In this paper, we proposed a new semi-supervised multi-manifold learning method, called semi- supervised sparse multi-manifold embedding (S3MME), for dimensionality reduction of hyperspectral image data. S3MME exploit...In this paper, we proposed a new semi-supervised multi-manifold learning method, called semi- supervised sparse multi-manifold embedding (S3MME), for dimensionality reduction of hyperspectral image data. S3MME exploits both the labeled and unlabeled data to adaptively find neighbors of each sample from the same manifold by using an optimization program based on sparse representation, and naturally gives relative importance to the labeled ones through a graph-based methodology. Then it tries to extract discriminative features on each manifold such that the data points in the same manifold become closer. The effectiveness of the proposed multi-manifold learning algorithm is demonstrated and compared through experiments on a real hyperspectral images.展开更多
Multi-label data with high dimensionality often occurs,which will produce large time and energy overheads when directly used in classification tasks.To solve this problem,a novel algorithm called multi-label dimension...Multi-label data with high dimensionality often occurs,which will produce large time and energy overheads when directly used in classification tasks.To solve this problem,a novel algorithm called multi-label dimensionality reduction via semi-supervised discriminant analysis(MSDA) was proposed.It was expected to derive an objective discriminant function as smooth as possible on the data manifold by multi-label learning and semi-supervised learning.By virtue of the latent imformation,which was provided by the graph weighted matrix of sample attributes and the similarity correlation matrix of partial sample labels,MSDA readily made the separability between different classes achieve maximization and estimated the intrinsic geometric structure in the lower manifold space by employing unlabeled data.Extensive experimental results on several real multi-label datasets show that after dimensionality reduction using MSDA,the average classification accuracy is about 9.71% higher than that of other algorithms,and several evaluation metrices like Hamming-loss are also superior to those of other dimensionality reduction methods.展开更多
In dealing with high-dimensional data, such as the global climate model, facial data analysis, human gene distribution and so on, the problem of dimensionality reduction is often encountered, that is, to find the low ...In dealing with high-dimensional data, such as the global climate model, facial data analysis, human gene distribution and so on, the problem of dimensionality reduction is often encountered, that is, to find the low dimensional structure hidden in high-dimensional data. Nonlinear dimensionality reduction facilitates the discovery of the intrinsic structure and relevance of the data and can make the high-dimensional data visible in the low dimension. The isometric mapping algorithm (Isomap) is an important algorithm for nonlinear dimensionality reduction, which originates from the traditional dimensionality reduction algorithm MDS. The MDS algorithm is based on maintaining the distance between the samples in the original space and the distance between the samples in the lower dimensional space;the distance used here is Euclidean distance, and the Isomap algorithm discards the Euclidean distance, and calculates the shortest path between samples by Floyd algorithm to approximate the geodesic distance along the manifold surface. Compared with the previous nonlinear dimensionality reduction algorithm, the Isomap algorithm can effectively compute a global optimal solution, and it can ensure that the data manifold converges to the real structure asymptotically.展开更多
As an effective way in finding the underlying parameters of a high-dimension space, manifold learning is popular in nonlinear dimensionality reduction which makes high-dimensional data easily to be observed and analyz...As an effective way in finding the underlying parameters of a high-dimension space, manifold learning is popular in nonlinear dimensionality reduction which makes high-dimensional data easily to be observed and analyzed. In this paper, Isomap, one of the most famous manifold learning algorithms, is applied to process closing prices of stocks of CSI 300 index from September 2009 to October 2011. Results indicate that Isomap algorithm not only reduces dimensionality of stock data successfully, but also classifies most stocks according to their trends efficiently.展开更多
Image feature optimization is an important means to deal with high-dimensional image data in image semantic understanding and its applications. We formulate image feature optimization as the establishment of a mapping...Image feature optimization is an important means to deal with high-dimensional image data in image semantic understanding and its applications. We formulate image feature optimization as the establishment of a mapping between highand low-dimensional space via a five-tuple model. Nonlinear dimensionality reduction based on manifold learning provides a feasible way for solving such a problem. We propose a novel globular neighborhood based locally linear embedding (GNLLE) algorithm using neighborhood update and an incremental neighbor search scheme, which not only can handle sparse datasets but also has strong anti-noise capability and good topological stability. Given that the distance measure adopted in nonlinear dimensionality reduction is usually based on pairwise similarity calculation, we also present a globular neighborhood and path clustering based locally linear embedding (GNPCLLE) algorithm based on path-based clustering. Due to its full consideration of correlations between image data, GNPCLLE can eliminate the distortion of the overall topological structure within the dataset on the manifold. Experimental results on two image sets show the effectiveness and efficiency of the proposed algorithms.展开更多
