This dissertation introduces and analyzes algorithms that aim to adaptively handle complex datasets arising in the real-world applications. It contains two major parts. The first part describes an adaptive model of 1-dimensional signals that lies in the field of adaptive time-frequency analysis. It explains a current state-of-the-art work, named the Synchrosqueezed transform, in this field. Then it illustrates two proposed algorithms that use non-parametric regression to reveal the underlying os- cillatory patterns of the targeted 1-dimensional signal, as well as to estimate the instantaneous information, e.g., instantaneous frequency, phase, or amplitude func-
tions, by a statistical pattern driven model.
The second part proposes a population-based imaging technique for human brain
bundle/connectivity recovery. It applies local streamlines as novelly adopted learn- ing/testing features to segment the brain white matter and thus reconstruct the whole brain information. It also develops a module, named as the streamline diffu- sion filtering, to improve the streamline sampling procedure.
Even though these two parts are not related directly, they both rely on an align- ment step to register the latent variables to some coordinate system and thus to facilitate the final inference. Numerical results are shown to validate all the pro- posed algorithms.
","abstract_html":"<p>This dissertation introduces and analyzes algorithms that aim to adaptively handle complex datasets arising in the real-world applications. It contains two major parts. The first part describes an adaptive model of 1-dimensional signals that lies in the field of adaptive time-frequency analysis. It explains a current state-of-the-art work, named the Synchrosqueezed transform, in this field. Then it illustrates two proposed algorithms that use non-parametric regression to reveal the underlying os- cillatory patterns of the targeted 1-dimensional signal, as well as to estimate the instantaneous information, e.g., instantaneous frequency, phase, or amplitude func-</p><p>tions, by a statistical pattern driven model.</p><p>The second part proposes a population-based imaging technique for human brain</p><p>bundle/connectivity recovery. It applies local streamlines as novelly adopted learn- ing/testing features to segment the brain white matter and thus reconstruct the whole brain information. It also develops a module, named as the streamline diffu- sion filtering, to improve the streamline sampling procedure.</p><p>Even though these two parts are not related directly, they both rely on an align- ment step to register the latent variables to some coordinate system and thus to facilitate the final inference. Numerical results are shown to validate all the pro- posed algorithms.</p>","abstract_has_math":false,"creators":["Xu, Jieren"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Xu, Jieren"],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018","date_published":"2018","updated_at":"2026-07-24T02:07:17Z","subjects":["Applied mathematics","Medical imaging","adaptive data analysis","mode decomposition","non-parametric regression","signal processing","statistical learning","structural connectivity analysis"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/10161/17503","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Xu, Jieren"]},{"key":"dc:creator","label":"Author","values":["Xu, Jieren"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2018-09-21T16:09:11Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2019-02-28T09:17:08Z"]},{"key":"dc:date.issued","label":"Date","values":["2018"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Applied mathematics","Medical imaging","adaptive data analysis","mode decomposition","non-parametric regression","signal processing","statistical learning","structural connectivity analysis"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10161/17503"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This dissertation introduces and analyzes algorithms that aim to adaptively handle complex datasets arising in the real-world applications. It contains two major parts. The first part describes an adaptive model of 1-dimensional signals that lies in the field of adaptive time-frequency analysis. It explains a current state-of-the-art work, named the Synchrosqueezed transform, in this field. Then it illustrates two proposed algorithms that use non-parametric regression to reveal the underlying os- cillatory patterns of the targeted 1-dimensional signal, as well as to estimate the instantaneous information, e.g., instantaneous frequency, phase, or amplitude func-
tions, by a statistical pattern driven model.
The second part proposes a population-based imaging technique for human brain
bundle/connectivity recovery. It applies local streamlines as novelly adopted learn- ing/testing features to segment the brain white matter and thus reconstruct the whole brain information. It also develops a module, named as the streamline diffu- sion filtering, to improve the streamline sampling procedure.
Even though these two parts are not related directly, they both rely on an align- ment step to register the latent variables to some coordinate system and thus to facilitate the final inference. Numerical results are shown to validate all the pro- posed algorithms.
"]},{"key":"dc:title","label":"Title","values":["Adaptive Data Representation and Analysis"]}]}],"canonical_facts":{"dc:contributor.advisor":["Xu, Jieren"],"dc:creator":["Xu, Jieren"],"dc:date.accessioned":["2018-09-21T16:09:11Z"],"dc:date.available":["2019-02-28T09:17:08Z"],"dc:date.issued":["2018"],"dc:description.abstract":["This dissertation introduces and analyzes algorithms that aim to adaptively handle complex datasets arising in the real-world applications. It contains two major parts. The first part describes an adaptive model of 1-dimensional signals that lies in the field of adaptive time-frequency analysis. It explains a current state-of-the-art work, named the Synchrosqueezed transform, in this field. Then it illustrates two proposed algorithms that use non-parametric regression to reveal the underlying os- cillatory patterns of the targeted 1-dimensional signal, as well as to estimate the instantaneous information, e.g., instantaneous frequency, phase, or amplitude func-
tions, by a statistical pattern driven model.
The second part proposes a population-based imaging technique for human brain
bundle/connectivity recovery. It applies local streamlines as novelly adopted learn- ing/testing features to segment the brain white matter and thus reconstruct the whole brain information. It also develops a module, named as the streamline diffu- sion filtering, to improve the streamline sampling procedure.
Even though these two parts are not related directly, they both rely on an align- ment step to register the latent variables to some coordinate system and thus to facilitate the final inference. Numerical results are shown to validate all the pro- posed algorithms.
"],"dc:identifier.uri":["https://hdl.handle.net/10161/17503"],"dc:subject":["Applied mathematics","Medical imaging","adaptive data analysis","mode decomposition","non-parametric regression","signal processing","statistical learning","structural connectivity analysis"],"dc:title":["Adaptive Data Representation and Analysis"],"dc:type":["Dissertation"]},"updated_at":"2026-07-24T02:07:17Z"}