教育测评知识图谱的构建及其表示学习

知识图谱旨在描述现实世界中存在的实体以及实体之间的关系.自2012年谷歌提出“Google Knowledge Graph”以来，知识图谱在学术界和工业界受到广泛关注.针对教育领域中信息缺乏系统性组织的不足，本文构建了面向高中的教育测评知识图谱（Educational Assessment Knowledge Graph，EAKG），其中EAKG的构建包括基于本体技术的知识图谱模式层构建和依托于模式层结构的知识图谱数据层构建.与传统通过网页爬虫等技术手段构建的知识图谱相比，本文构建的知识图谱优点在于逻辑结构清晰，实体间关系的刻画遵循知识图谱模式层的定义.EAKG为领域内知识共享，知识推理，知识表示学习等任务提供了良好的支撑.在真实模考数据上的实验结果表明：在试卷得分预测，知识点得分预测的实体链接预测和三元组分类嵌入式表示学习任务上，引入领域本体作为模式层构建的EAKG的性能优于没有领域本体模式层单纯由数据事实构成的EAKG，实验表明，领域本体的引入对知识图谱的表示学习具有一定的指导意义.     

The Forgiving Graph: a distributed data structure for low stretch under adversarial attack

We consider the problem of self-healing in peer-to-peer networks that are under repeated attack by an omniscient adversary. We assume that, over a sequence of rounds, an adversary either inserts a node with arbitrary connections or deletes an arbitrary node from the network. The network responds to each such change by quick “repairs,” which consist of adding or deleting a small number of edges. These repairs essentially preserve closeness of nodes after adversarial deletions, without increasing node degrees by too much, in the following sense. At any point in the algorithm, nodes v and w whose distance would have been ? in the graph formed by considering only the adversarial insertions (not the adversarial deletions), will be at distance at most ? log n in the actual graph, where n is the total number of vertices seen so far. Similarly, at any point, a node v whose degree would have been d in the graph with adversarial insertions only, will have degree at most 3d in the actual graph. Our distributed data structure, which we call the Forgiving Graph, has low latency and bandwidth requirements. The Forgiving Graph improves on the Forgiving Tree distributed data structure from Hayes et?al. (2008) in the following ways: 1) it ensures low stretch over all pairs of nodes, while the Forgiving Tree only ensures low diameter increase; 2) it handles both node insertions and deletions, while the Forgiving Tree only handles deletions; 3) it requires only a very simple and minimal initialization phase, while the Forgiving Tree initially requires construction of a spanning tree of the network.     

A nonparametric classification method based on K-associated graphs

Graph is a powerful representation formalism that has been widely employed in machine learning and data mining. In this paper, we present a graph-based classification method, consisting of the construction of a special graph referred to as K-associated graph, which is capable of representing similarity relationships among data cases and proportion of classes overlapping. The main properties of the K-associated graphs as well as the classification algorithm are described. Experimental evaluation indicates that the proposed technique captures topological structure of the training data and leads to good results on classification task particularly for noisy data. In comparison to other well-known classification techniques, the proposed approach shows the following interesting features: (1) A new measure, called purity, is introduced not only to characterize the degree of overlap among classes in the input data set, but also to construct the K-associated optimal graph for classification; (2) nonlinear classification with automatic local adaptation according to the input data. Contrasting to K-nearest neighbor classifier, which uses a fixed K, the proposed algorithm is able to automatically consider different values of K, in order to best fit the corresponding overlap of classes in different data subspaces, revealing both the local and global structure of input data. (3) The proposed classification algorithm is nonparametric, implicating high efficiency and no need for model selection in practical applications.     

Improving vector space embedding of graphs through feature selection algorithms

Graph based pattern representation offers a versatile alternative to vectorial data structures. Therefore, a growing interest in graphs can be observed in various fields. However, a serious limitation in the use of graphs is the lack of elementary mathematical operations in the graph domain, actually required in many pattern recognition algorithms. In order to overcome this limitation, the present paper proposes an embedding of a given graph population in a vector space Rⁿ. The key idea of this embedding approach is to interpret the distances of a graph g to a number of prototype graphs as numerical features of g. In previous works, the prototypes were selected beforehand with heuristic selection algorithms. In the present paper we take a more fundamental approach and regard the problem of prototype selection as a feature selection or dimensionality reduction problem, for which many methods are available. With several experiments we show the feasibility of graph embedding based on prototypes obtained from such feature selection algorithms and demonstrate their potential to outperform previous approaches.     

