Compiling conceptual graphs

The paper addresses problems in conceptual graph implementation: subsumption and classification in a taxonomy. Conceptual graphs are typically stored using a directed acyclic graph data structure based on the partial order over conceptual graphs. We give an improved algorithm for classifying conceptual graphs into this hierarchy. It prunes the search space in the database using the information gathered while searching. We show how conceptual graphs in this hierarchy can be compiled into instructions which represent specialized cases of the canonical formation rules. This compiles subsumption of conceptual graphs and compresses knowledge in a knowledge base. Conceptual graphs are compiled as differences between adjacent graphs in the hierarchy. The differences represent the rules used in deriving the graph from the adjacent graphs. We illustrate how the method compresses knowledge bases in some experiments. Compilation is effected in three ways: removal of redundant data, use of simple instructions which ignore redundant checks when performing matching, and by sharing common processing between graphs     

Social Network Clustering and Visualization using Hierarchical Edge Bundles

The hierarchical edge bundle (HEB) method generates useful visualizations of dense graphs, such as social networks, but requires a predefined clustering hierarchy, and does not easily benefit from existing straight‐line visualization improvements. This paper proposes a new clustering approach that extracts the community structure of a network and organizes it into a hierarchy that is flatter than existing community‐based clustering approaches and maps better to HEB visualization. Our method not only discovers communities and generates clusters with better modularization qualities, but also creates a balanced hierarchy that allows HEB visualization of unstructured social networks without predefined hierarchies. Results on several data sets demonstrate that this approach clarifies real‐world communication, collaboration and competition network structure and reveals information missed in previous visualizations. We further implemented our techniques into a social network visualization application on facebook.com and let users explore the visualization and community clustering of their own social networks.     

LEGClust—A Clustering Algorithm Based on Layered Entropic Subgraphs

Hierarchical clustering is a stepwise clustering method usually based on proximity measures between objects or sets of objects from a given data set. The most common proximity measures are distance measures. The derived proximity matrices can be used to build graphs, which provide the basic structure for some clustering methods. We present here a new proximity matrix based on an entropic measure and also a clustering algorithm (LEGCIust) that builds layers of subgraphs based on this matrix and uses them and a hierarchical agglomerative clustering technique to form the clusters. Our approach capitalizes on both a graph structure and a hierarchical construction. Moreover, by using entropy as a proximity measure, we are able, with no assumption about the cluster shapes, to capture the local structure of the data, forcing the clustering method to reflect this structure. We present several experiments on artificial and real data sets that provide evidence on the superior performance of this new algorithm when compared with competing ones.     

LEGClust- a clustering algorithm based on layered entropic subgraphs.

Hierarchical clustering is a stepwise clustering method usually based on proximity measures between objects or sets of objects from a given data set. The most common proximity measures are distance measures. The derived proximity matrices can be used to build graphs, which provide the basic structure for some clustering methods. We present here a new proximity matrix based on an entropic measure and also a clustering algorithm (LEGClust) that builds layers of subgraphs based on this matrix, and uses them and a hierarchical agglomerative clustering technique to form the clusters. Our approach capitalizes on both a graph structure and a hierarchical construction. Moreover, by using entropy as a proximity measure we are able, with no assumption about the cluster shapes, to capture the local structure of the data, forcing the clustering method to reflect this structure. We present several experiments on artificial and real data sets that provide evidence on the superior performance of this new algorithm when compared with competing ones.     

