基于概念格的空间聚类方法

空间聚类一直是空间数据挖掘研究的热点之一。现有的聚类方法大都局限于根据空间位置来进行空间聚类的,忽略了空间对象的专题属性,从而导致空间聚类结果有时完全不符合人的空间认知,缺乏合理的解释。为此,综合考虑空间对象的位置和专题属性,提出了一种基于概念格的空间聚类（Concept Lattices BasedSpatial Cluster,CLBSC）方法。该方法通过构建多维专题属性的概念格,简化了空间聚类计算。最后,通过两组实验对CLBSC算法进行了验证分析,研究结果表明：所提出的CLBSC算法是一种具有高可靠性和抗噪性的空间聚类算法。     

一种提高文本分类效果的改进流形学习算法

流形学习算法在模式识别领域有着重要应用,针对文本分类数据的特点,提出一种基于邻域选取进行修正的局部线性嵌入算法,用带有权值的欧式距离来构造文本数据的局部邻域,提高文本分类的识别率;同时,利用文本数据的类别信息,运用半监督局部线性嵌入算法构造分类器,提高文本分类的效果。实验表明,本文基于文本分类改进的流形学习算法,能够有效地对文本进行分类。     

基于局部线性空间划分的流形泛化算法

为了将流形学习算法获取的映射关系扩展到新的样本数据,提出一种基于局部线性空间划分的流形泛化算法.提出局部线性空间划分的局部性、曲率自适应性原则.在此基础上,构建定维投影距离测度,采用定维投影向量量化算法将整个流形划分为若干个局部线性空间.在局部空间上构建流形映射的线性近似映射.在流形映射重构的基础上,针对新样本数据,判断其局部线性空间的归属,进而采用线性近似映射获取低维空间上的映射估计值.在人工合成数据集以及手写数字图像库上的实验证明本文算法的有效性.     

基于云的概念空间模型研究

从认知科学出发,讨论了G?rdenfors的概念空间理论,用云模型对概念空间进行了形式化研究。由于概念、属性中存在着大量的模糊性和不确定性,将云模型和G?rdenfors的概念空间模型结合起来,建立了一套基于云的概念空间模型。并进一步对概念、相似性等进行定义,形成了一套新的基于云的概念空间模型方法。通过一个昆虫分类实例来进行概念空间的建模实验。用静态和动态两种不同的方法来验证基于云模型的概念空间的有效性。     

基于子空间流形的图像集识别方法

近年来,基于黎曼流形将图像集在线性子空间中进行表征的图像集识别方法已经被证实有良好的效果,针对该领域存在的图像线性子空间大多高维所导致现有黎曼流形的图像集识别方法存在计算成本高、适用性有限的问题,提出一种基于子空间流形的图像集识别方法。首先,从线性子空间的几何结构出发,利用Grassmann流形对线性子空间进行建模,得到基于Grassmann流形的联合黎曼度量。然后,通过该联合黎曼度量,从高维的Grassmann流形中学习到一个低维的Grassmann流形。最后,对通过学习得到的低维流形上的图像集数据进行图像集识别。实验结果表明,在ETH-80数据集上该方法的识别准确率比投影度量学习（PML）和图嵌入Grassmann判别分析（GGDA）都分别提升了2.5个百分点。证明了在通过提出的度量与方法学习到的低维流形上,图像集数据具有更好的分类结构,从而降低图像集识别计算成本,扩大适用范围,提升识别准确率。     

基于流形学习的单字符字体辨别

文字种类识别及字体辨别已成为继印刷体文字识别以后新的国内外研究的热点,关于单字的手写体和印刷体辨别的研究不多,但在表单中却极为常用。对于字体辨别问题,引入流形学习算法局部线性嵌套（LLE）,假定数据为存在于嵌入高维空间的一个低维流形。提出了用于单字字体辨别的LLE泛化方法及邻域和内在维数的参数估计方法,基于印刷体/手写体汉字字符及数字的辨别实验表明,其性能优于直接支持向量机（SVM）分类,且经过LLE降维后的数据直接用线性判别分析方法（LDA）分类可以获得与LLE计算后SVM分类相近甚至更高的正确率和更快的分类速度。     