Graph OLAP: a multi-dimensional framework for graph data analysis

Databases and data warehouse systems have been evolving from handling normalized spreadsheets stored in relational databases, to managing and analyzing diverse application-oriented data with complex interconnecting structures. Responding to this emerging trend, graphs have been growing rapidly and showing their critical importance in many applications, such as the analysis of XML, social networks, Web, biological data, multimedia data and spatiotemporal data. Can we extend useful functions of databases and data warehouse systems to handle graph structured data? In particular, OLAP (On-Line Analytical Processing) has been a popular tool for fast and user-friendly multi-dimensional analysis of data warehouses. Can we OLAP graphs? Unfortunately, to our best knowledge, there are no OLAP tools available that can interactively view and analyze graph data from different perspectives and with multiple granularities. In this paper, we argue that it is critically important to OLAP graph structured data and propose a novel Graph OLAP framework. According to this framework, given a graph dataset with its nodes and edges associated with respective attributes, a multi-dimensional model can be built to enable efficient on-line analytical processing so that any portions of the graphs can be generalized/specialized dynamically, offering multiple, versatile views of the data. The contributions of this work are three-fold. First, starting from basic definitions, i.e., what are dimensions and measures in the Graph OLAP scenario, we develop a conceptual framework for data cubes on graphs. We also look into different semantics of OLAP operations, and classify the framework into two major subcases: informational OLAP and topological OLAP. Second, we show how a graph cube can be materialized by calculating a special kind of measure called aggregated graph and how to implement it efficiently. This includes both full materialization and partial materialization where constraints are enforced to obtain an iceberg cube. As we can see, due to the increased structural complexity of data, aggregated graphs that depend on the underlying “network” properties of the graph dataset are much harder to compute than their traditional OLAP counterparts. Third, to provide more flexible, interesting and informative OLAP of graphs, we further propose a discovery-driven multi-dimensional analysis model to ensure that OLAP is performed in an intelligent manner, guided by expert rules and knowledge discovery processes. We outline such a framework and discuss some challenging research issues for discovery-driven Graph OLAP.     

A hierarchical structure for surface approximation

Hierarchical triangulation is a method for point selection and surface representation where the surface is approximated at successively finer levels of detail by triangular patches whose projections in the horizontal plane are nested. A tree data structure for this representation can be constructed in O(n²) worst case and O(n log n) average case time, where n is the number of data points considered. Efficient algorithms for approximation of the elevation of an arbitrary point, contour extraction, and conversion of the hierarchical structure into an ordinary triangulated irregular network, are demonstrated. The convergence and the optimality of the approximation and the relationship of the hierarchical triangulation to a structured graph representation are examined.     

Computing the relative neighborhood graph in the L1 and L∞ metrics

The Relative Neighborhood Graph (RNG) of a set of nk-dimensional points connects “relatively close” neighbors: two points are connected by an edge if they are at least as close to each other as to any other point. Toussaint recently investigated the properties of the RNG in the Euclidean metric and proposed algorithms for its computation. This note examines one of the open problems listed by Toussaint: the extension of the analysis to non-Euclidean metrics. It is shown that Bentley's range query data structures may be used to improve the speed of the best known RNG algorithm in the L_∞ (for k ? 2) and L₁ (for k = 2) metrics.     

Embedding Meshes on the Star Graph

We develop algorithms for mapping n-dimensional meshes on a star graph of degree n with expansion 1 and dilation 3. We show that an n-degree star graph can efficiently simulate an n-dimensional mesh.     

Curve skeleton extraction by coupled graph contraction and surface clustering

In this paper, we present a practical algorithm to extract a curve skeleton of a 3D shape. The core of our algorithm comprises coupled processes of graph contraction and surface clustering. Given a 3D shape represented by a triangular mesh, we first construct an initial skeleton graph by directly copying the connectivity and geometry information from the input mesh. Graph contraction and surface clustering are then performed iteratively. The former merges certain graph nodes based on computation of an approximate centroidal Voronoi diagram, seeded by subsampling the graph nodes from the previous iteration. Meanwhile, a coupled surface clustering process serves to regularize the graph contraction. Constraints are used to ensure that extremities of the graph are not shortened undesirably, to ensure that skeleton has the correct topological structure, and that surface clustering leads to an approximately-centered skeleton of the input shape. These properties lead to a stable and reliable skeleton graph construction algorithm.Experiments demonstrate that our skeleton extraction algorithm satisfies various desirable criteria. Firstly, it produces a skeleton homotopic with the input (the genus of both shapes agree) which is both robust (results are stable with respect to noise and remeshing of the input shape) and reliable (every boundary point is visible from at least one curve-skeleton location). It can also handle point cloud data if we first build an initial skeleton graph based on k-nearest neighbors. In addition, a secondary output of our algorithm is a skeleton-to-surface mapping, which can e.g. be used directly for skinning animation.Highlights(1) An algorithm for curve skeleton extraction from 3D shapes based on coupled graph contraction and surface clustering. (2) The algorithm meets various desirable criteria and can be extended to work for incomplete point clouds.     

