邻域参数动态变化的局部线性嵌入

局部线性嵌入是最有竞争力的非线性降维方法,有较强的表达能力和计算优势.但它们都采用全局一致的邻城大小,只适用于均匀分布的流形,无法处理现实中大量存在的非均匀分布流形.为此,提出一种邻域大小动态确定的新局部线性嵌入方法.它采用Hessian局部线性嵌入的概念框架,但用每个点的局部邻域估计此邻域内任意点之间的近似测地距离,然后根据近似测地距离与欧氏距离之间的关系动态确定该点的邻域大小,并以此邻域大小构造新的局部邻域.算法几何意义清晰,在观察数据稀疏和数据带噪音等情况下,都比现有算法有更强的鲁棒性.标准数据集上的实验结果验证了所提方法的有效性.     

Building k-connected neighborhood graphs for isometric data embedding

Isometric data embedding using geodesic distance requires the construction of a connected neighborhood graph so that the geodesic distance between every pair of data points can be estimated. This paper proposes an approach for constructing k-connected neighborhood graphs. The approach works by applying a greedy algorithm to add each edge, in a nondecreasing order of edge length, to a neighborhood graph if end vertices of the edge are not yet k-connected on the graph. The k-connectedness between vertices is tested using a network flow technique by assigning every vertex a unit flow capacity. This approach is applicable to a wide range of data. Experiments show that it gives better estimation of geodesic distances than other approaches, especially when the data are undersampled or nonuniformly distributed.     

正交化近邻关系保持的降维及分类算法

针对近邻关系保持嵌入（NPE）算法易于受到降低后的维数影响,而且性能依赖于正确的维数估计的问题,提出了一种正交化的近邻关系保持的嵌入降维方法——ONPE。ONPE方法是使用数据点间的近邻关系来构造邻接图,假设每个数据点都能由其近邻点的线性组合表示,则可以通过提取数据点的局部几何信息,并在降维中保持提取的局部几何信息,迭代地计算正交基来得到数据的低维嵌入坐标。同时,在ONPE算法的基础上,利用局部几何信息,提出了一种在低维空间中使用标签传递（LNP）的分类算法——ONPC。其是假设高维空间中的局部近邻关系在降维后的空间中依然得到保持,并且数据点的类别可由近邻点的类别得到。在人工数据和人脸数据上的实验表明,该算法在减少维数依赖的同时,能有效提高NPE算法的分类性能。     

Image clustering based on sparse patch alignment framework

Image clustering methods are efficient tools for applications such as content-based image retrieval and image annotation. Recently, graph based manifold learning methods have shown promising performance in extracting features for image clustering. Typical manifold learning methods adopt appropriate neighborhood size to construct the neighborhood graph, which captures local geometry of data distribution. Because the density of data points’ distribution may be different in different regions of the manifold, a fixed neighborhood size may be inappropriate in building the manifold. In this paper, we propose a novel algorithm, named sparse patch alignment framework, for the embedding of data lying in multiple manifolds. Specifically, we assume that for each data point there exists a small neighborhood in which only the points that come from the same manifold lie approximately in a low-dimensional affine subspace. Based on the patch alignment framework, we propose an optimization strategy for constructing local patches, which adopt sparse representation to select a few neighbors of each data point that span a low-dimensional affine subspace passing near that point. After that, the whole alignment strategy is utilized to build the manifold. Experiments are conducted on four real-world datasets, and the results demonstrate the effectiveness of the proposed method.     

基于矩阵的混合型邻域决策粗糙集增量式更新算法

决策粗糙集模型是当前粗糙集理论最为重要的研究分支之一.然而,由于现实环境下数据类型的复杂多样以及数据的动态更新,使得传统的决策粗糙集模型面临着一定的局限和不足,针对这一问题,提出一种混合型信息系统的邻域决策粗糙集模型,并设计出一种矩阵方法的邻域决策粗糙集增量式更新算法.首先,将传统的离散型决策粗糙集模型在混合型信息系统...     

