Hierarchical GTM: Constructing localized non-linear projection manifolds in a principled way

It has been argued that a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex data sets, and therefore a hierarchical visualization system is desirable. In this paper we extend an existing locally linear hierarchical visualization system PhiVis ¸iteBishop98a in several directions: bf(1) We allow for em non-linear projection manifolds. The basic building block is the Generative Topographic Mapping. bf(2) We introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree. General training equations are derived, regardless of the position of the model in the tree. bf(3) Using tools from differential geometry we derive expressions for local directional curvatures of the projection manifold. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. It enables the user to interactively highlight those data in the parent visualization plot which are captured by a child model. We also incorporate into our system a hierarchical, locally selective representation of magnification factors and directional curvatures of the projection manifolds. Such information is important for further refinement of the hierarchical visualization plot, as well as for controlling the amount of regularization imposed on the local models. We demonstrate the principle of the approach on a toy data set and apply our system to two more complex 12- and 19-dimensional data sets.

Using directional curvatures to visualize folding patterns of the GTM projection manifolds

In data visualization, characterizing local geometric properties of non-linear projection manifolds provides the user with valuable additional information that can influence further steps in the data analysis. We take advantage of the smooth character of GTM projection manifold and analytically calculate its local directional curvatures. Curvature plots are useful for detecting regions where geometry is distorted, for changing the amount of regularization in non-linear projection manifolds, and for choosing regions of interest when constructing detailed lower-level visualization plots.

Hierarchical GTM: constructing localized non-linear projection manifolds in a principled way

It has been argued that a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex data sets, and therefore a hierarchical visualization system is desirable. In this paper we extend an existing locally linear hierarchical visualization system PhiVis ¸iteBishop98a in several directions: bf(1) We allow for em non-linear projection manifolds. The basic building block is the Generative Topographic Mapping (GTM). bf(2) We introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree. General training equations are derived, regardless of the position of the model in the tree. bf(3) Using tools from differential geometry we derive expressions for local directional curvatures of the projection manifold. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. It enables the user to interactively highlight those data in the ancestor visualization plots which are captured by a child model. We also incorporate into our system a hierarchical, locally selective representation of magnification factors and directional curvatures of the projection manifolds. Such information is important for further refinement of the hierarchical visualization plot, as well as for controlling the amount of regularization imposed on the local models. We demonstrate the principle of the approach on a toy data set and apply our system to two more complex 12- and 18-dimensional data sets.

Integrated project evaluation and selection using multiple-attribute decision-making technique

The evaluation and selection of industrial projects before investment decision is customarily done using marketing, technical and financial information. Subsequently, environmental impact assessment and social impact assessment are carried out mainly to satisfy the statutory agencies. Because of stricter environment regulations in developed and developing countries, quite often impact assessment suggests alternate sites, technologies, designs, and implementation methods as mitigating measures. This causes considerable delay to complete project feasibility analysis and selection as complete analysis requires to be taken up again and again till the statutory regulatory authority approves the project. Moreover, project analysis through above process often results sub-optimal project as financial analysis may eliminate better options, as more environment friendly alternative will always be cost intensive. In this circumstance, this study proposes a decision support system, which analyses projects with respect to market, technicalities, and social and environmental impact in an integrated framework using analytic hierarchy process, a multiple-attribute decision-making technique. This not only reduces duration of project evaluation and selection, but also helps select optimal project for the organization for sustainable development. The entire methodology has been applied to a cross-country oil pipeline project in India and its effectiveness has been demonstrated. © 2005 Elsevier B.V. All rights reserved.

Multiple attribute decision making approach to petroleum pipeline route selection

Petroleum pipelines are the nervous system of the oil industry, as this transports crude oil from sources to refineries and petroleum products from refineries to demand points. Therefore, the efficient operation of these pipelines determines the effectiveness of the entire business. Pipeline route selection plays a major role when designing an effective pipeline system, as the health of the pipeline depends on its terrain. The present practice of route selection for petroleum pipelines is governed by factors such as the shortest distance, constructability, minimal effects on the environment, and approachability. Although this reduces capital expenditure, it often proves to be uneconomical when life cycle costing is considered. This study presents a route selection model with the application of an Analytic Hierarchy Process (AHP), a multiple attribute decision making technique. AHP considers all the above factors along with the operability and maintainability factors interactively. This system has been demonstrated here through a case study of pipeline route selection, from an Indian perspective. A cost-benefit comparison of the shortest route (conventionally selected) and optimal route establishes the effectiveness of the model.

