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Description
Feature learning and the discovery of nonlinear variation patterns in high-dimensional data is an important task in many problem domains, such as imaging, streaming data from sensors, and manufacturing. This dissertation presents several methods for learning and visualizing nonlinear variation in high-dimensional data. First, an automated method for discovering nonlinear variation patterns using deep learning autoencoders is proposed. The approach provides a functional mapping from a low-dimensional representation to the original spatially-dense data that is both interpretable and efficient with respect to preserving information. Experimental results indicate that deep learning autoencoders outperform manifold learning and principal component analysis in reproducing the original data from the learned variation sources.
A key issue in using autoencoders for nonlinear variation pattern discovery is to encourage the learning of solutions where each feature represents a unique variation source, which we define as distinct features. This problem of learning distinct features is also referred to as disentangling factors of variation in the representation learning literature. The remainder of this dissertation highlights and provides solutions for this important problem.
An alternating autoencoder training method is presented and a new measure motivated by orthogonal loadings in linear models is proposed to quantify feature distinctness in the nonlinear models. Simulated point cloud data and handwritten digit images illustrate that standard training methods for autoencoders consistently mix the true variation sources in the learned low-dimensional representation, whereas the alternating method produces solutions with more distinct patterns.
Finally, a new regularization method for learning distinct nonlinear features using autoencoders is proposed. Motivated in-part by the properties of linear solutions, a series of learning constraints are implemented via regularization penalties during stochastic gradient descent training. These include the orthogonality of tangent vectors to the manifold, the correlation between learned features, and the distributions of the learned features. This regularized learning approach yields low-dimensional representations which can be better interpreted and used to identify the true sources of variation impacting a high-dimensional feature space. Experimental results demonstrate the effectiveness of this method for nonlinear variation pattern discovery on both simulated and real data sets.
A key issue in using autoencoders for nonlinear variation pattern discovery is to encourage the learning of solutions where each feature represents a unique variation source, which we define as distinct features. This problem of learning distinct features is also referred to as disentangling factors of variation in the representation learning literature. The remainder of this dissertation highlights and provides solutions for this important problem.
An alternating autoencoder training method is presented and a new measure motivated by orthogonal loadings in linear models is proposed to quantify feature distinctness in the nonlinear models. Simulated point cloud data and handwritten digit images illustrate that standard training methods for autoencoders consistently mix the true variation sources in the learned low-dimensional representation, whereas the alternating method produces solutions with more distinct patterns.
Finally, a new regularization method for learning distinct nonlinear features using autoencoders is proposed. Motivated in-part by the properties of linear solutions, a series of learning constraints are implemented via regularization penalties during stochastic gradient descent training. These include the orthogonality of tangent vectors to the manifold, the correlation between learned features, and the distributions of the learned features. This regularized learning approach yields low-dimensional representations which can be better interpreted and used to identify the true sources of variation impacting a high-dimensional feature space. Experimental results demonstrate the effectiveness of this method for nonlinear variation pattern discovery on both simulated and real data sets.
ContributorsHoward, Phillip (Author) / Runger, George C. (Thesis advisor) / Montgomery, Douglas C. (Committee member) / Mirchandani, Pitu (Committee member) / Apley, Daniel (Committee member) / Arizona State University (Publisher)
Created2016
Description
The repertoire for guitar and piano duo is small in comparison with other chamber music instrumentation; therefore, it is important to broaden this repertoire. In addition to creating original compositions, arrangements of existing works contribute to this expansion.
This project focuses on an arrangement of Bachianas Brasileiras No. 1 by Brazilian composer Heitor Villa-Lobos (1887-1959), a work originally conceived for cello ensemble with a minimum of eight cellos. In order to contextualize the proposed arrangement, this study contains a brief historical listing of the repertoire for guitar and piano duo and of the guitar works by Villa-Lobos. Also, it includes a description of the Bachianas Brasileiras series and a discussion of the arranging methodology that shows how the original musical ideas of the composer were adapted using techniques that are idiomatic to the guitar and piano. The full arrangement is included in Appendix A.