基于对象变化的邻域决策粗糙集动态更新算法

针对现实环境下数据集不断动态变化的特性,提出一种邻域决策粗糙集模型的增量式更新算法。采用由简单到复杂的研究思路,分析了邻域型信息系统论域增加和减少单个对象时,目标近似集与邻域类之间概率的变化规律,进一步地利用这种规律来构造单个对象变化时邻域决策粗糙集模型上下近似集的增量式更新,在单个对象变化的基础上,通过逐步迭代的方式设计了对象批量变化时的增量式更新算法。实验分析表明,所提出的算法具有较高的增量式更新性能,适用于动态数据环境下邻域决策粗糙集模型的动态更新。     

流形距离与压缩感知核稀疏投影的局部线性嵌入算法

流形学习算法的目的是发现嵌入在高维数据空间中的低维表示,现有的流形学习算法对邻域参数k和噪声比较敏感。针对此问题,文中提出一种流形距离与压缩感知核稀疏投影的局部线性嵌入算法,其核心思想是集成局部线性嵌入算法对高维流形结构数据的降维有效性与压缩感知核稀疏投影的强鉴别性,以实现高效有降噪流形学习。首先,在选择各样本点的近邻域时,采用流形距离代替欧氏距离度量数据间相似度的方法,创建能够正确反映流形内部结构的邻域图,解决以欧氏距离作为相似性度量时对邻域参数的敏感。其次,利用压缩感知核稀疏投影作为从高维观测空间到低维嵌入空间的映射,增强算法的鉴别性。最后,利用Matlab工具对实验数据集进行仿真,进一步验证所提算法的有效性。     

基于邻域粒化条件熵的增量式属性约简算法

增量式属性约简是针对动态型数据的一种重要的数据挖掘方法,目前已提出的增量式属性约简算法大多基于离散型数据构建,很少有对数值型数据进行相关的研究.鉴于此,提出一种数值型信息系统中对象不断增加的增量式属性约简算法.首先,在数值型信息系统中建立一种分层的邻域粒化计算方法,并基于该方法提出邻域粒化的增量式计算;然后,在邻域粒化增量式计算的基础上给出邻域粒化条件熵的增量式更新方法,并基于该更新机制提出对应的增量式属性约简算法;最后,通过实验分析表明所提出算法对于数值型数据的增量式属性约简具有更高的有效性和优越性.     

An optimal distributed algorithm for finding articulation points in a network

This paper presents a distributed algorithm for finding the articulation points in an n node communication network represented by a connected undirected graph. For a given graph if the deletion of a node splits the graph into two or more components then that node is called an articulation point. The output of the algorithm is available in a distributed manner, i.e., when the algorithm terminates each node knows whether it is an articulation point or not. It is shown that the algorithm requires O(n) messages and O(n) units of time and is optimal in communication complexity to within a constant factor.     

Interpretable learning based Dynamic Graph Convolutional Networks for Alzheimer’s Disease analysis

Graph Convolutional Networks (GCNs) are widely applied in classification tasks by aggregating the neighborhood information of each sample to output robust node embedding. However, conventional GCN methods do not update the graph during the training process so that their effectiveness is always influenced by the quality of the input graph. Moreover, previous GCN methods lack the interpretability to limit their real applications. In this paper, a novel personalized diagnosis technique is proposed for early Alzheimer’s Disease (AD) diagnosis via coupling interpretable feature learning with dynamic graph learning into the GCN architecture. Specifically, the module of interpretable feature learning selects informative features to provide interpretability for disease diagnosis and abandons redundant features to capture inherent correlation of data points. The module of dynamic graph learning adjusts the neighborhood relationship of every data point to output robust node embedding as well as the correlations of all data points to refine the classifier. The GCN module outputs diagnosis results based on the learned inherent graph structure. All three modules are jointly optimized to perform reliable disease diagnosis at an individual level. Experiments demonstrate that our method outputs competitive diagnosis performance as well as provide interpretability for personalized disease diagnosis.     