On the equivalence and range of applicability of graph-based representations of logic programs

Logic programs under Answer Sets semantics can be studied, and actual computation can be carried out, by means of representing them by directed graphs. Several reductions of logic programs to directed graphs are now available. We compare our proposed representation, called Extended Dependency Graph, to the Block Graph representation recently defined by Linke [Proc. IJCAI-2001, 2001, pp. 641-648]. On the relevant fragment of well-founded irreducible programs, extended dependency and block graph turns out to be isomorphic. So, we argue that graph representation of general logic programs should be abandoned in favor of graph representation of well-founded irreducible programs, which are more concise, more uniform in structure while being equally expressive.     

Constrained multilinear detection for faster functional motif discovery

The Graph Motif problem asks whether a given multiset of colors appears on a connected subgraph of a vertex-colored graph. The fastest known parameterized algorithm for this problem is based on a reduction to the k-Multilinear Detection (k-MlD) problem: the detection of multilinear terms of total degree k in polynomials presented as circuits. We revisit k-MlD and define k-CMlD, a constrained version of it which reflects Graph Motif more faithfully. We then give a fast algorithm for k-CMlD. As a result we obtain faster parameterized algorithms for Graph Motif and variants of it.     

海德堡视网膜断层扫描仪的三维点云去噪方法研究

双边滤波法可以对海德堡视网膜断层扫描仪(HRT)扫描获得的三维点云数据进行有效的去噪处理。该算法在去噪的同时保留了图形的特征信息,缺点是多次迭代计算耗费了大量时间,所以该算法无法直接运用到实际的诊断中。邻域均值算法对位于某点一定邻域内所有点的Z坐标做均值处理,且根据距离中心点的远近取不同的权值,也能对图形进行去噪处理,只是单独使用虽耗费时间较少但效果远不及双边滤波算法。因此,本文提出采用邻域均值法作为双边滤波算法去噪的预处理。研究发现,该方法在保留图形特征的同时,并且在相同去噪效果的前提下可以显著减少计算时间,提高运行效率。     

Ribbons

Point clouds are usually represented either globally, as surfaces, or locally, as sets of points with small neighbourhoods. We propose an intermediate representation, called ribbons, which is obtained by partitioning a point cloud into one-dimensional strips. This representation is well suited to the placement of strokes in non-photorealistic rendering, and can be visualized efficiently using quad strips. Methods for performing hatching, cross-hatching, and silhouette renderings are presented. Ribbons also allow for the application of curve-based operations to the point cloud.     

Geometric Representation of Graphs in Low Dimension Using Axis Parallel Boxes

An axis-parallel k-dimensional box is a Cartesian product R ₁×R ₂×???×R _k where R _i (for 1≤i≤k) is a closed interval of the form [a _i ,b _i ] on the real line. For a graph G, its boxicity box?(G) is the minimum dimension k, such that G is representable as the intersection graph of (axis-parallel) boxes in k-dimensional space. The concept of boxicity finds applications in various areas such as ecology, operations research etc. A number of NP-hard problems are either polynomial time solvable or have much better approximation ratio on low boxicity graphs. For example, the max-clique problem is polynomial time solvable on bounded boxicity graphs and the maximum independent set problem for boxicity d graphs, given a box representation, has a $\lfloor 1+\frac{1}{c}\log n\rfloor^{d-1}An axis-parallel k-dimensional box is a Cartesian product R ₁×R ₂×⋅⋅⋅×R _k where R _i (for 1≤i≤k) is a closed interval of the form [a _i ,b _i ] on the real line. For a graph G, its boxicity box (G) is the minimum dimension k, such that G is representable as the intersection graph of (axis-parallel) boxes in k-dimensional space. The concept of boxicity finds applications in various areas such as ecology, operations research etc. A number of NP-hard problems are either polynomial time solvable or have much better approximation ratio on low boxicity graphs. For example, the max-clique problem is polynomial time solvable on bounded boxicity graphs and the maximum independent set problem for boxicity d graphs, given a box representation, has a ?1+\frac1clogn?^d-1\lfloor 1+\frac{1}{c}\log n\rfloor^{d-1} approximation ratio for any constant c≥1 when d≥2. In most cases, the first step usually is computing a low dimensional box representation of the given graph. Deciding whether the boxicity of a graph is at most 2 itself is NP-hard.     