流形学习概述

流形学习是一种新的非监督学习方法,近年来引起越来越多机器学习和认知科学工作者的重视.为了加深对流形学习的认识和理解,该文由流形学习的拓扑学概念入手,追溯它的发展过程.在明确流形学习的不同表示方法后,针对几种主要的流形算法,分析它们各自的优势和不足,然后分别引用Isomap和LLE的应用示例.结果表明,流形学习较之于传统的线性降维方法,能够有效地发现非线性高维数据的本质维数,利于进行维数约简和数据分析.最后对流形学习未来的研究方向做出展望,以期进一步拓展流形学习的应用领域.     

基于等维度独立多流形的DC-ISOMAP算法

流形学习已经成为机器学习与数据挖掘领域中一个重要的研究课题.目前的流形学习算法都假设所研究的高维数据存在于同一个流形上,并不能支持或者应用于大量存在的采样于多流形上的高维数据.针对等维度的独立多流形DC-ISOMAP算法,首先通过从采样密集点开始扩展切空间的方法将多流形准确分解为单个流形,并逐个计算其低维嵌入,然后基于各子流形间的内部位置关系将其低维嵌入组合起来,得到最终的嵌入结果.实验结果表明,该算法在人造数据和实际的人脸图像数据上都能有效地计算出高维数据的低维嵌入结果.     

增量Hessian LLE算法研究

利用基于Ritz加速的逆幂迭代算法,在经典的Hessian LLE算法基础上提出一种增量LLE算法,能够高效地处理新增的一个或多个样本。该算法的核心思想是将增量流形学习问题转化为一个增量特征值问题,利用数值线性代数的工具进行求解,并分析算法的收敛性。在合成数据集和图像数据集上,验证该增量算法的效率和精确度。     

基于抽样的概念层次挖掘算法

本文通过对数据挖掘的几种传统属性归纳算法的分析,发现它们存在以下不足：（1）不能处理不平衡的概念层次;（2）没有考虑实际数据分布对最后的泛化规则的影响。因此,本文提出了基于抽样的概念层次挖掘算法,它先采用抽样方法,对概念层次进行初步调整,然后扫描整个数据文件,利用扫描信息再次调整概念层次,最后通过统计调整后的概念层次的叶子信息就可以得到泛化规则。本算法不仅克服了传统算法的不足,而且具有最优的时间复杂度O（n)和空间复杂度O(c)。     

面向主题的概念检索研究

该文提出了一种基于概念网络和主题概念树的面向主题的文本检索算法。依托概念网络建立主题概念树,利用主题概念树对用户的查询请求进行语义扩展,实现同义和语义蕴涵检索。关联度的计算模型考虑了词与词之间,句与句之间的语义激励。通过关联度在主题概念树上的传播模型,实现复合概念关联度的计算。检索结果按关联度大小降序排列。基于主题概念树的概念检索导航为用户检索提供了便利。     