Hierarchical edge bundles: visualization of adjacency relations in hierarchical data

A compound graph is a frequently encountered type of data set. Relations are given between items, and a hierarchy is defined on the items as well. We present a new method for visualizing such compound graphs. Our approach is based on visually bundling the adjacency edges, i.e., non-hierarchical edges, together. We realize this as follows. We assume that the hierarchy is shown via a standard tree visualization method. Next, we bend each adjacency edge, modeled as a B-spline curve, toward the polyline defined by the path via the inclusion edges from one node to another. This hierarchical bundling reduces visual clutter and also visualizes implicit adjacency edges between parent nodes that are the result of explicit adjacency edges between their respective child nodes. Furthermore, hierarchical edge bundling is a generic method which can be used in conjunction with existing tree visualization techniques. We illustrate our technique by providing example visualizations and discuss the results based on an informal evaluation provided by potential users of such visualizations     

注意力流网络中节点影响力的层级性研究

复杂网络中节点影响力的层级性在网络结构与控制研究中至关重要。针对有向加权网络中节点影响力的层级性问题,基于海量在线用户行为数据,构建有向加权集体注意力流网络。通过定义节点的层级位置时间和位置约束指标,并结合节点的拓扑位置和时间序列,提出一种用于有向加权网络的节点影响力度量及排序算法。实验结果表明,该算法能有效区分网络层级结构,准确识别出最具影响力的节点,对于节点影响力评估与复杂网络可控性研究具有一定的借鉴意义和参考价值。     

Visualization of graph products

Graphs are a versatile structure and abstraction for binary relationships between objects. To gain insight into such relationships, their corresponding graph can be visualized. In the past, many classes of graphs have been defined, e.g. trees, planar graphs, directed acyclic graphs, and visualization algorithms were proposed for these classes. Although many graphs may only be classified as "general" graphs, they can contain substructures that belong to a certain class. Archambault proposed the TopoLayout framework: rather than draw any arbitrary graph using one method, split the graph into components that are homogeneous with respect to one graph class and then draw each component with an algorithm best suited for this class. Graph products constitute a class that arises frequently in graph theory, but for which no visualization algorithm has been proposed until now. In this paper, we present an algorithm for drawing graph products and the aesthetic criterion graph product's drawings are subject to. We show that the popular High-Dimensional Embedder approach applied to cartesian products already respects this aestetic criterion, but has disadvantages. We also present how our method is integrated as a new component into the TopoLayout framework. Our implementation is used for further research of graph products in a biological context.     

A browser for directed graphs

A general-purpose browser for directed graphs is described. The browser provides operations to examine and edit graphs and to generate a layout for a graph automatically that minimizes edge crossings. Two layout algorithms were implemented. A hierarchical graph layout algorithm was found to be best for directed graphs. The graph browser also has facilities that allow it to be integrated with other applications (e.g. a program browser). These facilities and our experiences building a program call-graph browser are described.     

Hierarchical growing cell structures: TreeGCS

We propose a hierarchical clustering algorithm (TreeGCS) based upon the Growing Cell Structure (GCS) neural network of B. Fritzke (1993). Our algorithm refines and builds upon the GCS base, overcoming an inconsistency in the original GCS algorithm, where the network topology is susceptible to the ordering of the input vectors. Our algorithm is unsupervised, flexible, and dynamic and we have imposed no additional parameters on the underlying GCS algorithm. Our ultimate aim is a hierarchical clustering neural network that is both consistent and stable and identifies the innate hierarchical structure present in vector-based data. We demonstrate improved stability of the GCS foundation and evaluate our algorithm against the hierarchy generated by an ascendant hierarchical clustering dendogram. Our approach emulates the hierarchical clustering of the dendogram. It demonstrates the importance of the parameter settings for GCS and how they affect the stability of the clustering     

Multi-level association rules and directed graphs for spatial data analysis

We propose a methodology that upgrades the methods of the Lagrangian analysis of surface sea-water parcels. This methodology includes data mining with efficient visualization techniques, namely, spatial–temporal association rules and multi-level directed graphs with different levels of space and time granularity. In the resulting multi-level directed graphs we can intertwine knowledge from various disciplines related to oceanography (in our application) and perform the mining of such graphs. We evaluate the proposed methodology on Lagrangian tracking of virtual particles in the velocity field of the numerical model called the Mediterranean Ocean Forecasting Model (MFS). We describe an efficient algorithm based on label propagation clustering, which finds cycles and paths in multi-level directed graphs and reveals how the number and size of the cycles depend on the seasons. In addition, we offer three interesting results of the visualization and mining of such graphs, that is, the 12 months periodicity of the exchange of water masses among sea areas, the separation of Mediterranean Sea circulation in summer and winter situations, obtained with the hierarchical clustering of multi-level directed graphs, and finally, with visualization with multi-level directed graphs we confirm the reversal of sea circulation in the Ionian Sea over the last decades. The aforementioned results received a very favorable evaluation from oceanographic experts.     