We present a new manifold learning algorithm called Local Orthogonality Preserving Alignment （LOPA）. Our algorithm is inspired by the Local Tangent Space Alignment （LTSA） method that aims to align multiple local n...We present a new manifold learning algorithm called Local Orthogonality Preserving Alignment （LOPA）. Our algorithm is inspired by the Local Tangent Space Alignment （LTSA） method that aims to align multiple local neighborhoods into a global coordinate system using affine transformations. However, LTSA often fails to preserve original geometric quantities such as distances and angles. Although an iterative alignment procedure for preserving orthogonality was suggested by the authors of LTSA, neither the corresponding initialization nor the experiments were given. Procrustes Subspaces Alignment （PSA） implements the orthogonality preserving idea by estimating each rotation transformation separately with simulated annealing. However, the optimization in PSA is complicated and multiple separated local rotations may produce globally contradictive results. To address these difficulties, we first use the pseudo-inverse trick of LTSA to represent each local orthogonal transformation with the unified global coordinates. Second the orthogonality constraints are relaxed to be an instance of semi-definite programming （SDP）. Finally a two-step iterative procedure is employed to further reduce the errors in orthogonal constraints. Extensive experiments products, and neighborhoods of the original datasets. In that of PSA and comparable to that of state-of-the-art significantly faster than that of PSA, MVU and MVE. show that LOPA can faithfully preserve distances, angles, inner comparison, the embedding performance of LOPA is better than algorithms like MVU and MVE, while the runtime of LOPA is展开更多
A new manifold learning method, called incremental alignment method （IAM）, is proposed for nonlinear dimensionality reduction of high dimensional data with intrinsic low dimensionality. The main idea is to increment...A new manifold learning method, called incremental alignment method （IAM）, is proposed for nonlinear dimensionality reduction of high dimensional data with intrinsic low dimensionality. The main idea is to incrementally align low-dimensional coordinates of input data patch-by-patch to iteratively generate the representation of the entire data.set. The method consists of two major steps, the incremental step and the alignment step. The incremental step incrementally searches neighborhood patch to be aligned in the next step, and the alignment step iteratively aligns the low-dimensional coordinates of the neighborhood patch searched to generate the embeddings of the entire dataset. Compared with the existing manifold learning methods, the proposed method dominates in several aspects： high efficiency, easy out-of-sample extension, well metric-preserving, and averting of the local minima issue. All these properties are supported by a series of experiments performed on the synthetic and real-life datasets. In addition, the computational complexity of the proposed method is analyzed, and its efficiency is theoretically argued and experimentally demonstrated.展开更多
Over the past few years,nonlinear manifold learning has been widely exploited in data analysis and machine learning.This paper presents a novel manifold learning algorithm,named atlas compatibility transformation(ACT)...Over the past few years,nonlinear manifold learning has been widely exploited in data analysis and machine learning.This paper presents a novel manifold learning algorithm,named atlas compatibility transformation(ACT),It solves two problems which correspond to two key points in the manifold definition:how to chart a given manifold and how to align the patches to a global coordinate space based on compatibility.For the first problem,we divide the manifold into maximal linear patch(MLP) based on normal vector field of the manifold.For the second problem,we align patches into an optimal global system by solving a generalized eigenvalue problem.Compared with the traditional method,the ACT could deal with noise datasets and fragment datasets.Moreover,the mappings between high dimensional space and low dimensional space are given.Experiments on both synthetic data and real-world data indicate the effection of the proposed algorithm.展开更多
As modern weapons and equipment undergo increasing levels of informatization,intelligence,and networking,the topology and traffic characteristics of battlefield data networks built with tactical data links are becomin...As modern weapons and equipment undergo increasing levels of informatization,intelligence,and networking,the topology and traffic characteristics of battlefield data networks built with tactical data links are becoming progressively complex.In this paper,we employ a traffic matrix to model the tactical data link network.We propose a method that utilizes the Maximum Variance Unfolding(MVU)algorithm to conduct nonlinear dimensionality reduction analysis on high-dimensional open network traffic matrix datasets.This approach introduces novel ideas and methods for future applications,including traffic prediction and anomaly analysis in real battlefield network environments.展开更多
局部线性嵌入法(Locally Linear Embedding,LLE)是一种基于流形学习的非线性降维方法。针对LLE近邻点个数选取、样本点分布以及计算速度的问题,提出基于模糊聚类的改进LLE算法。算法根据聚类中心含有大量的信息这一特点,基于模糊聚类原...局部线性嵌入法(Locally Linear Embedding,LLE)是一种基于流形学习的非线性降维方法。针对LLE近邻点个数选取、样本点分布以及计算速度的问题,提出基于模糊聚类的改进LLE算法。算法根据聚类中心含有大量的信息这一特点,基于模糊聚类原理,采用改进的样本点距离计算方法,定义了近似重构系数,提高了LLE计算速度,改进了模糊近邻点个数的选取。实验结果表明,改进的算法有效地降低了近邻点个数对算法的影响,具有更好的降维效果和更高的计算速度。展开更多
文摘In this paper, we proposed a new semi-supervised multi-manifold learning method, called semi- supervised sparse multi-manifold embedding (S3MME), for dimensionality reduction of hyperspectral image data. S3MME exploits both the labeled and unlabeled data to adaptively find neighbors of each sample from the same manifold by using an optimization program based on sparse representation, and naturally gives relative importance to the labeled ones through a graph-based methodology. Then it tries to extract discriminative features on each manifold such that the data points in the same manifold become closer. The effectiveness of the proposed multi-manifold learning algorithm is demonstrated and compared through experiments on a real hyperspectral images.