'They cooperate with us, so they are like me': perceived intergroup relationship moderates projection from self to outgroups

Whereas projection of self-attributes to ingroups is ubiquitous, projection of self-attributes to outgroups (outgroup projection) is an elusive phenomenon. Two experiments examined the moderating effect of perceived intergroup relationship on outgroup projection and explored underlying mechanisms. Perceived cooperation versus competition between ingroup and outgroup was manipulated using fictitious (Experiment 1) or natural groups (Experiment 2). In both experiments, participants judged the outgroup as more similar to the self in the cooperation condition than in the competition condition. This effect was independent of recategorization, perceived intergroup similarity, and ingroup-to-outgroup projection. These studies demonstrate the very existence of outgroup projection and extend previous work on moderators of projection from self to groups.

Constructing localized non-linear projection manifolds in a principled way:hierarchical generative topographic mapping

It has been argued that a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex data sets, and therefore a hierarchical visualization system is desirable. In this paper we extend an existing locally linear hierarchical visualization system PhiVis (Bishop98a) in several directions: 1. We allow for em non-linear projection manifolds. The basic building block is the Generative Topographic Mapping. 2. We introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree. General training equations are derived, regardless of the position of the model in the tree. 3. Using tools from differential geometry we derive expressions for local directionalcurvatures of the projection manifold. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. It enables the user to interactively highlight those data in the parent visualization plot which are captured by a child model.We also incorporate into our system a hierarchical, locally selective representation of magnification factors and directional curvatures of the projection manifolds. Such information is important for further refinement of the hierarchical visualization plot, as well as for controlling the amount of regularization imposed on the local models. We demonstrate the principle of the approach on a toy data set andapply our system to two more complex 12- and 19-dimensional data sets.

Rapid heuristic projection on simplicial cones

A very fast heuristic iterative method of projection on simplicial cones is presented. It consists in solving two linear systems at each step of the iteration. The extensive experiments indicate that the method furnishes the exact solution in more then 99.7 percent of the cases. The average number of steps is 5.67 (we have not found any examples which required more than 13 steps) and the relative number of steps with respect to the dimension decreases dramatically. Roughly speaking, for high enough dimensions the absolute number of steps is independent of the dimension.

Alzheimer's disease: Are cellular neurofibrillary tangles linked to beta/A4 formation at the projection sites?

The density of senile plaques (SP) and cellular neurofibrillary tabgles (NFT) revealed by the Glees and Gallyas stains; and beta/A4 deposits revealed by immunocytochemical staining, was estimated in the hippocampus and adjacent gyri in Alzheimer's disease (AD). Stepwise multiple regression was used to detemine whether the density of cellular NFT was related to the density of SP or beta/A4 deposits totalled over the projection sites. Cellular NFT density was only weakly correlated with the density of Glees SP and beta/A4 deposits at some of the projection sites. However, beta/A4 deposit density in a tissue was strongly correlated with the density of beta/A4 deposits at the projection sites suggesting that the lesions could spread through the brain. Hence, although there is a strong correlation between the density of beta/A4 deposits in different parts of the hippocampal formation there is little association between SP or beta/A4 and cellular NFT. These results do not provide strong evidence that beta/A4 protein is the cause of the neuritc changes in AD.

Projection and interpolation based techniques for structured and impulsive noise filtering

In this chapter we present the relevant mathematical background to address two well defined signal and image processing problems. Namely, the problem of structured noise filtering and the problem of interpolation of missing data. The former is addressed by recourse to oblique projection based techniques whilst the latter, which can be considered equivalent to impulsive noise filtering, is tackled by appropriate interpolation methods.

