Visual data mining: integrating machine learning with information visualization

Today, the data available to tackle many scientific challenges is vast in quantity and diverse in nature. The exploration of heterogeneous information spaces requires suitable mining algorithms as well as effective visual interfaces. Most existing systems concentrate either on mining algorithms or on visualization techniques. Though visual methods developed in information visualization have been helpful, for improved understanding of a complex large high-dimensional dataset, there is a need for an effective projection of such a dataset onto a lower-dimension (2D or 3D) manifold. This paper introduces a flexible visual data mining framework which combines advanced projection algorithms developed in the machine learning domain and visual techniques developed in the information visualization domain. The framework follows Shneiderman’s mantra to provide an effective user interface. The advantage of such an interface is that the user is directly involved in the data mining process. We integrate principled projection methods, such as Generative Topographic Mapping (GTM) and Hierarchical GTM (HGTM), with powerful visual techniques, such as magnification factors, directional curvatures, parallel coordinates, billboarding, and user interaction facilities, to provide an integrated visual data mining framework. Results on a real life high-dimensional dataset from the chemoinformatics domain are also reported and discussed. Projection results of GTM are analytically compared with the projection results from other traditional projection methods, and 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.

The acceptability of alcohol fuels for automobile engines

The aim of this project was to carry out an investigastion into suitable alternatives to gasoline for use in modern automobiles. The fuel would provide the western world with a means of extending the natural gasoline resources and the third world a way of cutting down their dependence on the oil producing countries for their energy supply. Alcohols, namely methanol and ethanol, provide this solution. They can be used as gasoline extenders or as fuels on their own.In order to fulfil the aims of the project a literature study was carried out to investigate methods and costs of producing these fuels. An experimental programme was then set up in which the performance of the alcohols was studied on a conventional engine. The engine used for this purpose was the Fiat 127 930cc four cylinder engine. This engine was used because of its popularity in the European countries. The Weber fixed jet carburettor, since it was designed to be used with gasoline, was adapted so that the alcohol fuels and the blends could be used in the most efficient way. This was mainly to take account of the lower heat content of the alcohols. The adaptation of the carburettor was in the form of enlarging the main metering jet. Allowances for the alcohol's lower specfic gravity were made during fuel metering.Owing to the low front end volatility of methanol and ethanol, it was expected that `start up' problems would occur. An experimental programme was set up to determine the temperature range for a minimum required percentage `take off' that would ease start-up since it was determined that a `take off' of about 5% v/v liquid in the vapour phase would be sufficient for starting. Additions such as iso-pentane and n-pentane were used to improve the front end volatility. This proved to be successful.The lower heat content of the alcohol fuels also meant that a greater charge of fuel would be required. This was seen to pose further problems with fuel distribution from the carburettor to the individual cylinders on a multicylinder engine. Since it was not possible to modify the existing manifold on the Fiat 127 engine, experimental tests on manifold geometry were carried out using the Ricardo E6 single cylinder variable compression engine. Results from these tests showed that the length, shape and cross-sectional area of the manifold play an important part in the distribution of the fuel entering the cylinder, ie. vapour phase, vapour/small liquid droplet/liquid film phase, vapour/large liquid droplet/liquid film phase etc.The solvent properties of the alcohols and their greater electrical conductivity suggested that the materials used on the engine would be prone to chemical attack. In order to determine the type and rate of chemical attack, an experimental programme was set up whereby carburettor and other components were immersed in the alcohols and in blends of alcohol with gasoline. The test fuels were aerated and in some instances kept at temperatures ranging from 50oC to 90oC. Results from these tests suggest that not all materials used in the conventional engine are equally suitable for use with alcohols and alcohol/gasoline blends. Aluminium for instance was severely attacked by methanol causing pitting and pin-holing in the surface.In general this whole experimental programme gave valuable information on the acceptability of substitute fuels. While the long term effects of alcohol use merit further study, it is clear that methanol and ethanol will be increasingly used in place of gasoline.