Intelligent fault diagnosis for rolling bearings based on graph shift regularization with directed graphs

Graph shift regularization is a new and effective graph-based semi-supervised classification method, but its performance is closely related to the representation graphs. Since directed graphs can convey more information about the relationship between vertices than undirected graphs, an intelligent method called graph shift regularization with directed graphs (GSR-D) is presented for fault diagnosis of rolling bearings. For greatly improving the diagnosis performance of GSR-D, a directed and weighted k-nearest neighbor graph is first constructed by treating each sample (i.e., each vibration signal segment) as a vertex, in which the similarity between samples is measured by cosine distance instead of the commonly used Euclidean distance, and the edge weights are also defined by cosine distance instead of the commonly used heat kernel. Then, the labels of samples are considered as the graph signals indexed by the vertices of the representation graph. Finally, the states of unlabeled samples are predicted by finding a graph signal that has minimal total variation and satisfies the constraint given by labeled samples as much as possible. Experimental results indicate that GSR-D is better and more stable than the standard convolutional neural network and support vector machine in rolling bearing fault diagnosis, and GSR-D only has two tuning parameters with certain robustness.     

Cliques, holes and the vertex coloring polytope

Certain subgraphs of a given graph G restrict the minimum number χ(G) of colors that can be assigned to the vertices of G such that the endpoints of all edges receive distinct colors. Some of such subgraphs are related to the celebrated Strong Perfect Graph Theorem, as it implies that every graph G contains a clique of size χ(G), or an odd hole or an odd anti-hole as an induced subgraph. In this paper, we investigate the impact of induced maximal cliques, odd holes and odd anti-holes on the polytope associated with a new 0-1 integer programming formulation of the graph coloring problem. We show that they induce classes of facet defining inequalities.     

Graph embeddings and simplicial maps

An undirected graph is viewed as a simplicial complex. The notion of a graph embedding of a guest graph in a host graph is generalized to the realm of simplicial maps. Dilation is redefined in this more general setting. Lower bounds on dilation for various guest and host graphs are considered. Of particular interest are graphs that have been proposed as communication networks for parallel architectures. Bhattet al. provide a lower bound on dilation for embedding a planar guest graph in a butterfly host graph. Here, this lower bound is extended in two directions. First, a lower bound that applies to arbitrary guest graphs is derived, using tools from algebraic topology. Second, this lower bound is shown to apply to arbitrary host graphs through a new graph-theoretic measure, called bidecomposability. Bounds on the bidecomposability of the butterfly graph and of thek-dimensional torus are determined. As corollaries to the main lower-bound theorem, lower bounds are derived for embedding arbitrary planar graphs, genusg graphs, andk-dimensional meshes in a butterfly host graph. This research was supported by National Science Foundation Grant CCR-9009953. A preliminary version of some of this research appears in “Lower Bounds for Graph Embeddings via Algebraic Topology (Extended Abstract),”Proceedings of the 5th Annual ACM Symposium on Parallel Algorithms and Architectures, 1993, pp. 311–317.     

A characterization of partial blocks in weighted graphs

Some of the classical connectivity concepts in Graph theory are generalized in this article. Strong and strongest strong cycles are introduced. Partial blocks are characterized using strongest paths. Some necessary and sufficient conditions for a weighted graph to be a partial block are also presented.     

Parallelism and concurrency of graph manipulations

Graph manipulations are formalized as graph derivations within the framework of graph grammar theory. In this paper we generalize recently published ‘Church–Rosser’ and ‘Parallelism’ Theorems for graph derivations. Given a ‘sequential independent’ sequence of graph derivations G?H ?X the Parallelism Theorem states that there is also a sequential independent sequence via the same productions applied in reverse order, and a direct derivation G ? X via the corresponding parallel production.In our ‘Concurrency Theorem’, the main result of this paper, the assumption of sequential independence is dropped. For each sequence of productions together with dependence relations (allowing later rules to depend on the effects of earlier productions), we construct a single ‘concurrent production’. The Concurrency Theorem states that each graph derivation sequence via the given sequence of productions, which respects all the dependence relations, can be performed in a single direct derivation via the ‘concurrent production’. Moreover this assignment becomes a bijective correspondence.This Concurrency Theorem is formulated and proved in the framework of the algebraic theory of graph grammars using new pushout and pullback lemmas for the 3- and 4- dimensional cubes. As corollaries we obtain the Parallelism Theorem and a theorem reducing the strong to the weak Church–Rosser-property of graph derivations. Applications of these results to various fields in computer science especially to data base systems, are sketched in the introduction.