[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-124165-en":3,"doc-seo-124165-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},124165,13056703019404,"Miles","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Machine Learning on Induced Geometries - Dissertation","Many high performance machine learning methods rely on dataset geometry to extract features efficiently. This dissertation introduces induced geometry derived from intrinsic measures on a feature network, enabling those high performance techniques to operate on general datasets. The work studies convolutional, graph, and transformer approaches by building minimally sufficient geometries using correlation structures and Isomap projections. Experiments include sentiment analysis and show mixed gains: accuracy can improve while computational costs rise and feature geometry recovery remains partial. Graph networks are made tractable via correlation thresholds and graph coarsening, yielding strong accuracy versus comparable multilayer perceptrons.","Boston University  \nOpenBU [http://open.bu.edu](http://open.bu.edu)  \n\n| Boston University Theses & Dissertations | Boston University Theses & Dissertations |\n| --- | --- |\n| 2024\u003Cbr>Machine learning on | induced geometries |\n\n[https://hdl.handle.net/2144/49961](https://hdl.handle.net/2144/49961)  \n\"Downloaded from OpenBU. Boston University's institutional repository. \"  \nBOSTON UNIVERSITY  \nGRADUATE SCHOOL OF ARTS AND SCIENCES  \nDissertation  \nMACHINE LEARNING ON INDUCED GEOMETRIES  \nby  \nSCOTT DOUTHIT  \nB.S. , Washington State University, 1999  \nM.S. , University of West Florida, 2016  \nSubmitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy  \n© 2024 by  \nSCOTT DOUTHITAll rights reserved  \nApproved by  \nFirst Reader  \nMark Kon, PhD  \nProfessor of Mathematics and Statistics  \nSecond Reader  \nAshis Gangopadhyay, PhD  \nAssociate Professor of Mathematics and Statistics  \nThird Reader  \nJulio Castrillon, PhD  \nResearch Assistant Professor of Mathematics and Statistics  \nFourth Reader  \nMamikon Ginovyan, PhD  \nSenior Lecturer of Mathematics and Statistics  \nWe should be taught not to wait for inspiration to start a thing. Action alawys generates inspiration.  \nInspiration seldom generates action.  \nFrank Tibolt  \niv  \nAcknowledgments  \nI would like to thank Professor Mark Kon for his tireless support though a very long process. I felt I could overcome any setbacks after our conversations. He allowed me the opportunity to explore my own interest and develop my own direction for these task. I am a better writer, better thinker and better statistician because of his efforts.  \nI owe an enormous debt to my family. My wife who stood by me throughout this endeavour, even when it absorbed most of my time. My sister who stepped in to take care of our mother when I was consumed with writing.  \nMACHINE LEARNING ON INDUCED GEOMETRIES  \nSCOTT DOUTHIT  \nBoston University, Graduate School of Arts and Sciences, 2024  \nMajor Professor: Mark Kon, PhD  \nProfessor of Mathematics and Statistics  \nABSTRACT  \nMany high performance machine learning techniques exploit the geometry of the dataset for efficient feature extraction. We produced induced geometry to allow for the use of these high performance methods on general datasets. The induced geometry is based on intrinsic measures from the feature network of the dataset.  \nConvolutional neural networks use the geometry of the dataset to apply re-used filters. Using the correlation structure of the feature network we attempted to create a minimally sufficient geometry for convolution. The technique first created small receptive fields based on highest correlation. It then used the Isomap algorithm to project correlations into the plane, this provided insight into the effectiveness of the method. The method was general and could apply to any dataset including a bag-ofwords model. When used on an unstructured sentiment analysis dataset the results were mixed. While the technique was superior when compared against an identity filter, there was a significant computation cost and the effect size of the performance gain was marginal, due to the partial recovery of the underlying feature geometry. However, the principle of recovery of an underlying feature geometry using feature networks was partially successful and speaks to future improvements.  \nGraph networks exploit the graph structure of a dataset. The application of a graph structure using correlation has a significant drawback; the graph will be fully  \nconnected. Every node will connect to all other nodes. This creates an incredible computational cost on a network and we found that it also produced very poor inference. We developed two methods of addressing this issue. First the use of a correlation threshold value prevented many edges from forming. This reduced overhead and improved accuracy. The second method was the use of a graph coarsening system, merging connected nodes in the training set. These techniques pe","cbCaisS0uwkscTeV","https://ap.wps.com/l/cbCaisS0uwkscTeV","pdf",2593424,1,141,"English","en",105,"# Contents\n## 1 Introduction\n## 1.1 A Brief History of Machine Learning\n## 1.1.1 Early Years\n## 1.1.2 Convolutional Neural Networks\n## 1.1.3 Graph Networks\n## 1.1.4 Transformer Networks\n## 2 Convolutional Feature Extraction for Unstructured Data\n## 2.1 Introduction\n## 2.1.1 Convolutional Neural Networks\n## 2.1.2 Convolutions on Unstructured Data\n## 2.1.3 Isomap\n## 2.1.4 MNIST\n## 2.2 Finding Local Receptive Fields\n## 2.2.1 Correlation Ordering for Adjacency Detection\n## 2.2.2 Adjacency with Correlation Cutoffs\n## 2.2.3 Adjacency with Isomap\n## 2.2.4 Receptive Field Quality Based on Multiple Isomaps\n## 2.2.5 Combined Methods\n## 2.3 Pixel Locations Inside Receptive Fields\n## 2.3.1 Structure Induced by Correlation Ordering\n## 2.3.2 Ordering Methods\n## 2.4 Network Results and Benchmarks\n## 2.4.1 Results Using Perfect Receptive Fields\n## 2.4.2 Correlation Based Networks\n## 2.4.3 Cutoff Comparisons\n## 2.4.4 High Noise and Low","[{\"question\":\"What is induced geometry in this dissertation?\",\"answer\":\"Induced geometry is constructed from intrinsic measures derived from the dataset’s feature network, allowing geometry-aware learning methods to be applied to general datasets.\"},{\"question\":\"How does the convolutional approach create a minimally sufficient geometry?\",\"answer\":\"It uses correlation structure in the feature network to build small receptive fields, then projects correlations into a plane using Isomap to evaluate the method’s effectiveness.\"},{\"question\":\"Why were graph networks difficult to apply directly, and how were they improved?\",\"answer\":\"Directly using correlation leads to a fully connected graph, causing high computational cost and poor inference. The dissertation improves this with correlation thresholds to reduce edges and graph coarsening to merge connected nodes.\"}]","Machine Learning on Induced Geometries - Dissertation | PDF",1785820812,355,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"machine-learning-on-induced-geometries-dissertation","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/machine-learning-on-induced-geometries-dissertation/124165/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-04",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What is induced geometry in this dissertation?","Question",{"text":75,"@type":76},"Induced geometry is constructed from intrinsic measures derived from the dataset’s feature network, allowing geometry-aware learning methods to be applied to general datasets.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the convolutional approach create a minimally sufficient geometry?",{"text":80,"@type":76},"It uses correlation structure in the feature network to build small receptive fields, then projects correlations into a plane using Isomap to evaluate the method’s effectiveness.",{"name":82,"@type":73,"acceptedAnswer":83},"Why were graph networks difficult to apply directly, and how were they improved?",{"text":84,"@type":76},"Directly using correlation leads to a fully connected graph, causing high computational cost and poor inference. 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