Outlier detection in scatterometer data:Neural network approaches

Satellite-borne scatterometers are used to measure backscattered micro-wave radiation from the ocean surface. This data may be used to infer surface wind vectors where no direct measurements exist. Inherent in this data are outliers owing to aberrations on the water surface and measurement errors within the equipment. We present two techniques for identifying outliers using neural networks; the outliers may then be removed to improve models derived from the data. Firstly the generative topographic mapping (GTM) is used to create a probability density model; data with low probability under the model may be classed as outliers. In the second part of the paper, a sensor model with input-dependent noise is used and outliers are identified based on their probability under this model. GTM was successfully modified to incorporate prior knowledge of the shape of the observation manifold; however, GTM could not learn the double skinned nature of the observation manifold. To learn this double skinned manifold necessitated the use of a sensor model which imposes strong constraints on the mapping. The results using GTM with a fixed noise level suggested the noise level may vary as a function of wind speed. This was confirmed by experiments using a sensor model with input-dependent noise, where the variation in noise is most sensitive to the wind speed input. Both models successfully identified gross outliers with the largest differences between models occurring at low wind speeds. © 2003 Elsevier Science Ltd. All rights reserved.

Characterization of the hairpin vortex solution in plane Couette flow

Quantitative evidence that establishes the existence of the hairpin vortex state (HVS) in plane Couette flow (PCF) is provided in this work. The evidence presented in this paper shows that the HVS can be obtained via homotopy from a flow with a simple geometrical configuration, namely, the laterally heated flow (LHF). Although the early stages of bifurcations of LHF have been previously investigated, our linear stability analysis reveals that the root in the LHF yields multiple branches via symmetry breaking. These branches connect to the PCF manifold as steady nonlinear amplitude solutions. Moreover, we show that the HVS has a direct bifurcation route to the Rayleigh-Bénard convection. © 2010 The American Physical Society.

The effects of mailing design characteristics on direct mail campaign performance

Designing effective direct mail pieces is considered a key success factor in direct marketing. However, related published empirical research is scarce while design recommendations are manifold and often conflicting. Compared with prior work, our study aims to provide more elaborate and empirically validated findings for the effects of direct mail design characteristics by analyzing 677 direct mail campaigns from non-profit organizations and financial service providers. We investigate the effects of (1) various envelope characteristics and observable cues on opening rates, and (2) characteristics of the envelope content on the keeping rates of direct mail campaigns. We show that visual design elements on the outer envelope – rather than sender-related details – are the predominant drivers of opening rates. Factors such as letter length, provision of sender information in the letter, and personalization positively influence the keeping rate. We also observe that opening and keeping rates are uncorrelated at the campaign level, implying that opening direct mail pieces is only a necessary condition for responding to offers, but not per se a driver of direct mail response.

Bifurcation study for a vertical channel with constant flux and large aspect ratio

Using suitable coupled Navier-Stokes Equations for an incompressible Newtonian fluid we investigate the linear and non-linear steady state solutions for both a homogeneously and a laterally heated fluid with finite Prandtl Number (Pr=7) in the vertical orientation of the channel. Both models are studied within the Large Aspect Ratio narrow-gap and under constant flux conditions with the channel closed. We use direct numerics to identify the linear stability criterion in parametric terms as a function of Grashof Number (Gr) and streamwise infinitesimal perturbation wavenumber (making use of the generalised Squire’s Theorem). We find higher harmonic solutions at lower wavenumbers with a resonance of 1:3exist, for both of the heating models considered. We proceed to identify 2D secondary steady state solutions, which bifurcate from the laminar state. Our studies show that 2D solutions are found not to exist in certain regions of the pure manifold, where we find that 1:3 resonant mode 2D solutions exist, for low wavenumber perturbations. For the homogeneously heated fluid, we notice a jump phenomenon existing between the pure and resonant mode secondary solutions for very specific wavenumbers .We attempt to verify whether mixed mode solutions are present for this model by considering the laterally heated model with the same geometry. We find mixed mode solutions for the laterally heated model showing that a bridge exists between the pure and 1:3 resonant mode 2D solutions, of which some are stationary and some travelling. Further, we show that for the homogeneously heated fluid that the 2D solutions bifurcate in hopf bifurcations and there exists a manifold where the 2D solutions are stable to Eckhaus criterion, within this manifold we proceed to identify 3D tertiary solutions and find that the stability for said 3D bifurcations is not phase locked to the 2D state. For the homogeneously heated model we identify a closed loop within the neutral stability curve for higher perturbation wavenumubers and analyse the nature of the multiple 2D bifurcations around this loop for identical wavenumber and find that a temperature inversion occurs within this loop. We conclude that for a homogeneously heated fluid it is possible to have abrup ttransitions between the pure and resonant 2D solutions, and that for the laterally heated model there exist a transient bifurcation via mixed mode solutions.