Editorial of the Special Issue on Manifold Learning

In many information analysis tasks, one is often confronted with thousands to millions dimensional data, such as images, documents, videos, web data, bioinformatics data, etc. Conventional statistical and computational tools are severely inadequate for processing and analysing high-dimensional data due to the curse of dimensionality, where we often need to conduct inference with a limited number of samples. On the other hand, naturally occurring data may be generated by structured systems with possibly much fewer degrees of freedom than the ambient dimension would suggest. Recently, various works have considered the case when the data is sampled from a submanifold embedded in the much higher dimensional Euclidean space. Learning with full consideration of the low dimensional manifold structure, or specifically the intrinsic topological and geometrical properties of the data manifold is referred to as manifold learning, which has been receiving growing attention in our community in recent years. This special issue is to attract articles that (a) address the frontier problems in the scientific principles of manifold learning, and (b) report empirical studies and applications of manifold learning algorithms, including but not limited to pattern recognition, computer vision, web mining, image processing and so on. A total of 13 submissions were received. The papers included in this special issue are selected based on the reviews by experts in the subject area according to the journal''s procedure and quality standard. Each paper is reviewed by at least two reviewers and some of the papers were revised for two rounds according to the reviewers'' comments. The special issue includes 6 papers in total: 3 papers on the foundational theories of manifold learning, 2 papers on graph-based methods, and 1 paper on the application of manifold learning to video compression. The papers on the foundational theories of manifold learning cover the topics about the generalization ability of manifold learning, manifold ranking, and multi-manifold factorization. In the paper entitled ``Manifold Learning: Generalizing Ability and Tangential Proximity'', Bernstein and Kuleshov propose a tangential proximity based technique to address the generalized manifold learning problem. The proposed method ensures not only proximity between the points and their reconstructed values but also proximity between the corresponding tangent spaces. The traditional manifold ranking methods are based on the Laplacian regularization, which suffers from the issue that the solution is biased towards constant functions. To overcome this issue, in the paper entitled ``Manifold Ranking using Hessian Energy'', Guan et al. propose to use the second-order Hessian energy as regularization for manifold ranking. In the paper entitled ``Multi-Manifold Concept Factorization for Data Clustering'', Li et al. incorporate the multi-manifold ensemble learning into concept factorization to better preserve the local structure of the data, thus yielding more satisfactory clustering results. The papers on graph-based methods cover the topics about label propagation and graph-based dimensionality reduction. In the paper entitled ``Bidirectional Label Propagation over Graphs'', Liu et al. propose a novel label propagation algorithm to propagate labels along positive and negative edges in the graph. The construction of the graph is novel against the conventional approach by incorporating the dissimilarity among data points into the affinity matrix. In the paper entitled ``Locally Regressive Projections'', Lijun Zhang proposes a novel graph-based dimensionality reduction method that captures the local discriminative structure of the data space. The key idea is to fit a linear model locally around each data point, and then use the fitting error to measure the performance of dimensionality reduction. In the last paper entitled ``Combining Active and Semi-Supervised Learning for Video Compression'', motivated from manifold regularization, Zhang and Ji propose a machine learning approach for video compression. Active learning is used to select the most representative pixels in the encoding process, and semi-supervised learning is used to recover the color video in the decoding process. One remarking property of this approach is that the active learning algorithm shares the same loss function as the semi-supervised learning algorithm, providing a unified framework for video compression. Many people have been involved in making this special issue possible. The guest editor would like to express his gratitude to all the contributing authors for their insightful work on manifold learning. The guest editor would like to thank the reviewers for their comments and useful suggestions in order to improve the quality of the papers. The guest editor would also like to thank Prof. Ruqian Lu, the editor-in-chief of the International Journal of Software and Informatics, for providing the precious opportunity to publish this special issue. Finally, we hope the reader will enjoy this special issue and find it useful.     

机械产品概念设计中的知识表示

研究了计算机辅助概念设计中的关键技术——知识表示．将行为域引入公理化设计作为功能域和载体域之间的转换桥梁，针对该域结构定义扩展“之”字映射，建立了不同层次功能、行为和载体之间的映射关系；构造了概念设计方案的知识表示模型——域结构模板；针对一类产品的知识表示模型——概念空间，给出了基于概念空间的概念设计方案生成过程．最后以工业平缝机为例对所述模型和方法加以说明。     

异构人脸在流形空间中的相似模型研究

人脸艺术造型与其原型人脸的相似性是造型成功与否的关键指标之一。传统相似性研究建立在同构数据特征基础之上,对呈异构形态的二维图像人脸和三维网格人脸之间的相似性计算问题的研究还很少见。采用双层拉普拉斯流形对齐方法,通过对相同样本数的二维人脸数据集和三维人脸数据集进行协同降维,发现两者的共享流形嵌入,建立异构的二维人脸图像与三维网格人脸之间的相似模型,实现对异构人脸之间相似性的定量计算。通过实验,证明了该方法的合理性与有效性。     