3D scattered data interpolation and approximation with multilevel compactly supported RBFs

In this paper, we propose a hierarchical approach to 3D scattered data interpolation and approximation with compactly supported radial basis functions. Our numerical experiments suggest that the approach integrates the best aspects of scattered data fitting with locally and globally supported basis functions. Employing locally supported functions leads to an efficient computational procedure, while a coarse-to-fine hierarchy makes our method insensitive to the density of scattered data and allows us to restore large parts of missed data. Given a point cloud distributed over a surface, we first use spatial down sampling to construct a coarse-to-fine hierarchy of point sets. Then we interpolate (approximate) the sets starting from the coarsest level. We interpolate (approximate) a point set of the hierarchy, as an offsetting of the interpolating function computed at the previous level. The resulting fitting procedure is fast, memory efficient, and easy to implement.     

基于图匹配的分层布局算法

针对节点数目较大并且度数比较平均的无向图,根据分层扩展的思想,提出一种基于图匹配的分层布局算法（Graph Matching Hierarchy,GMH）。基于图匹配思想对大图进行递归化简,然后应用FR算法对最粗化图进行布局,最后利用质心布局算法对图进行扩展。实验结果表明,GMH算法能够提高可视化效率,改善布局效果,且分层布局的结果更易于理解。      

A novel ant colony optimization based single path hierarchical classification algorithm for predicting gene ontology

There exist numerous state of the art classification algorithms that are designed to handle the data with nominal or binary class labels. Unfortunately, less attention is given to the genre of classification problems where the classes are organized as a structured hierarchy; such as protein function prediction (target area in this work), test scores, gene ontology, web page categorization, text categorization etc. The structured hierarchy is usually represented as a tree or a directed acyclic graph (DAG) where there exist IS-A relationship among the class labels. Class labels at upper level of the hierarchy are more abstract and easy to predict whereas class labels at deeper level are most specific and challenging for correct prediction. It is helpful to consider this class hierarchy for designing a hypothesis that can handle the tradeoff between prediction accuracy and prediction specificity. In this paper, a novel ant colony optimization (ACO) based single path hierarchical classification algorithm is proposed that incorporates the given class hierarchy during its learning phase. The algorithm produces IF–THEN ordered rule list and thus offer comprehensible classification model. Detailed discussion on the architecture and design of the proposed technique is provided which is followed by the empirical evaluation on six ion-channels data sets (related to protein function prediction) and two publicly available data sets. The performance of the algorithm is encouraging as compared to the existing methods based on the statistically significant Student's t-test (keeping in view, prediction accuracy and specificity) and thus confirm the promising ability of the proposed technique for hierarchical classification task.     

基于动作空间划分的MAXQ自动分层方法

针对分层强化学习需要人工给出层次结构这一问题,同时考虑到基于状态空间的自动分层方法在环境状态中没有明显子目标时分层效果并不理想的情况,提出一种基于动作空间的自动构造层次结构方法。首先,根据动作影响的状态分量将动作集合划分为多个不相交的子集;然后,分析Agent在不同状态下的可用动作,并识别瓶颈动作;最后,由瓶颈动作与执行次序确定动作子集之间的上下层关系,并构造层次结构。此外,对MAXQ方法中子任务的终止条件进行修改,使所提算法构造的层次结构可以通过MAXQ方法找到最优策略。实验结果表明,所提算法可以自动构造层次结构,而不会受环境变化的干扰。与Q学习、Sarsa算法相比,MAXQ方法根据该结构得到最优策略的时间更短,获得回报更高。验证了所提算法能够有效地自动构造MAXQ层次结构,并使寻找最优策略更加高效。     

On the Equivalence Between Hierarchical Segmentations and Ultrametric Watersheds

We study hierarchical segmentation in the framework of edge-weighted graphs. We define ultrametric watersheds as topological watersheds null on the minima. We prove that there exists a bijection between the set of ultrametric watersheds and the set of hierarchical segmentations. We end this paper by showing how to use the proposed framework in practice on the example of constrained connectivity; in particular it allows to compute such a hierarchy following a classical watershed-based morphological scheme, which provides an efficient algorithm to compute the whole hierarchy.     