云计算环境下高复杂度动态数据的增量密度快速聚类算法研究

针对传统的聚类算法存在开销大、聚类质量差、聚类速度慢等问题,提出一种新的云计算环境下高复杂度动态数据的增量密度快速聚类算法。首先,依据密度对云计算环境下高复杂度动态数据进行聚类,从数据空间中找到部分子空间,使得数据映射至该空间后可产生高密度点集区域,将连通区域的集合看作聚类结果;其次,通过DBSCAN算法进行增量聚类,并对插入或删除数据导致的原聚类合并或分裂进行研究;最后,在更新的过程中通过改变核心状态数据的邻域中含有的全部核心数据进行处理,从插入或删除数据两方面进行增量聚类分析。实验结果表明,所提算法开销低、聚类速度快、聚类质量高。     

Fast Updating of Delaunay Triangulation of Moving Points by Bi‐cell Filtering

Updating a Delaunay triangulation when data points are slightly moved is the bottleneck of computation time in variational methods for mesh generation and remeshing. Utilizing the connectivity coherence between two consecutive Delaunay triangulations for computation speedup is the key to solving this problem. Our contribution is an effective filtering technique that confirms most bi‐cells whose Delaunay connectivities remain unchanged after the points are perturbed. Based on bi‐cell flipping, we present an efficient algorithm for updating two‐dimensional and three‐dimensional Delaunay triangulations of dynamic point sets. Experimental results show that our algorithm outperforms previous methods.     

Enhanced locality preserving projections using robust path based similarity

Curse of dimensionality is a bothering problem in high dimensional data analysis. To enhance the performances of classification or clustering on these data, their dimensionalities should be reduced beforehand. Locality Preserving Projections (LPP) is a widely used linear dimensionality reduction method. It seeks a subspace in which the neighborhood graph structure of samples is preserved. However, like most dimensionality reduction methods based on graph embedding, LPP is sensitive to noise and outliers, and its effectiveness depends on choosing suitable parameters for constructing the neighborhood graph. Unfortunately, it is difficult to choose effective parameters for LPP. To address these problems, we propose an Enhanced LPP (ELPP) using a similarity metric based on robust path and a Semi-supervised ELPP (SELPP) with pairwise constraints. In comparison with original LPP, our methods are not only robust to noise and outliers, but also less sensitive to parameters selection. Besides, SELPP makes use of pairwise constraints more efficiently than other comparing methods. Experimental results on real world face databases confirm their effectiveness.     

Complete neighborhood preserving embedding for face recognition

Neighborhood preserving embedding (NPE) is a linear approximation to the locally linear embedding algorithm which can preserve the local neighborhood structure on the data manifold. However, in typical face recognition where the number of data samples is smaller than the dimension of data space, it is difficult to directly apply NPE to high dimensional matrices because of computational complexity. Moreover, in such case, NPE often suffers from the singularity problem of eigenmatrix, which makes the direct implementation of the NPE algorithm almost impossible. In practice, principal component analysis or singular value decomposition is applied as a preprocessing step to attack these problems. Nevertheless, this strategy may discard dimensions that contain important discriminative information and the eigensystem computation of NPE could be unstable. Towards a practical dimensionality reduction method for face data, we develop a new scheme in this paper, namely, the complete neighborhood preserving embedding (CNPE). CNPE transforms the singular generalized eigensystem computation of NPE into two eigenvalue decomposition problems. Moreover, a feasible and effective procedure is proposed to alleviate the computational burden of high dimensional matrix for typical face image data. Experimental results on the ORL face database and the Yale face database show that the proposed CNPE algorithm achieves better performance than other feature extraction methods, such as Eigenfaces, Fisherfaces and NPE, etc.     

Semi-supervised dimension reduction based on hypergraph embedding for hyperspectral images

Dimension reduction (DR) is an efficient and effective preprocessing step of hyperspectral images (HSIs) classification. Graph embedding is a frequently used model for DR, which preserves some geometric or statistical properties of original data set. The embedding using simple graph only considers the relationship between two data points, while in real-world application, the complex relationship between several data points is more important. To overcome this problem, we present a linear semi-supervised DR method based on hypergraph embedding (SHGE) which is an improvement of semi-supervised graph learning (SEGL). The proposed SHGE method aims to find a projection matrix through building a semi-supervised hypergraph which can preserve the complex relationship of the data and the class discrimination for DR. Experimental results demonstrate that our method achieves better performance than some existing DR methods for HSIs classification and is time saving compared with the existed method SEGL which used simple graph.     

