Learning the Structure of High-Dimensional Manifolds with Self-Organizing Maps for Accurate Information Extraction

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dc.contributor.advisorMerenyi, Erzsebeten_US
dc.creatorZhang, Lilien_US
dc.date.accessioned2013-03-08T00:40:24Zen_US
dc.date.available2013-03-08T00:40:24Zen_US
dc.date.issued2011en_US
dc.description.abstractThis work aims to improve the capability of accurate information extraction from high-dimensional data, with a specific neural learning paradigm, the Self-Organizing Map (SOM). The SOM is an unsupervised learning algorithm that can faithfully sense the manifold structure and support supervised learning of relevant information from the data. Yet open problems regarding SOM learning exist. We focus on the following two issues. (1) Evaluation of topology preservation. Topology preservation is essential for SOMs in faithful representation of manifold structure. However, in reality, topology violations are not unusual, especially when the data have complicated structure. Measures capable of accurately quantifying and informatively expressing topology violations are lacking. One contribution of this work is a new measure, the Weighted Differential Topographic Function ( WDTF ), which differentiates an existing measure, the Topographic Function ( TF ), and incorporates detailed data distribution as an importance weighting of violations to distinguish severe violations from insignificant ones. Another contribution is an interactive visual tool, TopoView, which facilitates the visual inspection of violations on the SOM lattice. We show the effectiveness of the combined use of the WDTF and TopoView through a simple two-dimensional data set and two hyperspectral images. (2) Learning multiple latent variables from high-dimensional data. We use an existing two-layer SOM-hybrid supervised architecture, which captures the manifold structure in its SOM hidden layer, and then, uses its output layer to perform the supervised learning of latent variables. In the customary way, the output layer only uses the strongest output of the SOM neurons. This severely limits the learning capability. We allow multiple, k , strongest responses of the SOM neurons for the supervised learning. Moreover, the fact that different latent variables can be best learned with different values of k motivates a new neural architecture, the Conjoined Twins, which extends the existing architecture with additional copies of the output layer, for preferential use of different values of k in the learning of different latent variables. We also automate the customization of k for different variables with the statistics derived from the SOM. The Conjoined Twins shows its effectiveness in the inference of two physical parameters from Near-Infrared spectra of planetary ices.en_US
dc.format.extent182 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS STAT. 2011 ZHANGen_US
dc.identifier.citationZhang, Lili. "Learning the Structure of High-Dimensional Manifolds with Self-Organizing Maps for Accurate Information Extraction." (2011) Diss., Rice University. <a href="https://hdl.handle.net/1911/70515">https://hdl.handle.net/1911/70515</a>.en_US
dc.identifier.digitalZhangLilien_US
dc.identifier.urihttps://hdl.handle.net/1911/70515en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectApplied sciencesen_US
dc.subjectPure sciencesen_US
dc.subjectManifold learningen_US
dc.subjectSelf-organizing mapsen_US
dc.subjectNeural networksen_US
dc.subjectComputer engineeringen_US
dc.subjectTheoretical physicsen_US
dc.titleLearning the Structure of High-Dimensional Manifolds with Self-Organizing Maps for Accurate Information Extractionen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentStatisticsen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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