Self-organizing topological tree for online vector quantization and data clustering.

The self-organizing Maps (SOM) introduced by Kohonen implement two important operations: vector quantization (VQ) and a topology-preserving mapping. In this paper, an online self-organizing topological tree (SOTT) with faster learning is proposed. A new learning rule delivers the efficiency and topology preservation, which is superior of other structures of SOMs. The computational complexity of the proposed SOTT is O(log N) rather than O(N) as for the basic SOM. The experimental results demonstrate that the reconstruction performance of SOTT is comparable to the full-search SOM and its computation time is much shorter than the full-search SOM and other vector quantizers. In addition, SOTT delivers the hierarchical mapping of codevectors and the progressive transmission and decoding property, which are rarely supported by other vector quantizers at the same time. To circumvent the shortcomings of clustering performance of classical partition clustering algorithms, a hybrid clustering algorithm that fully exploit the online learning and multiresolution characteristics of SOTT is devised. A new linkage metric is proposed which can be updated online to accelerate the time consuming agglomerative hierarchical clustering stage. Besides the enhanced clustering performance, due to the online learning capability, the memory requirement of the proposed SOTT hybrid clustering algorithm is independent of the size of the data set, making it attractive for large database.     

一种结构自适应的径向基函数神经网络

提出了一种新的结构自适应的径向基函数(RBF)神经网络模型。在该模型中,自组织映射(SOM)神经网络作为聚类网络,采用无监督学习算法对输入样本进行自组织分类,并将分类中心及其对应的权值向量传递给RBF神经网络,分别作为径向基函数的中心和相应的权值向量;RBF神经网络作为基础网络,采用高斯函数实现输入层到隐层的非线性映射,输出层则采用有监督学习算法训练网络的权值,从而实现输入层到输出层的非线性映射。通过对字母数据集进行仿真,表明该网络具有较好的性能。     

Structural pattern recognition using genetic algorithms

This paper presents a genetic algorithm (GA) based optimization procedure for the solution of structural pattern recognition problem using the attributed relational graph representation and matching technique. In this study, candidate solutions are represented by integer strings and the population is randomly initialized. The GA is employed to generate a monomorphic mapping. As all the mapping constraints are not enforced during the search phase in order to speedup the search, an efficient pose clustering algorithm is used to eliminate spurious matches and to determine the presence of the model in the scene. The performance of the proposed approach to pattern recognition by subgraph isomorphism is demonstrated using line patterns and silhouette images.     

Self-organizing maps for the skeletonization of sparse shapes

This paper presents a method for computing the skeleton of planar shapes and objects which exhibit sparseness (lack of connectivity), within their image regions. Such sparseness in images may occur due to poor lighting conditions, incorrect thresholding or image sub-sampling. Furthermore, in document image analysis, sparse shapes are characteristic of texts faded due to aging and/or poor ink quality. Given the pixel distribution for a shape, the proposed method involves an iterative evolution of a piecewise-linear approximation of the shape skeleton by using a minimum spanning tree-based self-organizing map (SOM). By constraining the SOM to lie on the edges of the Delaunay triangulation of the shape distribution, the adjacency relationships between regions in the shape are detected and used in the evolution of the skeleton. The SOM, on convergence, gives the final skeletal shape. The skeletonization is invariant to Euclidean transformations. The potential of the method is demonstrated on a variety of sparse shapes from different application domains.     

自组织映射网络的可视化研究

提出了一种自组织映射网络训练结果的可视化方法—距离映射法,该方法根据输入向量与竞争层神经元权向量距离的大小来计算相似度,然后对所有相似度与对应神经元坐标之积求和,把输入向量映射到二维平面。对故障数据的试验分析表明,该方法能提供更加清晰的可视化表示。     

Model-Based Clustering by Probabilistic Self-Organizing Maps

In this paper, we consider the learning process of a probabilistic self-organizing map (PbSOM) as a model-based data clustering procedure that preserves the topological relationships between data clusters in a neural network. Based on this concept, we develop a coupling-likelihood mixture model for the PbSOM that extends the reference vectors in Kohonen's self-organizing map (SOM) to multivariate Gaussian distributions. We also derive three expectation-maximization (EM)-type algorithms, called the SOCEM, SOEM, and SODAEM algorithms, for learning the model (PbSOM) based on the maximum-likelihood criterion. SOCEM is derived by using the classification EM (CEM) algorithm to maximize the classification likelihood; SOEM is derived by using the EM algorithm to maximize the mixture likelihood; and SODAEM is a deterministic annealing (DA) variant of SOCEM and SOEM. Moreover, by shrinking the neighborhood size, SOCEM and SOEM can be interpreted, respectively, as DA variants of the CEM and EM algorithms for Gaussian model-based clustering. The experimental results show that the proposed PbSOM learning algorithms achieve comparable data clustering performance to that of the deterministic annealing EM (DAEM) approach, while maintaining the topology-preserving property.     