The measurement properties of the menorrhagia multi-attribute quality-of-life scale:a psychometric analysis

Menorrhagia, or heavy menstrual bleeding (HMB), is a common gynaecological condition. As the aim of treatment is to improve women's wellbeing and quality of life (QoL), it is necessary to have effective ways to measure this. This study investigated the reliability and validity of the menorrhagia multi-attribute scale (MMAS), a menorrhagia-specific QoL instrument. Participants (n = 431) completed the MMAS and a battery of other tests as part of the baseline assessment of the ECLIPSE (Effectiveness and Cost-effectiveness of Levonorgestrel-containing Intrauterine system in Primary care against Standard trEatment for menorrhagia) trial. Analyses of their responses suggest that the MMAS has good measurement properties and is therefore an appropriate condition-specific instrument to measure the outcome of treatment for HMB. © 2011 The Authors BJOG An International Journal of Obstetrics and Gynaecology © 2011 RCOG.

How brand attribute typicality and consumer commitment moderate the influence of comparative advertising

This study examines how product attribute typicality and brand commitment influence the effects of comparative versus non-comparative ads on brand attitudes. Employing perspectives from the literatures on typicality and commitment, the study examines the effects of commitment to the comparison brand on the effectiveness of comparative versus non-comparative advertising. A between-informants experiment uses data from 466 student informants. It is hypothesized that (a) when the attribute under consideration is typical (atypical), among comparison brand committed informants, a non-comparative ad is more (no more) persuasive than a comparative ad, (b) when the attribute under consideration is typical, among comparison brand non-committed informants, a comparative ad is more persuasive than a non-comparative ad, and (c) when the attribute under consideration is atypical, among comparison brand non-committed informants, a comparative ad is likely to be more persuasive than a non-comparative ad, but the effect will be weaker than in the case of a typical attribute. Hypothesis (a) is supported while (b) has directional support. The results support a three-way interaction between consumer commitment, attribute typicality, and type of advertisement. The findings are relevant to a variety of contexts, such as markets characterized by high levels of market share and commitment for the market leader as well as fragmented markets where market share and commitment levels are low.

Visual data mining using principled projection algorithms and information visualization techniques

We introduce a flexible visual data mining framework which combines advanced projection algorithms from the machine learning domain and visual techniques developed in the information visualization domain. The advantage of such an interface is that the user is directly involved in the data mining process. We integrate principled projection algorithms, such as generative topographic mapping (GTM) and hierarchical GTM (HGTM), with powerful visual techniques, such as magnification factors, directional curvatures, parallel coordinates and billboarding, to provide a visual data mining framework. Results on a real-life chemoinformatics dataset using GTM are promising and have been analytically compared with the results from the traditional projection methods. It is also shown that the HGTM algorithm provides additional value for large datasets. The computational complexity of these algorithms is discussed to demonstrate their suitability for the visual data mining framework. Copyright 2006 ACM.

2D-3D registration of CT vertebra volume to fluoroscopy projection:a calibration model assessment

This study extends a previous research concerning intervertebral motion registration by means of 2D dynamic fluoroscopy to obtain a more comprehensive 3D description of vertebral kinematics. The problem of estimating the 3D rigid pose of a CT volume of a vertebra from its 2D X-ray fluoroscopy projection is addressed. 2D-3D registration is obtained maximising a measure of similarity between Digitally Reconstructed Radiographs (obtained from the CT volume) and real fluoroscopic projection. X-ray energy correction was performed. To assess the method a calibration model was realised a sheep dry vertebra was rigidly fixed to a frame of reference including metallic markers. Accurate measurement of 3D orientation was obtained via single-camera calibration of the markers and held as true 3D vertebra position; then, vertebra 3D pose was estimated and results compared. Error analysis revealed accuracy of the order of 0.1 degree for the rotation angles of about 1mm for displacements parallel to the fluoroscopic plane, and of order of 10mm for the orthogonal displacement. © 2010 P. Bifulco et al.

Analyzing evacuation decisions using multi-attribute utility theory (MAUT)

Emergency managers are faced with critical evacuation decisions. These decisions must balance conflicting objectives as well as high levels of uncertainty. Multi-Attribute Utility Theory (MAUT) provides a framework through which objective trade-offs can be analyzed to make optimal evacuation decisions. This paper is the result of data gathered during the European Commission Project, Evacuation Responsiveness by Government Organizations (ERGO) and outlines a preliminary decision model for the evacuation decision. The illustrative model identifies levels of risk at which point evacuation actions should be taken by emergency managers in a storm surge scenario with forecasts at 12 and 9 hour intervals. The results illustrate how differences in forecast precision affect the optimal evacuation decision. Additional uses for this decision model are also discussed along with improvements to the model through future ERGO data-gathering.