Infer user interests via link structure regularization

Learning user interests from online social networks helps to better understand user behaviors and provides useful guidance to design user-centric applications. Apart from analyzing users' online content, it is also important to consider users' social connections in the social Web. Graph regularization methods have been widely used in various text mining tasks, which can leverage the graph structure information extracted from data. Previously, graph regularization methods operate under the cluster assumption that nearby nodes are more similar and nodes on the same structure (typically referred to as a cluster or a manifold) are likely to be similar. We argue that learning user interests from complex, sparse, and dynamic social networks should be based on the link structure assumption under which node similarities are evaluated based on the local link structures instead of explicit links between two nodes. We propose a regularization framework based on the relation bipartite graph, which can be constructed from any type of relations. Using Twitter as our case study, we evaluate our proposed framework from social networks built from retweet relations. Both quantitative and qualitative experiments show that our proposed method outperforms a few competitive baselines in learning user interests over a set of predefined topics. It also gives superior results compared to the baselines on retweet prediction and topical authority identification. © 2014 ACM.

Some Para-Hermitian Related Complex Structures and Non-existence of Semi-Riemannian Metric on Some Spheres

It is shown that the spheres S^(2n) (resp: S^k with k ≡ 1 mod 4) can be given neither an indefinite metric of any signature (resp: of signature (r, k − r) with 2 ≤ r ≤ k − 2) nor an almost paracomplex structure. Further for every given Riemannian metric on an almost para-Hermitian manifold with the associated 2-form φ one can construct an almost Hermitian structure (under certain conditions, two different almost Hermitian structures) whose associated 2-form(s) is φ.

Equivariant Embeddings of Differentiable Spaces

Given a differentiable action of a compact Lie group G on a compact smooth manifold V , there exists [3] a closed embedding of V into a finite-dimensional real vector space E so that the action of G on V may be extended to a differentiable linear action (a linear representation) of G on E. We prove an analogous equivariant embedding theorem for compact differentiable spaces (∞-standard in the sense of [6, 7, 8]).

A Product Twistor Space

∗Research supported in part by NSF grant INT-9903302.

Highest Weight Modules of W1+∞, Darboux Transformations and the Bispectral Problem

This paper is a survey of our recent results on the bispectral problem. We describe a new method for constructing bispectral algebras of any rank and illustrate the method by a series of new examples as well as by all previously known ones. Next we exhibit a close connection of the bispectral problem to the representation theory of W1+∞–algerba. This connection allows us to explain and generalise to any rank the result of Magri and Zubelli on the symmetries of the manifold of the bispectral operators of rank and order two.

Application of Lyapunov's Direct Method to the Existence of Integral Manifolds of Impulsive Differential Equations

The present paper investigates the existence of integral manifolds for impulsive differential equations with variable perturbations. By means of piecewise continuous functions which are generalizations of the classical Lyapunov’s functions, sufficient conditions for the existence of integral manifolds of such equations are found.

Deformation Lemma, Ljusternik-Schnirellmann Theory and Mountain Pass Theorem on C1-Finsler Manifolds

∗Partially supported by Grant MM409/94 Of the Ministy of Science and Education, Bulgaria. ∗∗Partially supported by Grant MM442/94 of the Ministy of Science and Education, Bulgaria.

On Maximal Function on the Laguerre Hypergroup

2000 Mathematics Subject Classification: 42B20, 42B25, 42B35

On a Class Almost Contact Manifolds with Norden Metric

Certain curvature properties and scalar invariants of the mani- folds belonging to one of the main classes almost contact manifolds with Norden metric are considered. An example illustrating the obtained results is given and studied.