Non-linear metric learning using pairwise similarity and dissimilarity constraints and the geometrical structure of data

The problem of clustering with side information has received much recent attention and metric learning has been considered as a powerful approach to this problem. Until now, various metric learning methods have been proposed for semi-supervised clustering. Although some of the existing methods can use both positive (must-link) and negative (cannot-link) constraints, they are usually limited to learning a linear transformation (i.e., finding a global Mahalanobis metric). In this paper, we propose a framework for learning linear and non-linear transformations efficiently. We use both positive and negative constraints and also the intrinsic topological structure of data. We formulate our metric learning method as an appropriate optimization problem and find the global optimum of this problem. The proposed non-linear method can be considered as an efficient kernel learning method that yields an explicit non-linear transformation and thus shows out-of-sample generalization ability. Experimental results on synthetic and real-world data sets show the effectiveness of our metric learning method for semi-supervised clustering tasks.     

Learning a Mahalanobis distance metric for data clustering and classification

Distance metric is a key issue in many machine learning algorithms. This paper considers a general problem of learning from pairwise constraints in the form of must-links and cannot-links. As one kind of side information, a must-link indicates the pair of the two data points must be in a same class, while a cannot-link indicates that the two data points must be in two different classes. Given must-link and cannot-link information, our goal is to learn a Mahalanobis distance metric. Under this metric, we hope the distances of point pairs in must-links are as small as possible and those of point pairs in cannot-links are as large as possible. This task is formulated as a constrained optimization problem, in which the global optimum can be obtained effectively and efficiently. Finally, some applications in data clustering, interactive natural image segmentation and face pose estimation are given in this paper. Experimental results illustrate the effectiveness of our algorithm.     

基于约束动态更新的半监督层次聚类算法

提出了一种基于约束动态更新的半监督层次聚类算法. 与现存的半监督层次聚类算法类似, 该算法也使用了必连和不连约束. 但不同的是, 该算法并不是在对满足必连约束的数据样本点进行预先划分的基础上依据不连约束进行聚合操作, 而是首先将约束扩展为一个闭包, 然后在这此基础上直接依据不连约束进行聚合操作, 并在聚合的过程中依据聚类结果动态地更新必连和不连约束, 以保证最终的聚类结果同时满足必连和不连约束. 该算法的优势在于省略了对必连约束的数据样本点进行预先划分的步骤, 这一改进能够保证数据样本点获得更为合理的聚合顺序, 从而得到更为准确的聚类结果. 本文具体给出了该算法基于Ward 层次聚类算法的实现, 提出了C-Ward算法.实验表明, 与其他同类算法相比, 无论是在人工模拟数据集还是在现实数据集上, 本文提出的算法都表现出了更高的准确性和更强的稳定性.     

Constraint-based clustering selection

Clustering requires the user to define a distance metric, select a clustering algorithm, and set the hyperparameters of that algorithm. Getting these right, so that a clustering is obtained that meets the users subjective criteria, can be difficult and tedious. Semi-supervised clustering methods make this easier by letting the user provide must-link or cannot-link constraints. These are then used to automatically tune the similarity measure and/or the optimization criterion. In this paper, we investigate a complementary way of using the constraints: they are used to select an unsupervised clustering method and tune its hyperparameters. It turns out that this very simple approach outperforms all existing semi-supervised methods. This implies that choosing the right algorithm and hyperparameter values is more important than modifying an individual algorithm to take constraints into account. In addition, the proposed approach allows for active constraint selection in a more effective manner than other methods.     

On semi-supervised fuzzy c-means clustering for data with clusterwise tolerance by opposite criteria

This paper presents a new semi-supervised fuzzy c-means clustering for data with clusterwise tolerance by opposite criteria. In semi-supervised clustering, pairwise constraints, that is, must-link and cannot-link, are frequently used in order to improve clustering performances. From the viewpoint of handling pairwise constraints, a new semi-supervised fuzzy c-means clustering is proposed by introducing clusterwise tolerance-based pairwise constraints. First, a concept of clusterwise tolerance-based pairwise constraints is introduced. Second, the optimization problems of the proposed method are formulated. Especially, must-link and cannot-link are handled by opposite criteria in our proposed method. Third, a new clustering algorithm is constructed based on the above discussions. Finally, the effectiveness of the proposed algorithm is verified through numerical examples.     

