Influence Graph Research Articles

On the size of a random sphere of influence graph

We approach sphere of influence graphs (SIGs) from a probabilistic perspective. Ordinary SIGs were first introduced by Toussaint as a type of proximity graph for use in pattern recognition, computer vision and other low-level vision tasks. A random sphere of influence graph (RSIG) is constructed as follows. Consider n points uniformly and independently distributed within the unit square in d dimensions. Around each point, Xi, draw an open ball (‘sphere of influence’) with radius equal to the distance to Xi's nearest neighbour. Finally, draw an edge between two points if their spheres of influence intersect. Asymptotically exact values for the expected number of edges in a RSIG are determined for all values of d; previously, just upper and lower bounds were known for this quantity. A modification of the Azuma-Hoeffding exponential inequality is employed to exhibit the sharp concentration of the number of edges around its expected value.

On the size of a random sphere of influence graph

We approach sphere of influence graphs (SIGs) from a probabilistic perspective. Ordinary SIGs were first introduced by Toussaint as a type of proximity graph for use in pattern recognition, computer vision and other low-level vision tasks. A random sphere of influence graph (RSIG) is constructed as follows. Consider n points uniformly and independently distributed within the unit square in d dimensions. Around each point, X i , draw an open ball (‘sphere of influence’) with radius equal to the distance to X i 's nearest neighbour. Finally, draw an edge between two points if their spheres of influence intersect. Asymptotically exact values for the expected number of edges in a RSIG are determined for all values of d; previously, just upper and lower bounds were known for this quantity. A modification of the Azuma-Hoeffding exponential inequality is employed to exhibit the sharp concentration of the number of edges around its expected value.

Sphere of influence graphs in general metric spaces

Let χ = { X 1…, X n } be a set of points in a metric space ( n ≥ 2). Let r i , denote the minimum distance between X i and the other points in χ. The sphere of influence at X i is the open ball with center X i and radius r i . The sphere of influence graph has vertex set χ with an edge joining a pair of distinct vertices provided the corresponding spheres of influence intersect. This proximity graph was introduced by Toussaint to model computer vision and pattern recognition problems in the Euclidean plane. We discuss the abstract properties of sphere of influence graphs in general metric spaces with emphasis on normed linear spaces. Our work generalizes and simplifies some theorems in the literature on sphere of influence graphs and lays the groundwork for future work.

Sphere of influence graphs in general metric spaces

Let @g = {X1..., Xn} be a set of points in a metric space (n >= 2). Let ri, denote the minimum distance between Xi and the other points in @g. The sphere of influence at Xi is the open ball wi...

On the variance of the random sphere of influence graph

We show that the variance of the number of edges in the random sphere of influence graph built on n i.i.d. sites which are uniformly distributed over the unit cube in Rd, grows linearly with n. This is then used to establish a central limit theorem for the number of edges in the random sphere of influence graph built on a Poisson number of sites. Some related proximity graphs are discussed as well. ©1999 John Wiley & Sons, Inc. Random Struct. Alg., 14, 139–152, 1999

Reduction of the Markovian system by the influence graph method: error bound and reliability computation

Abstract In a previous article, a new method allowing the treatment of large Markovian problems was presented. Based on a graph describing the influences between the components of the system, it performs successive approximate aggregations on the exact Markovian system to reduce its size. The main drawback of this method, as of any approximate method, is to assess its validity. That is why we develop a new presentation of the method here and we define, from this presentation, error bounds for the approximate results. They are then tested for two applications, one being very large with more than 10 30 states for the exact Markovian system. We also extend the method, initially defined for availability problems, to reliability problems.

An integrated fault diagnostic mechanism based on statistical characteristics of products for heterogeneous manufacturing environments

A fault diagnosis mechanism for heterogeneous manufacturing environments is developed. Using the correlation coefficient among quality characteristic values (QCVs) of products enables the functional correlation between processes to be uniformly treated according to causal relations among processes, despite their functional heterogeneity. Complex causal relations between QCVs are graphically represented by the influence graph, which is developed to model the diagnostic knowledge of our method. This mechanism realizes more accurate diagnostic capabilities than black-box methods, and still, does not require exhaustive modelling of the entire process, unlike model-based reasoning methods. The viability of this diagnostic approach was verified via simulation.

Analysis of Fractal Operator Convergence by Graph Methods

The convergence of fractal operator F used in image compression is investigated by analysis of block influence graph and pixel influence graph. The graph stability condition in block influence graph implies eventual contractivity condition which is sufficient for the operator iteration convergence. The graph stability condition in pixel influence graph appears to be sufficient and necessary for convergence of selecting fractal operators.

ASSESSMENT OF LOCAL INFLUENCE IN MULTIVARIATE ANALYSIS

A recent method for assessing the local influence is introduced by Cook(1986), in which the normal curvature of the influence graph based on the likelihood displacement is used to monitor the influence of small perturbation. Since then this method has been applied to various kind of models. However, the local influence in multivariate analysis is still an unexplored area because the influence for many statistics in multivariate analysis is not convenient to handle based on the Cook's likelihood displacement. In this paper, we suggest a method with a slight modification in Cook's approach to assess the local influence of small perturbation on a certain statistic. The local influence of the perturbation on eigenvalue and eigenvector of variance-covariance matrix in theoretical and sample version is assessed, some results for the other statistics in multivariate analysis such as generalized variance, canonical correlations are studied. Finally, two examples are analysed for illustration.

