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Full-Text Articles in Physical Sciences and Mathematics
Machine Learning With Topological Data Analysis, Ephraim Robert Love
Machine Learning With Topological Data Analysis, Ephraim Robert Love
Doctoral Dissertations
Topological Data Analysis (TDA) is a relatively new focus in the fields of statistics and machine learning. Methods of exploiting the geometry of data, such as clustering, have proven theoretically and empirically invaluable. TDA provides a general framework within which to study topological invariants (shapes) of data, which are more robust to noise and can recover information on higher dimensional features than immediately apparent in the data. A common tool for conducting TDA is persistence homology, which measures the significance of these invariants. Persistence homology has prominent realizations in methods of data visualization, statistics and machine learning. Extending ML with …
Data Analysis Methods Using Persistence Diagrams, Andrew Marchese
Data Analysis Methods Using Persistence Diagrams, Andrew Marchese
Doctoral Dissertations
In recent years, persistent homology techniques have been used to study data and dynamical systems. Using these techniques, information about the shape and geometry of the data and systems leads to important information regarding the periodicity, bistability, and chaos of the underlying systems. In this thesis, we study all aspects of the application of persistent homology to data analysis. In particular, we introduce a new distance on the space of persistence diagrams, and show that it is useful in detecting changes in geometry and topology, which is essential for the supervised learning problem. Moreover, we introduce a clustering framework directly …
On The Role Of Genetic Algorithms In The Pattern Recognition Task Of Classification, Isaac Ben Sherman
On The Role Of Genetic Algorithms In The Pattern Recognition Task Of Classification, Isaac Ben Sherman
Masters Theses
In this dissertation we ask, formulate an apparatus for answering, and answer the following three questions: Where do Genetic Algorithms fit in the greater scheme of pattern recognition? Given primitive mechanics, can Genetic Algorithms match or exceed the performance of theoretically-based methods? Can we build a generic universal Genetic Algorithm for classification? To answer these questions, we develop a genetic algorithm which optimizes MATLAB classifiers and a variable length genetic algorithm which does classification based entirely on boolean logic. We test these algorithms on disparate datasets rooted in cellular biology, music theory, and medicine. We then get results from these …
Accuracy Of Supervised Classification Of Cropland In Sub–Saharan Africa, Sarah Lynn Lewis-Gonzales
Accuracy Of Supervised Classification Of Cropland In Sub–Saharan Africa, Sarah Lynn Lewis-Gonzales
Masters Theses
Mali is a country in sub–Saharan Africa where monitoring of cropped land area would greatly benefit food security initiatives and aid organizations. More importantly village–scale studies on cropped land are fundamental to making a difference in the way we look at cropped land area and food availability in this region of the world. Using Landsat surface reflectance imagery and World View–2 derived labeled data, this study focuses on accuracy of supervised classification methods while addressing various levels of scale. Several classification methods are taken into account to determine the best method possible to produce cropped area estimates using this data. …