This project focuses on an arrangement of Bachianas Brasileiras No. 1 by Brazilian composer Heitor Villa-Lobos (1887-1959), a work originally conceived for cello ensemble with a minimum of eight cellos. In order to contextualize the proposed arrangement, this study contains a brief historical listing of the repertoire for guitar and piano duo and of the guitar works by Villa-Lobos. Also, it includes a description of the Bachianas Brasileiras series and a discussion of the arranging methodology that shows how the original musical ideas of the composer were adapted using techniques that are idiomatic to the guitar and piano. The full arrangement is included in Appendix A.
ContributorsFigueiredo Bartoloni, Fabio (Author) / Koonce, Frank (Thesis advisor) / Suzuki, Kotoka (Committee member) / Landschoot, Thomas (Committee member) / Arizona State University (Publisher)
Created2016
ContributorsASU Library. Music Library (Publisher)
Created2018-01-31
Description
This investigation develops small-size reduced order models (ROMs) that provide an accurate prediction of the response of only part of a structure, referred to as component-centric ROMs. Four strategies to construct such ROMs are presented, the first two of which are based on the Craig-Bampton Method and start with a set of modes for the component of interest (the β component). The response in the rest of the structure (the α component) induced by these modes is then determined and optimally represented by applying a Proper Orthogonal Decomposition strategy using Singular Value Decomposition. These first two methods are effectively basis reductions techniques of the CB basis. An approach based on the “Global - Local” Method generates the “global” modes by “averaging” the mass property over α and β comp., respectively (to extract a “coarse” model of α and β) and the “local” modes orthogonal to the “global” modes to add back necessary “information” for β. The last approach adopts as basis for the entire structure its linear modes which are dominant in the β component response. Then, the contributions of other modes in this part of the structure are approximated in terms of those of the dominant modes with close natural frequencies and similar mode shapes in the β component. In this manner, the non-dominant modal contributions are “lumped” onto the dominant ones, to reduce the number of modes for a prescribed accuracy. The four approaches are critically assessed on the structural finite element model of a 9-bay panel with the modal lumping-based method leading to the smallest sized ROMs. Therefore, it is extended to the nonlinear geometric situation and first recast as a rotation of the modal basis to achieve unobservable modes. In the linear case, these modes completely disappear from the formulation owing to orthogonality. In the nonlinear case, however, the generalized coordinates of these modes are still present in the nonlinear terms of the observable modes. A closure-type algorithm is then proposed to eliminate the unobserved generalized coordinates. This approach, its accuracy and computational savings, was demonstrated on a simple beam model and the 9-bay panel model.
ContributorsWang, Yuting (Author) / Mignolet, Marc P (Thesis advisor) / Jiang, Hanqing (Committee member) / Liu, Yongming (Committee member) / Oswald, Jay (Committee member) / Rajan, Subramaniam D. (Committee member) / Spottswood, Stephen M (Committee member) / Arizona State University (Publisher)
Created2017
Description
Phantom Sun is a ten-minute piece in three sections, and is composed for flute, clarinet in b-flat, violin, cello, and percussion. The three-part structure for this work is a representation of the atmospheric phenomenon after which the composition is named. A phantom sun, also called a parhelion or sundog, is a weather-related phenomenon caused by the horizontal refraction of sunlight in the upper atmosphere. This refraction creates the illusion of three suns above the horizon, and is often accompanied by a bright halo called the circumzenithal arc. The halo is caused by light bending at 22° as it passes through hexagonal ice crystals. Consequently, the numbers six and 22 are important figures, and have been encoded into this piece in various ways.
The first section, marked “With concentrated intensity,” is characterized by the juxtaposition of tonal ambiguity and tonal affirmation, as well as the use of polymetric counterpoint (often 7/8 against 4/4 or 7/8 against 3/4). The middle section, marked “Crystalline,” provides contrast in its use of unmetered sections and independent tempos. The refraction of light is represented in this movement by a 22-note row based on a hexachord (B-flat, F, C, G, A, E) introduced in measure 164 of the first section. The third section, marked “With frenetic energy,” begins without pause on an arresting entrance of the drums playing an additive rhythmic pattern. This pattern (5+7+9+1) amounts to 22 eighth-note pulses and informs much of the motivic and structural considerations for the remainder of the piece.