双层随机游走半监督聚类

半监督聚类旨在根据用户给出的必连和不连约束,把所有数据点划分到不同的簇中,从而获得更准确、更加符合用户要求的聚类结果.目前的半监督聚类算法大多数通过修改已有的聚类算法或者结合度规学习,使聚类结果与点对约束尽可能地保持一致,却很少考虑点对约束对周围无约束数据的显式影响程度.提出一种由在顶点上的低层随机游走和在组件上的高层随机游走两部分构成的双层随机游走半监督聚类算法,其中,低层随机游走主要负责计算选出的约束顶点对其他顶点的影响范围和影响程度,称为组件;高层随机游走则进一步将各个点对约束以自适应的强度在组件上进行约束传播,把它们在每个顶点上的影响综合在一个簇指示矩阵中.UCI数据集和大型真实数据集上的实验结果表明,双层随机游走半监督聚类算法比其他半监督聚类算法更准确,也比较高效.     

A scalable kernel-based semisupervised metric learning algorithm with out-of-sample generalization ability

In recent years, metric learning in the semisupervised setting has aroused a lot of research interest. One type of semisupervised metric learning utilizes supervisory information in the form of pairwise similarity or dissimilarity constraints. However, most methods proposed so far are either limited to linear metric learning or unable to scale well with the data set size. In this letter, we propose a nonlinear metric learning method based on the kernel approach. By applying low-rank approximation to the kernel matrix, our method can handle significantly larger data sets. Moreover, our low-rank approximation scheme can naturally lead to out-of-sample generalization. Experiments performed on both artificial and real-world data show very promising results.     

基于约束投影的支持向量机选择性集成

提出两种基于约束投影的支持向量机选择性集成算法。首先利用随机选取的must-link和cannot-link成对约束集确定投影矩阵,将原始训练样本投影到不同的低维空间训练一组基分类器;然后,分别采用遗传优化和最小化偏离度误差两种选择性集成技术对基分类器进行组合。基于UCI数据的实验表明,提出的两种集成算法均能有效提高支持向量机的泛化性能,显著优于Bagging,Boosting,特征Bagging及LoBag等集成算法。     

A Lagrangian-based score for assessing the quality of pairwise constraints in semi-supervised clustering

Clustering algorithms help identify homogeneous subgroups from data. In some cases, additional information about the relationship among some subsets of the data exists. When using a semi-supervised clustering algorithm, an expert may provide additional information to constrain the solution based on that knowledge and, in doing so, guide the algorithm to a more useful and meaningful solution. Such additional information often takes the form of a cannot-link constraint (i.e., two data points cannot be part of the same cluster) or a must-link constraint (i.e., two data points must be part of the same cluster). A key challenge for users of such constraints in semi-supervised learning algorithms, however, is that the addition of inaccurate or conflicting constraints can decrease accuracy and little is known about how to detect whether expert-imposed constraints are likely incorrect. In the present work, we introduce a method to score each must-link and cannot-link pairwise constraint as likely incorrect. Using synthetic experimental examples and real data, we show that the resulting impact score can successfully identify individual constraints that should be removed or revised.

     

Semi-supervised clustering with metric learning: An adaptive kernel method

Most existing representative works in semi-supervised clustering do not sufficiently solve the violation problem of pairwise constraints. On the other hand, traditional kernel methods for semi-supervised clustering not only face the problem of manually tuning the kernel parameters due to the fact that no sufficient supervision is provided, but also lack a measure that achieves better effectiveness of clustering. In this paper, we propose an adaptive Semi-supervised Clustering Kernel Method based on Metric learning (SCKMM) to mitigate the above problems. Specifically, we first construct an objective function from pairwise constraints to automatically estimate the parameter of the Gaussian kernel. Then, we use pairwise constraint-based K-means approach to solve the violation issue of constraints and to cluster the data. Furthermore, we introduce metric learning into nonlinear semi-supervised clustering to improve separability of the data for clustering. Finally, we perform clustering and metric learning simultaneously. Experimental results on a number of real-world data sets validate the effectiveness of the proposed method.     