基金Project(60425310) supported by the National Science Fund for Distinguished Young ScholarsProject(10JJ6094) supported by the Hunan Provincial Natural Foundation of China
文摘Multi-label data with high dimensionality often occurs,which will produce large time and energy overheads when directly used in classification tasks.To solve this problem,a novel algorithm called multi-label dimensionality reduction via semi-supervised discriminant analysis(MSDA) was proposed.It was expected to derive an objective discriminant function as smooth as possible on the data manifold by multi-label learning and semi-supervised learning.By virtue of the latent imformation,which was provided by the graph weighted matrix of sample attributes and the similarity correlation matrix of partial sample labels,MSDA readily made the separability between different classes achieve maximization and estimated the intrinsic geometric structure in the lower manifold space by employing unlabeled data.Extensive experimental results on several real multi-label datasets show that after dimensionality reduction using MSDA,the average classification accuracy is about 9.71% higher than that of other algorithms,and several evaluation metrices like Hamming-loss are also superior to those of other dimensionality reduction methods.
文摘In dealing with high-dimensional data, such as the global climate model, facial data analysis, human gene distribution and so on, the problem of dimensionality reduction is often encountered, that is, to find the low dimensional structure hidden in high-dimensional data. Nonlinear dimensionality reduction facilitates the discovery of the intrinsic structure and relevance of the data and can make the high-dimensional data visible in the low dimension. The isometric mapping algorithm (Isomap) is an important algorithm for nonlinear dimensionality reduction, which originates from the traditional dimensionality reduction algorithm MDS. The MDS algorithm is based on maintaining the distance between the samples in the original space and the distance between the samples in the lower dimensional space;the distance used here is Euclidean distance, and the Isomap algorithm discards the Euclidean distance, and calculates the shortest path between samples by Floyd algorithm to approximate the geodesic distance along the manifold surface. Compared with the previous nonlinear dimensionality reduction algorithm, the Isomap algorithm can effectively compute a global optimal solution, and it can ensure that the data manifold converges to the real structure asymptotically.
文摘As an effective way in finding the underlying parameters of a high-dimension space, manifold learning is popular in nonlinear dimensionality reduction which makes high-dimensional data easily to be observed and analyzed. In this paper, Isomap, one of the most famous manifold learning algorithms, is applied to process closing prices of stocks of CSI 300 index from September 2009 to October 2011. Results indicate that Isomap algorithm not only reduces dimensionality of stock data successfully, but also classifies most stocks according to their trends efficiently.
基金Project (No 2008AA01Z132) supported by the National High-Tech Research and Development Program of China
文摘Image feature optimization is an important means to deal with high-dimensional image data in image semantic understanding and its applications. We formulate image feature optimization as the establishment of a mapping between highand low-dimensional space via a five-tuple model. Nonlinear dimensionality reduction based on manifold learning provides a feasible way for solving such a problem. We propose a novel globular neighborhood based locally linear embedding (GNLLE) algorithm using neighborhood update and an incremental neighbor search scheme, which not only can handle sparse datasets but also has strong anti-noise capability and good topological stability. Given that the distance measure adopted in nonlinear dimensionality reduction is usually based on pairwise similarity calculation, we also present a globular neighborhood and path clustering based locally linear embedding (GNPCLLE) algorithm based on path-based clustering. Due to its full consideration of correlations between image data, GNPCLLE can eliminate the distortion of the overall topological structure within the dataset on the manifold. Experimental results on two image sets show the effectiveness and efficiency of the proposed algorithms.