The first section, marked “With concentrated intensity,” is characterized by the juxtaposition of tonal ambiguity and tonal affirmation, as well as the use of polymetric counterpoint (often 7/8 against 4/4 or 7/8 against 3/4). The middle section, marked “Crystalline,” provides contrast in its use of unmetered sections and independent tempos. The refraction of light is represented in this movement by a 22-note row based on a hexachord (B-flat, F, C, G, A, E) introduced in measure 164 of the first section. The third section, marked “With frenetic energy,” begins without pause on an arresting entrance of the drums playing an additive rhythmic pattern. This pattern (5+7+9+1) amounts to 22 eighth-note pulses and informs much of the motivic and structural considerations for the remainder of the piece.
ContributorsMitton, Stephen LeRoy (Author) / DeMars, James (Thesis advisor) / Norton, Kay (Committee member) / Rogers, Rodney (Committee member) / Arizona State University (Publisher)
Created2017
ContributorsHsu, Gabrielle (Performer) / Kierum, Caitlin (Performer) / Song, Yiqian (Performer) / Fox, Matt (Performer) / Lougheed, Julia (Performer) / Jones, Evelyn (Performer) / Miller, Isaac (Performer) / ASU Library. Music Library (Publisher)
Created2018-03-14
ContributorsMoonitz, Olivia (Performer) / ASU Library. Music Library (Publisher)
Created2018-03-13
Description
The focus of this investigation includes three aspects. First, the development of nonlinear reduced order modeling techniques for the prediction of the response of complex structures exhibiting "large" deformations, i.e. a geometrically nonlinear behavior, and modeled within a commercial finite element code. The present investigation builds on a general methodology, successfully validated in recent years on simpler panel structures, by developing a novel identification strategy of the reduced order model parameters, that enables the consideration of the large number of modes needed for complex structures, and by extending an automatic strategy for the selection of the basis functions used to represent accurately the displacement field. These novel developments are successfully validated on the nonlinear static and dynamic responses of a 9-bay panel structure modeled within Nastran. In addition, a multi-scale approach based on Component Mode Synthesis methods is explored. Second, an assessment of the predictive capabilities of nonlinear reduced order models for the prediction of the large displacement and stress fields of panels that have a geometric discontinuity; a flat panel with a notch was used for this assessment. It is demonstrated that the reduced order models of both virgin and notched panels provide a close match of the displacement field obtained from full finite element analyses of the notched panel for moderately large static and dynamic responses. In regards to stresses, it is found that the notched panel reduced order model leads to a close prediction of the stress distribution obtained on the notched panel as computed by the finite element model. Two enrichment techniques, based on superposition of the notch effects on the virgin panel stress field, are proposed to permit a close prediction of the stress distribution of the notched panel from the reduced order model of the virgin one. A very good prediction of the full finite element results is achieved with both enrichments for static and dynamic responses. Finally, computational challenges associated with the solution of the reduced order model equations are discussed. Two alternatives to reduce the computational time for the solution of these problems are explored.
ContributorsPerez, Ricardo Angel (Author) / Mignolet, Marc (Thesis advisor) / Oswald, Jay (Committee member) / Spottswood, Stephen (Committee member) / Peralta, Pedro (Committee member) / Jiang, Hanqing (Committee member) / Arizona State University (Publisher)
Created2012
ContributorsAnderle, Jeff (Performer) / Wegehaupt, David (Performer) / Bennett, Joshua (Performer) / Clements, Katrina (Performer) / Dominguez, Vincent (Performer) / Druesedow, Libby (Performer) / Englert, Patrick (Performer) / Liang, Jack (Performer) / Moonitz, Olivia (Performer) / Ruth, Jeremy (Performer) / ASU Library. Music Library (Publisher)
Created2018-04-09
ContributorsNeidermayer, Tyler (Performer) / Karam, Andrea Luque (Performer) / White, Jonathan (Performer) / Manka, Andrew (Performer) / Chaston, Aubrey (Performer) / ASU Library. Music Library (Publisher)
Created2018-03-31