A Kernel Approach for Semisupervised Metric Learning

While distance function learning for supervised learning tasks has a long history, extending it to learning tasks with weaker supervisory information has only been studied recently. In particular, some methods have been proposed for semisupervised metric learning based on pairwise similarity or dissimilarity information. In this paper, we propose a kernel approach for semisupervised metric learning and present in detail two special cases of this kernel approach. The metric learning problem is thus formulated as an optimization problem for kernel learning. An attractive property of the optimization problem is that it is convex and, hence, has no local optima. While a closed-form solution exists for the first special case, the second case is solved using an iterative majorization procedure to estimate the optimal solution asymptotically. Experimental results based on both synthetic and real-world data show that this new kernel approach is promising for nonlinear metric learning     

半监督典型相关分析算法

在典型相关分析算法(canonical correlation analysis,简称CCA)的基础上,通过引入以成对约束形式给出的监督信息,提出了一种半监督的典型相关分析算法(Semi-CCA).在此算法中,除了考虑大量的无标号样本以外,还考虑成对约束信息,即已知两样本属于同一类(正约束)或不属于同一类(负约束),同时验证了两者的相对重要性.在人工数据集、多特征手写体数据集和人脸数据集(Yale和AR)上的实验结果表明,Semi-CCA能够有效地利用少量的监督信息采提高分类性能.     

Integrating local and global topological structures for semi-supervised dimensionality reduction

Dimensionality reduction plays an important role in many machine learning tasks. This paper studies semi-supervised dimensionality reduction using pairwise constraints. In this setting, domain knowledge is given in the form of pairwise constraint, which specifies whether a pair of instances belongs to the same class (must-link constraint) or different classes (cannot-link constraint). In this paper, a novel semi-supervised dimensionality reduction method called LGS3DR is proposed, which can integrate both local and global topological structures of the data as well as pairwise constraints. The LGS3DR method is effective and has a closed form solution. Experiments on data visualization and face recognition show that LGS3DR is superior to many existing dimensionality reduction methods.     

Constraint scores for semi-supervised feature selection: A comparative study

Recent feature selection scores using pairwise constraints (must-link and cannot-link) have shown better performances than the unsupervised methods and comparable to the supervised ones. However, these scores use only the pairwise constraints and ignore the available information brought by the unlabeled data. Moreover, these constraint scores strongly depend on the given must-link and cannot-link subsets built by the user. In this paper, we address these problems and propose a new semi-supervised constraint score that uses both pairwise constraints and local properties of the unlabeled data. Experiments using Kendall’s coefficient and accuracy rates, show that this new score is less sensitive to the given constraints than the previous scores while providing similar performances.     

辅助信息自动生成的时间序列距离度量学习

对于时间序列聚类任务而言,一个有效的距离度量至关重要.为了提高时间序列聚类的性能,考虑借助度量学习方法,从数据中学习一种适用于时序聚类的距离度量.然而,现有的度量学习未注意到时序的特性,且时间序列数据存在成对约束等辅助信息不易获取的问题.提出一种辅助信息自动生成的时间序列距离度量学习(distancemetric learning based on side information autogeneration for time series,简称SIADML)方法.该方法利用动态时间弯曲(dynamic time warping,简称DTW)距离在捕捉时序特性上的优势,自动生成成对约束信息,使习得的度量尽可能地保持时序之间固有的近邻关系.在一系列时间序列标准数据集上的实验结果表明,采用该方法得到的度量能够有效改善时间序列聚类的性能.     

融合块对角约束的鲁棒低秩多核聚类

针对现有的多核学习(multiple kernel learning, MKL)子空间聚类方法忽略噪声和特征空间中数据的低秩结构问题,提出一种新的鲁棒多核子空间聚类方法(low-rank robust multiple kernel clustering, LRMKC),该方法结合块对角表示(block diagonal representation, BDR)与低秩共识核(low-rank consensus kernel, LRCK)学习,可以更好地挖掘数据的潜在结构.为了学习最优共识核,设计一种基于混合相关熵度量(mixture correntropy induced metric,MCIM)的自动加权策略,其不仅为每个核设置最优权重,而且通过抑制噪声提高模型的鲁棒性;为了探索特征空间数据的低秩结构,提出一种非凸低秩共识核学习方法;考虑到亲和度矩阵的块对角性质,对系数矩阵应用块对角约束. LRMKC将MKL、LRCK与BDR巧妙融合,以迭代提高各种方法的效率,最终形成一个处理非线性结构数据的全局优化方法.与最先进的MKL子空间聚类方法相比,通过在图像和文本数据集上的大量实验验证了...     

