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.

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.

A principled approach to interactive hierarchical non-linear visualization of high-dimensional data

Hierarchical visualization systems are desirable because a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex high-dimensional data sets. We extend an existing locally linear hierarchical visualization system PhiVis [1] 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, bf(3) we describe folding patterns of low-dimensional projection manifold in high-dimensional data space by computing and visualizing the manifold's local directional curvatures. Quantities such as magnification factors [3] and directional curvatures are helpful for understanding the layout of the nonlinear projection manifold in the data space and for further refinement of the hierarchical visualization plot. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. We demonstrate the visualization system principle of the approach on a complex 12-dimensional data set and mention possible applications in the pharmaceutical industry.

Development and evaluation of a non-destructive adhesion test

The object of this work was to further develop the idea introduced by Muaddi et al (1981) which enables some of the disadvantages of earlier destructive adhesion test methods to be overcome. The test is non-destructive in nature but it does need to be calibrated against a destructive method. Adhesion is determined by measuring the effect of plating on internal friction. This is achieved by determining the damping of vibrations of a resonating specimen before and after plating. The level of adhesion was considered by the above authors to influence the degree of damping. In the major portion of the research work the electrodeposited metal was Watt's nickel, which is ductile in nature and is therefore suitable for peel adhesion testing. The base metals chosen were aluminium alloys S1C and HE9 as it is relatively easy to produce varying levels of adhesion between the substrate and electrodeposited coating by choosing the appropriate process sequence. S1C alloy is the commercially pure aluminium and was used to produce good adhesion. HE9 aluminium alloy is a more difficult to plate alloy and was chosen to produce poorer adhesion. The "Modal Testing" method used for studying vibrations was investigated as a possible means of evaluating adhesion but was not successful and so research was concentrated on the "Q" meter. The method based on the use of a "Q" meter involves the principle of exciting vibrations in a sample, interrupting the driving signal and counting the number of oscillations of the freely decaying vibrations between two known preselected amplitudes of oscillations. It was not possible to reconstruct a working instrument using Muaddi's thesis (1982) as it had either a serious error or the information was incomplete. Hence a modified "Q" meter had to be designed and constructed but it was then difficult to resonate non-magnetic materials, such as aluminium, therefore, a comparison before and after plating could not be made. A new "Q" meter was then developed based on an Impulse Technique. A regulated miniature hammer was used to excite the test piece at the fundamental mode instead of an electronic hammer and test pieces were supported at the two predetermined nodal points using nylon threads. This instrument developed was not very successful at detecting changes due to good and poor pretreatments given before plating, however, it was more sensitive to changes at the surface such as room temperature oxidation. Statistical analysis of test results from untreated aluminium alloys show that the instrument is not always consistent, the variation was even bigger when readings were taken on different days. Although aluminium is said to form protective oxides at room temperature there was evidence that the aluminium surface changes continuously due to film formation, growth and breakdown. Nickel plated and zinc alloy immersion coated samples also showed variation in Q with time. In order to prove that the variations in Q were mainly due to surface oxidation, aluminium samples were lacquered and anodised Such treatments enveloped the active surfaces reacting with the environment and the Q variation with time was almost eliminated especially after hard anodising. This instrument detected major differences between different untreated aluminium substrates.Also Q values decreased progressively as coating thicknesses were increased. This instrument was also able to detect changes in Q due to heat-treatment of aluminium alloys.

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.

Applications of Reissner's principle to structural dynamics

The analysis and prediction of the dynamic behaviour of s7ructural components plays an important role in modern engineering design. :n this work, the so-called "mixed" finite element models based on Reissnen's variational principle are applied to the solution of free and forced vibration problems, for beam and :late structures. The mixed beam models are obtained by using elements of various shape functions ranging from simple linear to complex cubic and quadratic functions. The elements were in general capable of predicting the natural frequencies and dynamic responses with good accuracy. An isoparametric quadrilateral element with 8-nodes was developed for application to thin plate problems. The element has 32 degrees of freedom (one deflection, two bending and one twisting moment per node) which is suitable for discretization of plates with arbitrary geometry. A linear isoparametric element and two non-conforming displacement elements (4-node and 8-node quadrilateral) were extended to the solution of dynamic problems. An auto-mesh generation program was used to facilitate the preparation of input data required by the 8-node quadrilateral elements of mixed and displacement type. Numerical examples were solved using both the mixed beam and plate elements for predicting a structure's natural frequencies and dynamic response to a variety of forcing functions. The solutions were compared with the available analytical and displacement model solutions. The mixed elements developed have been found to have significant advantages over the conventional displacement elements in the solution of plate type problems. A dramatic saving in computational time is possible without any loss in solution accuracy. With beam type problems, there appears to be no significant advantages in using mixed models.

Non-invasive respiratory monitoring using long-period fiber grating sensors

In non-invasive ventilation, continuous monitoring of respiratory volumes is essential. Here, we present a method for the measurement of respiratory volumes by a single fiber-grating sensor of bending and provide the proof-of-principle by applying a calibration-test measurement procedure on a set of 18 healthy volunteers. Results establish a linear correlation between a change in lung volume and the corresponding change in a local thorax curvature. They also show good sensor accuracy in measurements of tidal and minute respiratory volumes for different types of breathing. The proposed technique does not rely on the air flow through an oronasal mask or the observation of chest movement by a clinician, which distinguishes it from the current clinical practice. © 2014 Optical Society of America.