基金This work was supported by the National Basic Research 973 Program of China under Grant No. 2011CB302202, the National Natural Science Foundation of China under Grant Nos. 61375051 and 61075119, and the Seeding Grant for Medicine and Information Sciences of Peking University of China under Grant No. 2014-MI-21.
文摘We present a new manifold learning algorithm called Local Orthogonality Preserving Alignment （LOPA）. Our algorithm is inspired by the Local Tangent Space Alignment （LTSA） method that aims to align multiple local neighborhoods into a global coordinate system using affine transformations. However, LTSA often fails to preserve original geometric quantities such as distances and angles. Although an iterative alignment procedure for preserving orthogonality was suggested by the authors of LTSA, neither the corresponding initialization nor the experiments were given. Procrustes Subspaces Alignment （PSA） implements the orthogonality preserving idea by estimating each rotation transformation separately with simulated annealing. However, the optimization in PSA is complicated and multiple separated local rotations may produce globally contradictive results. To address these difficulties, we first use the pseudo-inverse trick of LTSA to represent each local orthogonal transformation with the unified global coordinates. Second the orthogonality constraints are relaxed to be an instance of semi-definite programming （SDP）. Finally a two-step iterative procedure is employed to further reduce the errors in orthogonal constraints. Extensive experiments products, and neighborhoods of the original datasets. In that of PSA and comparable to that of state-of-the-art significantly faster than that of PSA, MVU and MVE. show that LOPA can faithfully preserve distances, angles, inner comparison, the embedding performance of LOPA is better than algorithms like MVU and MVE, while the runtime of LOPA is
基金supported by the National Basic Research 973 Program of China under Grant No.2007CB311002the National Natural Science Foundation of China under Grant No.60905003
文摘A new manifold learning method, called incremental alignment method （IAM）, is proposed for nonlinear dimensionality reduction of high dimensional data with intrinsic low dimensionality. The main idea is to incrementally align low-dimensional coordinates of input data patch-by-patch to iteratively generate the representation of the entire data.set. The method consists of two major steps, the incremental step and the alignment step. The incremental step incrementally searches neighborhood patch to be aligned in the next step, and the alignment step iteratively aligns the low-dimensional coordinates of the neighborhood patch searched to generate the embeddings of the entire dataset. Compared with the existing manifold learning methods, the proposed method dominates in several aspects： high efficiency, easy out-of-sample extension, well metric-preserving, and averting of the local minima issue. All these properties are supported by a series of experiments performed on the synthetic and real-life datasets. In addition, the computational complexity of the proposed method is analyzed, and its efficiency is theoretically argued and experimentally demonstrated.
基金supported by National Natural Science Foundation of China(No.61171145)Shanghai Educational Development Fundation(No.12ZZ083)
文摘Over the past few years,nonlinear manifold learning has been widely exploited in data analysis and machine learning.This paper presents a novel manifold learning algorithm,named atlas compatibility transformation(ACT),It solves two problems which correspond to two key points in the manifold definition:how to chart a given manifold and how to align the patches to a global coordinate space based on compatibility.For the first problem,we divide the manifold into maximal linear patch(MLP) based on normal vector field of the manifold.For the second problem,we align patches into an optimal global system by solving a generalized eigenvalue problem.Compared with the traditional method,the ACT could deal with noise datasets and fragment datasets.Moreover,the mappings between high dimensional space and low dimensional space are given.Experiments on both synthetic data and real-world data indicate the effection of the proposed algorithm.
文摘As modern weapons and equipment undergo increasing levels of informatization,intelligence,and networking,the topology and traffic characteristics of battlefield data networks built with tactical data links are becoming progressively complex.In this paper,we employ a traffic matrix to model the tactical data link network.We propose a method that utilizes the Maximum Variance Unfolding(MVU)algorithm to conduct nonlinear dimensionality reduction analysis on high-dimensional open network traffic matrix datasets.This approach introduces novel ideas and methods for future applications,including traffic prediction and anomaly analysis in real battlefield network environments.
文摘局部线性嵌入法(Locally Linear Embedding,LLE)是一种基于流形学习的非线性降维方法。针对LLE近邻点个数选取、样本点分布以及计算速度的问题,提出基于模糊聚类的改进LLE算法。算法根据聚类中心含有大量的信息这一特点,基于模糊聚类原理,采用改进的样本点距离计算方法,定义了近似重构系数,提高了LLE计算速度,改进了模糊近邻点个数的选取。实验结果表明,改进的算法有效地降低了近邻点个数对算法的影响,具有更好的降维效果和更高的计算速度。