基于遗传算法的有向无环图画图算法

在研究了现有画有向无环图的主要方法的基础上提出一种基于遗传算法的有向无环图画图算法,将一般有向无环图的画图问题转换为函数优化问题,用遗传算法求目标函数最优解的近似值。实验表明此算法具有算法统一、方法简单、容易实现、易于修改,并且具有自适应、自学习和易于并行化的特点。     

Financial distress prediction using support vector machines: Ensemble vs. individual

Financial distress prediction (FDP) is of great importance to both inner and outside parts of companies. Though lots of literatures have given comprehensive analysis on single classifier FDP method, ensemble method for FDP just emerged in recent years and needs to be further studied. Support vector machine (SVM) shows promising performance in FDP when compared with other single classifier methods. The contribution of this paper is to propose a new FDP method based on SVM ensemble, whose candidate single classifiers are trained by SVM algorithms with different kernel functions on different feature subsets of one initial dataset. SVM kernels such as linear, polynomial, RBF and sigmoid, and the filter feature selection/extraction methods of stepwise multi discriminant analysis (MDA), stepwise logistic regression (logit), and principal component analysis (PCA) are applied. The algorithm for selecting SVM ensemble's base classifiers from candidate ones is designed by considering both individual performance and diversity analysis. Weighted majority voting based on base classifiers’ cross validation accuracy on training dataset is used as the combination mechanism. Experimental results indicate that SVM ensemble is significantly superior to individual SVM classifier when the number of base classifiers in SVM ensemble is properly set. Besides, it also shows that RBF SVM based on features selected by stepwise MDA is a good choice for FDP when individual SVM classifier is applied.     

Interactive volume rendering of large sparse data sets using adaptive mesh refinement hierarchies

In this paper, we present an algorithm that accelerates 3D texture-based volume rendering of large, sparse data sets, i.e., data sets where only a traction of the voxels contain relevant information. In texture-based approaches, the rendering performance is affected by the fill-rate, the size of texture memory, and the texture I/O bandwidth. For sparse data, these limitations can be circumvented by restricting most of the rendering work to the relevant parts of the volume. In order to efficiently enclose the corresponding regions with axis-aligned boxes, we employ a hierarchical data structure, known as an AMR (adaptive mesh refinement) tree. The hierarchy is generated utilizing a clustering algorithm. A good balance is thereby achieved between the size of the enclosed volume, i.e., the amount to render in graphics hardware and the number of axis-aligned regions, i.e., the number of texture coordinates to compute in software. The waste of texture memory by the power-of-two restriction is minimized by a 3D packing algorithm which arranges texture bricks economically in memory. Compared to an octree approach, the rendering performance is significantly increased and less parameter tuning is necessary.     

Multiclass classifier based on boundary complexity

This paper presents several criteria for partition of classes for the support vector machine based hierarchical classification. Our clustering algorithm combines support vector machine and binary tree, it is a divisive (top-down) approach in which a set of classes is automatically separated into two smaller groups at each node of the hierarchy, it splits the classes based on the normalized cuts clustering algorithm. Our clustering algorithm considers the involved classes rather than the individual data samples. In the new proposed measures, similarity between classes is determined based on boundary complexity. In these measures, concepts such as the upper bound of error and Kolmogorov complexity are used. We reported results on several data sets and five distance/similarity measures. Experimental results demonstrate the superiority of the proposed measures compared to other measures; even when applied to nonlinearly separable data, the new criteria perform well.