Graph matching based on spectral embedding with missing value

This paper proposes an efficient algorithm for inexact graph matching based on spectral embedding with missing value. We commence by building an association graph model based on initial matching algorithm. Then, by dot product representation of graph with missing value, a new embedding method (co-embedding), where the correspondences between unmatched nodes are treated as missing data in an association graph, is presented. At last, a new graph matching algorithm which alternates between the co-embedding and point pattern matching is proposed. Convictive experimental results on both synthetic and real-world data demonstrate the effectiveness of the proposed graph matching algorithm.     

保持局部邻域关系的增量Hessian LLE算法

Hessian LLE算法是一种经典的流形学习算法,但该方法是以批处理的方式进行的,当新的数据点加入时,必须重新运行整个算法,计算所有数据点低维嵌入,原来的运算结果被全部丢弃。鉴于此,提出了一种保持局部邻域关系的增量Hessian LLE(LIHLLE)算法,该方法通过保证流形新增样本点在原空间和嵌入空间局部邻域的线性关系不变,用其已有邻域点的低维坐标线性表示新增样本点,来得到新增点的低维嵌入,实现增量学习。在Swiss roll withhole和frey_rawface数据集上的实验表明,该方法简便、有效可行。     

Neighborhood graphs for indexing and retrieving multi-dimensional data

We propose a methodology based on a structure called neighborhood graphs for indexing and retrieving multi-dimensional data. In accordance with the increase of the quantity of data, it gets more and more important to process multi-dimensional data. Processing of data includes various tasks, for instance, mining, classifying, clustering, to name a few. However, to enable the effective processing of such multi-dimensional data, it is often necessary to locate each data precisely in the multi-dimensional space where the data reside so that each data can be effectively retrieved for processing. This amounts to solving the point location problem (neighborhood search) for multi-dimensional space. In this paper, in order to utilize the structure of neighborhood graphs as an indexing structure for multi-dimensional data, we propose the following: i) a local insertion and deletion method, and ii) an incremental neighborhood graph construction method. The first method enables to cope with the problem incurred from the updating of the graph. The second method realizes fast neighborhood graph construction from scratch, through the recursive application of the first method. Several experiments are conducted to evaluate the proposed approach, and the results indicate the effectiveness of our approach.     

Graph embedding and extensions: a general framework for dimensionality reduction

A large family of algorithms - supervised or unsupervised; stemming from statistics or geometry theory - has been designed to provide different solutions to the problem of dimensionality reduction. Despite the different motivations of these algorithms, we present in this paper a general formulation known as graph embedding to unify them within a common framework. In graph embedding, each algorithm can be considered as the direct graph embedding or its linear/kernel/tensor extension of a specific intrinsic graph that describes certain desired statistical or geometric properties of a data set, with constraints from scale normalization or a penalty graph that characterizes a statistical or geometric property that should be avoided. Furthermore, the graph embedding framework can be used as a general platform for developing new dimensionality reduction algorithms. By utilizing this framework as a tool, we propose a new supervised dimensionality reduction algorithm called marginal Fisher analysis in which the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring points of the same class, while the penalty graph connects the marginal points and characterizes the interclass separability. We show that MFA effectively overcomes the limitations of the traditional linear discriminant analysis algorithm due to data distribution assumptions and available projection directions. Real face recognition experiments show the superiority of our proposed MFA in comparison to LDA, also for corresponding kernel and tensor extensions     

散乱数据点集曲线重构的最短路逼近算法

给出了散乱数据点集曲线重构的最短路逼近算法．算法根据数据点的分布构造带权连通图，通过求解带权连通图的最短路径，将散乱数据点集的曲线重构问题转化为有序数据点集的曲线重构问题．算法可以对单连通、多连通和封闭的数据点集进行重构．重构曲线较好地保持了数据点集的形状和走向，尤其是带尖点的数据点集的形状特征．最后给出不同拓扑结构的数据点集的重构曲线实例．