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New Computational Geometry Methods f...

Wang, Xiangyu.

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New Computational Geometry Methods for Some Fundamental Machine Learning Problems.

Record Type:	Electronic resources : Monograph/item
Title/Author:	New Computational Geometry Methods for Some Fundamental Machine Learning Problems./
Author:	Wang, Xiangyu.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2018,
Description:	110 p.
Notes:	Source: Dissertation Abstracts International, Volume: 80-02(E), Section: B.
Contained By:	Dissertation Abstracts International80-02B(E).
Subject:	Computer science. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10846523
ISBN:	9780438455696

New Computational Geometry Methods for Some Fundamental Machine Learning Problems.
Wang, Xiangyu.

New Computational Geometry Methods for Some Fundamental Machine Learning Problems. - Ann Arbor : ProQuest Dissertations & Theses, 2018 - 110 p.

Source: Dissertation Abstracts International, Volume: 80-02(E), Section: B.

Thesis (Ph.D.)--State University of New York at Buffalo, 2018.

Machine learning concerns the construction of techniques that can learn from and make predictions on data. The computational geometry can play a crucial and natural role in machine learning when exploring the data structure. In this research work, we develop several geometric algorithms to solve three fundamental but important machine learning problems. First, we propose a novel collaborative filtering approach for predicting the unobserved links in a network (or graph) with both topological and node features. Our approach improves the well-known compressed sensing based matrix completion method by introducing a new multiple-independent-Bernoulli-distribution model as the data sampling mask. It makes better link predictions since the model is more general and better matches the data distributions in many real-world networks, such as social networks like Facebook. Second, we consider the problem of clustering a set of uncertain data, where each of them consists of a point-set indicating its possible locations. The objective is to identify the representative point for each uncertain data point and group them into k clusters so as to minimize the total clustering cost. Our problem does not assume any given probability distribution for each uncertain data point, and thus needs to consider all points to determine its representative point. We propose a novel sparse Non-negative Matrix Factorization (NMF) method which measures the similarity of uncertain points by their most commonly shared features. Consequently, a divide-and-conquer approach can be adopted to dramatically improve the efficiency. A novel diagonal l0-constraint and its l1 relaxation are proposed to overcome the challenge of determining the representative points. Third, we address a fundamental re-weighted low rank approximation problem by proposing a novel accelerated Alternative Minimization (ALM) framework with momentum. In our problem, the method needs to synchronically adjust the weights according to related constraints, while factorizing the input matrix. We first eliminate the normal ALM procedures by performing an effective variable reduction on the original objective function. Then, to improve the robustness and further accelerate the ALM, we design a new intermediate acceleration stage on the weights and impose it into the existing Nesterov Accelerated Gradient Descent (NAG) scheme. Besides, our method is built for general ALM, including both convex and non-convex kernels. The outperforming convergence rate is confirmed by a solid analysis based on Kurdyka- Lojasiewicz property. The effectiveness of all the three works is fully supported by related theoretical analysis and experimental results on some benchmark datasets.

ISBN: 9780438455696Subjects--Topical Terms:

523869
Computer science.

New Computational Geometry Methods for Some Fundamental Machine Learning Problems.
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520 $a Machine learning concerns the construction of techniques that can learn from and make predictions on data. The computational geometry can play a crucial and natural role in machine learning when exploring the data structure. In this research work, we develop several geometric algorithms to solve three fundamental but important machine learning problems. First, we propose a novel collaborative filtering approach for predicting the unobserved links in a network (or graph) with both topological and node features. Our approach improves the well-known compressed sensing based matrix completion method by introducing a new multiple-independent-Bernoulli-distribution model as the data sampling mask. It makes better link predictions since the model is more general and better matches the data distributions in many real-world networks, such as social networks like Facebook. Second, we consider the problem of clustering a set of uncertain data, where each of them consists of a point-set indicating its possible locations. The objective is to identify the representative point for each uncertain data point and group them into k clusters so as to minimize the total clustering cost. Our problem does not assume any given probability distribution for each uncertain data point, and thus needs to consider all points to determine its representative point. We propose a novel sparse Non-negative Matrix Factorization (NMF) method which measures the similarity of uncertain points by their most commonly shared features. Consequently, a divide-and-conquer approach can be adopted to dramatically improve the efficiency. A novel diagonal l0-constraint and its l1 relaxation are proposed to overcome the challenge of determining the representative points. Third, we address a fundamental re-weighted low rank approximation problem by proposing a novel accelerated Alternative Minimization (ALM) framework with momentum. In our problem, the method needs to synchronically adjust the weights according to related constraints, while factorizing the input matrix. We first eliminate the normal ALM procedures by performing an effective variable reduction on the original objective function. Then, to improve the robustness and further accelerate the ALM, we design a new intermediate acceleration stage on the weights and impose it into the existing Nesterov Accelerated Gradient Descent (NAG) scheme. Besides, our method is built for general ALM, including both convex and non-convex kernels. The outperforming convergence rate is confirmed by a solid analysis based on Kurdyka- Lojasiewicz property. The effectiveness of all the three works is fully supported by related theoretical analysis and experimental results on some benchmark datasets.
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