nos. 61573150, 61573152, 61370185, 61403085, and 51275094)Guangzhou Project Nos. 201604016113 and 201604046018
文摘The problem of robust alignment of batches of images can be formulated as a low-rank matrix optimization problem, relying on the similarity of well-aligned images. Going further, observing that the images to be aligned are sampled from a union of low-rank subspaces, we propose a new method based on subspace recovery techniques to provide more robust and accurate alignment. The proposed method seeks a set of domain transformations which are applied to the unaligned images so that the resulting images are made as similar as possible. The resulting optimization problem can be linearized as a series of convex optimization problems which can be solved by alternative sparsity pursuit techniques. Compared to existing methods like robust alignment by sparse and low-rank models, the proposed method can more effectively solve the batch image alignment problem,and extract more similar structures from the misaligned images.
基金the National Nature Science Foundation of China under Grant No.61271259 and 61301123,the Chongqing Nature Science Foundation under Grant No.CTSC2011jjA40006,and the Research Project of Chongqing Education Commission under Grant No.KJ120501 and KJ120502
文摘The interference alignment （IA） algorithm based on FDPM subspace tracking （FDPM-ST IA） is proposed for MIMO cognitive network （CRN） with multiple primary users in this paper. The feasibility conditions of FDPM-ST IA is also got. Futherly, IA scheme of secondary network and IA scheme of primary network are given respectively without assuming a priori knowledge of interference covariance matrices. Moreover, the paper analyses the computational complexity of FDPM-ST IA. Simulation results and theoretical calculations show that the proposed algorithm can achieve higher sum rate with lower computational complexity.