Towards building an intelligent decision support system for project management

Management of large projects, especially the ones in which a major component of R&D is involved and those requiring knowledge from diverse specialised and sophisticated fields, may be classified as semi-structured problems. In these problems, there is some knowledge about the nature of the work involved, but there are also uncertainties associated with emerging technologies. In order to draw up a plan and schedule of activities of such a large and complex project, the project manager is faced with a host of complex decisions that he has to take, such as, when to start an activity, for how long the activity is likely to continue, etc. An Intelligent Decision Support System (IDSS) which aids the manager in decision making and drawing up a feasible schedule of activities while taking into consideration the constraints of resources and time, will have a considerable impact on the efficient management of the project. This report discusses the design of an IDSS that helps in project planning phase through the scheduling phase. The IDSS uses a new project scheduling tool, the Project Influence Graph (PIG).

Sphere of influence graphs: Edge density and clique size

Let X={X 1,…,X n} be a set of n points( n ≥ 2) in the metric space M. Let r i denote the minimum distance between X i and any other point in X . The closed ball B̄ i with center X i and radius r i is the closed sphere of influence at X i . The closed sphere of influence graph CSIG ( M, X ) has vertex set X with distinct vertices X i and X j adjacent provided B i∩ B j≠∅ . The graph G is an M-CSIG provided G is isomorphic to CSIG( M, X ) for some set X of points in M. We prove that, for any metric space M, the clique number is bounded over the class of M-CSIGs if and only if there is a constant C̄, so that the inequality |E| ≤ C|V| holds whenever G = ( V, E) is an M-CSIG. The proof uses Ramsey's Theorem. We also prove that if M = ( R d, ρ) is a d-dimensional Minkowski space, then C ≤ 5 d − 3 2 .

The use of the component influence graph to reduce the size of Markovian availability problems

Abstract In this paper we will develop a new method of solution of large Markovian problems by means of auxiliary problems of smaller size. The influence graph of the physical components is built, each edge of the digraph symbolizing the influence (if any) of the composant (node of the graph) on the rate of failure or repair of another component. The analysis of the digraph introduces a natural ordering and the buildup of approximate differential systems which are solved recursively for the conditional probabilities. Two examples are given to illustrate the method.

Model Structure Determination for a Heat Pump System

In this paper principles of model structure determination by selection between candidate structures of underlying linearized ordinary differential equation models aredescribed. The principles are exemplified on a simple heat pump system. The identification procedure applying influence graph models, qualitative prediction tables taking results on structural stability analysis into account, is demonstrated for the example. The same methodology may be applied using other qualitative structural properties (e.g. qualitative correlation tables, structural observability and controllability analysis etc.) Structure identification methods based on qualitative models may complement conventional identification methods serving as structure determination tools in the early stages of modelling.

Relative effectiveness of androgen withdrawal therapies as measured by changes in the intracellular distributions of androgen receptors and dihydrotestosterone

Human personality plays a crucial role in decision-making and it has paramount importance when individuals negotiate with each other to reach a common group decision. Such situations are conceivable, for instance, when a group of individuals want to watch a movie together. It is well known that people influence each other’s decisions, the more assertive a person is, the more influence they will have on the final decision. In order to obtain a more realistic group recommendation system (GRS), we need to accommodate the assertiveness of the different group members’ personalities. Although pairwise preferences are long-established in group decision-making (GDM), they have received very little attention in the recommendation systems community. Driven by the advantages of pairwise preferences on ratings in the recommendation systems domain, we have further pursued this approach in this paper, however we have done so for GRS. We have devised a three-stage approach to GRS in which we 1) resort to three binary matrix factorization methods, 2) develop an influence graph that includes assertiveness and cooperativeness as personality traits, and 3) apply an opinion dynamics model in order to reach consensus. We have shown that the final opinion is related to the stationary distribution of a Markov chain associated with the influence graph. Our experimental results demonstrate that our approach results in high precision and fairness.

The relative neighborhood graph for mixed feature variables

The rectangular influence graph (RIG) is presented as an extension of the relative neighborhood graph (RNG). The RNG is an efficient tool for analyzing the clustering of multidimensional feature vectors when all the features are quantitative. The RIG is a similar tool that can accommodate feature vectors some of whose components are qualitative. We show that the RIG is a superset of the Gabriel graph with respect to any Minkowski metric. As tools to analyze interclass structure, the interclass RIG (IRIG) and the mutual neighborhood graph (MNG) are presented. These graphs can be used to reduce the training set in the design of piecewise linear classifiers. The MNG leads also to a sufficient condition for the linear separability between classes.

On Logarithmic Norms

This paper discusses some normlike properties of the logarithmic norm and related efficiency questions. Some computational questions are raised and some examples of use are indicated.