Self-Organising Maps as a Relevance Feedback Technique in Content-Based Image Retrieval

Self-Organising Maps (SOMs) can be used in implementing a powerful relevance feedback mechanism for Content-Based Image Retrieval (CBIR). This paper introduces the PicSOM CBIR system, and describes the use of SOMs as a relevance feedback technique in it. The technique is based on the SOM’s inherent property of topology-preserving mapping from a high-dimensional feature space to a two-dimensional grid of artificial neurons. On this grid similar images are mapped in nearby locations. As image similarity must, in unannotated databases, be based on low-level visual features, the similarity of images is dependent on the feature extraction scheme used. Therefore, in PicSOM there exists a separate tree-structured SOM for each different feature type. The incorporation of the relevance feedback and the combination of the outputs from the SOMs are performed as two successive processing steps. The proposed relevance feedback technique is described, analysed qualitatively, and visualised in the paper. Also, its performance is compared with a reference method.     

Efficient schema-based XML-to-Relational data mapping

Storing and querying XML documents using a RDBMS is a challenging problem since one needs to resolve the conflict between the hierarchical, ordered nature of the XML data model and the flat, unordered nature of the relational data model. This conflict can be resolved by the following XML-to-Relational mappings: schema mapping, data mapping and query mapping. In this paper, we propose: (i) a lossless schema mapping algorithm to generate a database schema from a DTD, which makes several improvements over existing algorithms, (ii) two linear data mapping algorithms based on DOM and SAX, respectively, to map ordered XML data to relational data. To our best knowledge, there is no published linear schema-based data mapping algorithm for mapping ordered XML data to relational data. Experimental results are presented to show that our algorithms are efficient and scalable.     

一种自动抽取图像中可判别区域的新方法

图像分割是图像处理中的一个难题，为了自动抽取图像中的可差别区域，提出了一种基于自组织图归约算法的区域抽取新方法，首先，利用包括颜色、纹理以及位置在内的多模特征抽算法，原始图像被转换成特征，接着，通过自组织映射学习算法，特征图映射成自组织图，然后，对自组织图实施归纳算法得到一族约简的自组织图谱系；最后，利用一个 综合的聚类有效性分析指标从约简的自组织图谱系中得到一个最优约简的自组织图，以此实现图像区域的分割，新方法的有效性通过两个评价实验得到了验证。     

ViSOM - a novel method for multivariate data projection andstructure visualization

When used for visualization of high-dimensional data, the self-organizing map (SOM) requires a coloring scheme, such as the U-matrix, to mark the distances between neurons. Even so, the structures of the data clusters may not be apparent and their shapes are often distorted. In this paper, a visualization-induced SOM (ViSOM) is proposed to overcome these shortcomings. The algorithm constrains and regularizes the inter-neuron distance with a parameter that controls the resolution of the map. The mapping preserves the inter-point distances of the input data on the map as well as the topology. It produces a graded mesh in the data space such that the distances between mapped data points on the map resemble those in the original space, like in the Sammon mapping. However, unlike the Sammon mapping, the ViSOM can accommodate both training data and new arrivals and is much simpler in computational complexity. Several experimental results and comparisons with other methods are presented.     

A SOM prototype-based cluster analysis methodology

Data clustering is aimed at finding groups of data that share common hidden properties. These kinds of techniques are especially critical at early stages of data analysis where no information about the dataset is available. One of the mayor shortcomings of the clustering algorithms is the difficulty for non-experts users to configure them and, in some cases, interpret the results. In this work a computational approach with a two-layer structure based on Self-Organizing Map (SOM) is presented for cluster analysis. In the first level, a quantization of the data samples using topology-preserving metrics to automatically determine the number of units in the SOM is proposed. In the second level the obtained SOM prototypes are clustered by means of a connectivity analysis to explore the quality of the partitioning with different number of clusters. The most important benefit of this two-layer procedure is that computational load decreases considerably in comparison with data based clustering methods, making it possible to cluster large data sets and to consider several different clustering alternatives in a limited time. This methodology produces a two-dimensional map representation of the, usually, high dimensional input space, along with quantitative information on viable clustering alternatives, which facilitates the exploration of the possible partitions in a dataset. The efficiency and interpretation of the methodology is illustrated by its application to artificial, benchmark and real complex biological datasets. The experimental results demonstrate the ability of the method to identify possible segmentations in a dataset, compared to algorithms that only yield a single clustering solution. The proposed algorithm tackles the intrinsic limitations of SOM and the parameter settings associated with the clustering methodology, without requiring the number of clusters or the SOM architecture as a prerequisite, among others. This way, it makes possible its application even by researchers with a limited expertise in machine learning.     