Locally linear metric adaptation with application to semi-supervised clustering and image retrieval

Many computer vision and pattern recognition algorithms are very sensitive to the choice of an appropriate distance metric. Some recent research sought to address a variant of the conventional clustering problem called semi-supervised clustering, which performs clustering in the presence of some background knowledge or supervisory information expressed as pairwise similarity or dissimilarity constraints. However, existing metric learning methods for semi-supervised clustering mostly perform global metric learning through a linear transformation. In this paper, we propose a new metric learning method that performs nonlinear transformation globally but linear transformation locally. In particular, we formulate the learning problem as an optimization problem and present three methods for solving it. Through some toy data sets, we show empirically that our locally linear metric adaptation (LLMA) method can handle some difficult cases that cannot be handled satisfactorily by previous methods. We also demonstrate the effectiveness of our method on some UCI data sets. Besides applying LLMA to semi-supervised clustering, we have also used it to improve the performance of content-based image retrieval systems through metric learning. Experimental results based on two real-world image databases show that LLMA significantly outperforms other methods in boosting the image retrieval performance.     

联合低秩稀疏的多核子空间聚类算法

针对多核子空间谱聚类算法没有考虑噪声和关系图结构的问题，提出了一种新的联合低秩稀疏的多核子空间聚类算法(JLSMKC)。首先，通过联合低秩与稀疏表示进行子空间学习，使关系图具有低秩和稀疏结构属性；其次，建立鲁棒的多核低秩稀疏约束模型，用于减少噪声对关系图的影响和处理数据的非线性结构；最后，通过多核方法充分利用共识核矩阵来增强关系图质量。7个数据集上的实验结果表明，所提算法JLSMKC在聚类精度(ACC)、标准互信息(NMI)和纯度(Purity)上优于5种流行的多核聚类算法，同时减少了聚类时间，提高了关系图块对角质量。该算法在聚类性能上有较大优势。     

基于半监督学习的增量图像分类方法

为有效使用大量未标注的图像进行分类,提出一种基于半监督学习的图像分类方法。通过共同的隐含话题桥接少量已标注的图像和大量未标注的图像,利用已标注图像的Must-link约束和Cannot-link约束提高未标注图像分类的精度。实验结果表明,该方法有效提高Caltech-101数据集和7类图像集约10%的分类精度。此外,针对目前绝大部分半监督图像分类方法不具备增量学习能力这一缺点,提出该方法的增量学习模型。实验结果表明,增量学习模型相比无增量学习模型提高近90%的计算效率。关键词半监督学习,图像分类,增量学习中图法分类号TP391。41IncrementalImageClassificationMethodBasedonSemi-SupervisedLearningLIANGPeng^1,2,LIShao-Fa²,QINJiang-Wei²,LUOJian-Gao³¹(SchoolofComputerScienceandEngineering,GuangdongPolytechnicNormalUniversity,Guangzhou510665)²(SchoolofComputerScienceandEngineering,SouthChinaUniversityofTechnology,Guangzhou510006)³(DepartmentofComputer,GuangdongAIBPolytechnicCollege,Guangzhou510507)ABSTRACTInordertouselargenumbersofunlabeledimageseffectively,animageclassificationmethodisproposedbasedonsemi-supervisedlearning。Theproposedmethodbridgesalargeamountofunlabeledimagesandlimitednumbersoflabeledimagesbyexploitingthecommontopics。Theclassificationaccuracyisimprovedbyusingthemust-linkconstraintandcannot-linkconstraintoflabeledimages。TheexperimentalresultsonCaltech-101and7-classesimagedatasetdemonstratethattheclassificationaccuracyimprovesabout10%bytheproposedmethod。Furthermore,duetothepresentsemi-supervisedimageclassificationmethodslackingofincrementallearningability,anincrementalimplementationofourmethodisproposed。Comparingwithnon-incrementallearningmodelinliterature,theincrementallearningmethodimprovesthecomputationefficiencyofnearly90%。     

混杂数据的多核几何平均度量学习

在机器学习和模式识别任务中,选择一种合适的距离度量方法是至关重要的.度量学习主要利用判别性信息学习一个马氏距离或相似性度量.然而,大多数现有的度量学习方法都是针对数值型数据的,对于一些有结构的数据（比如符号型数据）,用传统的距离度量来度量两个对象之间的相似性是不合理的;其次,大多数度量学习方法会受到维度的困扰,高维度使得训练时间长,模型的可扩展性差.提出了一种基于几何平均的混杂数据度量学习方法.采用不同的核函数将数值型数据和符号型数据分别映射到可再生核希尔伯特空间,从而避免了特征的高维度带来的负面影响.同时,提出了一个基于几何平均的多核度量学习模型,将混杂数据的度量学习问题转化为求黎曼流形上两个点的中心点问题.在UCI数据集上的实验结果表明,针对混杂数据的多核度量学习方法与现有的度量学习方法相比,在准确性方面展现出更优异的性能.