计算机辅助概念设计研究进展

以第4届国际计算机辅助工业设计与概念设计会议为背景，阐明了产品概念设计的内涵，指出计算机辅助概念设计CACD要解决的三大问题：概念设计方法学、产品信息模型及求解方法、计算机辅助概念设计技术；进而从智能概念设计技术、协同概念设计技术、虚拟概念设计技术、需求驱动概念设计技术等多个方面总结了CACD技术的研究进展，最后指出了CACD的发展趋势，并提出了CACD的三层架构．     

Manifold Learning: Generalization Ability and Tangent Proximity

One of the ultimate goals of Manifold Learning (ML) is to reconstruct an unknown nonlinear low-dimensional Data Manifold (DM) embedded in a high-dimensional observation space from a given set of data points sampled from the manifold. We derive asymptotic expansion and local lower and upper bounds for the maximum reconstruction error in a small neighborhood of an arbitrary point. The expansion and bounds are defined in terms of the distance between tangent spaces to the original DM and the Reconstructed Manifold (RM) at the selected point and its reconstructed value, respectively. We propose an amplification of the ML, called Tangent Bundle ML, in which proximity is required not only between the DM and RM but also between their tangent spaces. We present a new geometrically motivated Grassman & Stiefel Eigenmaps algorithm that solves this problem and gives a new solution for the ML also.     

流形学习中的算法研究

详细介绍了一种新的机器学习的方法--流形学习.流形学习是一种新的非监督学习方法,可以有效地发现高维非线性数据集的内在维数并进行维数约简,近年来越来越受到机器学习和认知科学领域的研究者的重视.目前已经出现了很多有效的流形学习算法,如等度规映射(ISOMAP)、局部线性嵌套(Locally Linear Embedding ,LLE)等.详细讲述了当前常用的几种流形学习算法以及在流形方面已经取得的研究成果,并对流形学习目前在各方面的应用作了较为细致的阐述.最后展望了流形学习的研究发展趋势,且提出了流形学习中仍需解决的关键问题.     

Conceptual Spaces for Computer Vision Representations

A framework for high-level representations in computer vision architectures is described. The framework is based on the notion of conceptual space. This approach allows us to define a conceptual semantics for the symbolic representations of the vision system. In this way, the semantics of the symbols can be grounded to the data coming from the sensors. In addition, the proposed approach generalizes the most popular frameworks adopted in computer vision.     

基于概念向量空间模型的中文自动文摘系统

文章提出了一种基于hownet提取出词语的词义,用词语的词义代替传统的词形频率统计方法,并基于词义排歧建立主题语义概念向量空间模型。通过对抽取出的语句进行句子相似度的计算提高文摘精确度,设计实现了一个中文自动文摘系统。     

基于切空间判别学习的流形降维算法

在基于图像集的流形降维问题中,许多算法的核心思想都是把一个高维的流形直接降到一个维数相对较低、同时具有的判别信息更加充分的流形上.投影度量学习（projection metric learning,简称PML）是一种Grassmann流形降维算法.该算法是基于投影度量,并且使用RCG（Riemannian conjugate gradient）算法优化目标函数,其在多个数据集上都取得了较好的实验结果,但是对于复杂的人脸数据集,如YTC其实验结果相对较差,只取得了66.69%的正确率.同时,RCG算法的时间效率较差.基于上述原因,提出了基于切空间判别学习的流形降维算法.该算法首先对于PML中的投影矩阵添加扰动,使其成为对称正定（symmetric positive definite,简称SPD）矩阵;然后,使用LEM（log-euclidean metric）将其映射到切空间中;最后,利用基于特征值分解的迭代优化算法构造判别函数,得到变换矩阵.对提算法在多个标准数据集上进行了实验验证,并取得了较好的实验结果,从而验证了该算法的有效性.