算法到脉动阵列处理器的映射

文中讨论了将含有循环的算法映射到脉动阵列的一般方法。这一映射方法是建立在下标集和数据相关向量的数学变换基础上，并给出了带有常数据相关的算法中存在有效变换的充要条件。最后给出了许所有点对之间最短路径问题的映射过程。     

A combined measure for quantifying and qualifying the topology preservation of growing self-organizing maps

The Self-Organizing Map (SOM) is a neural network model that performs an ordered projection of a high dimensional input space in a low-dimensional topological structure. The process in which such mapping is formed is defined by the SOM algorithm, which is a competitive, unsupervised and nonparametric method, since it does not make any assumption about the input data distribution. The feature maps provided by this algorithm have been successfully applied for vector quantization, clustering and high dimensional data visualization processes. However, the initialization of the network topology and the selection of the SOM training parameters are two difficult tasks caused by the unknown distribution of the input signals. A misconfiguration of these parameters can generate a feature map of low-quality, so it is necessary to have some measure of the degree of adaptation of the SOM network to the input data model. The topology preservation is the most common concept used to implement this measure. Several qualitative and quantitative methods have been proposed for measuring the degree of SOM topology preservation, particularly using Kohonen's model. In this work, two methods for measuring the topology preservation of the Growing Cell Structures (GCSs) model are proposed: the topographic function and the topology preserving map.     

Application of self-organising maps for data mining with incomplete data sets

Self-organising maps (SOM) have become a commonly-used cluster analysis technique in data mining. However, SOM are not able to process incomplete data. To build more capability of data mining for SOM, this study proposes an SOM-based fuzzy map model for data mining with incomplete data sets. Using this model, incomplete data are translated into fuzzy data, and are used to generate fuzzy observations. These fuzzy observations, along with observations without missing values, are then used to train the SOM to generate fuzzy maps. Compared with the standard SOM approach, fuzzy maps generated by the proposed method can provide more information for knowledge discovery.     

A non-interactive method for the automatic generation of finite element meshes using the schwarz-christoffel transformation

This paper describes a particular conformal mapping, the Schwarz-Christoffel transformation. A practical method for evaluating the parameters defining this transformation is described and two such transformations are used to construct a mapping between any two polygons. The desirable properties of a finite element mesh are stated and a method is described which attempts to generate such a mesh in any simply-connected region, using conformal mappings. This computer method is non-interactive and attempts to produce a good mesh with the minimum of input data. Some examples are included.     

一种新的基于SOM的数据可视化算法

SOM（self—organizing map）所具有的拓扑保持特性使之可用来对高维数据进行低维展现,但由于数据间的距离信息在映射到低维空间中固定有序的神经元上时被丢掉了,因此数据的结构通常是被扭曲了的．为了更自然地展现数据的结构,提出了一种新的基于SOM的数据可视化算法——DPSOM（distance-preserving SOM）,它能够按照相应的距离信息对神经元的位置进行自适应调节,从而实现了对数据间距离信息的直观展现,特别地,该算法还能自动避免神经元的过度收缩问题,从而极大地提高了算法的可控性和数据可视化的质量．     

Edge detection in multispectral images using the self-organizing map

In this paper, two new methods for edge detection in multispectral images are presented. They are based on the use of the self-organizing map (SOM) and a grayscale edge detector. With the 2-dimensional SOM the ordering of pixel vectors is obtained by applying the Peano scan, whereas this can be omitted using the 1-dimensional SOM. It is shown that using the R-ordering based methods some parts of the edges may be missed. However, they can be found using the proposed methods. Using them it is also possible to find edges in images which consist of metameric colors. Finally, it is shown that the proposed methods find the edges properly from real multispectral airplane images. The size of the SOM determines the amount of found edges. If the SOM is taught using a large color vector database, the same SOM can be utilized for numerous images.     

A Non-local Topology-Preserving Segmentation-Guided Registration Model

In this paper, we address the issue of designing a theoretically well-motivated segmentation-guided registration method capable of handling large and smooth deformations. The shapes to be matched are viewed as hyperelastic materials and more precisely as Saint Venant–Kirchhoff ones and are implicitly modeled by level set functions. These are driven in order to minimize a functional containing both a nonlinear-elasticity-based regularizer prescribing the nature of the deformation, and a criterion that forces the evolving shape to match intermediate topology-preserving segmentation results. Theoretical results encompassing existence of minimizers, existence of a weak viscosity solution of the related evolution problem and asymptotic results are given. The study is then complemented by the derivation of the discrete counterparts of the asymptotic results provided in the continuous domain. Both a pure quadratic penalization method and an augmented Lagrangian technique (involving a related dual problem) are investigated with convergence results.