Spatial correlation tensor and query-augmented active clustering

Deng, Yujia

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https://hdl.handle.net/2142/112986 Copy

Description

Title

Spatial correlation tensor and query-augmented active clustering

Author(s)

Deng, Yujia

Issue Date

2021-07-08

Director of Research (if dissertation) or Advisor (if thesis)

Qu, Annie

Doctoral Committee Chair(s)

Qu, Annie

Committee Member(s)

• Shao, Xiaofeng
• Yang, Yun
• Zhu, Ruoqing

Department of Study

Statistics

Discipline

Statistics

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• tensor
• correlation
• imaging data
• active learning
• metric learning
• constrained clustering

Abstract

The emergence of the high-dimensional personalized data in recent years has created many new tasks and challenges for statistical analysis, including precise medicine, personalized recommendation, auto annotating, etc. These topics have received great attention in the statistics community and could have significant impact on future life. This thesis provides new perspective on solving two problems: how to detect the early breast cancer by multimodality imaging data, and how to do guide the machine to auto-label the dataset efficiently. In the first part, we classify multimodal imaging data by incorporating the pixel correlations. Multi-dimensional tensor data has gained increasing attention recently, especially in biomedical imaging analyses. However, most existing tensor models are only based on the mean information of imaging pixels. Motivated by multimodal optical imaging data in a breast cancer study, we develop a new tensor learning approach to utilize pixel-wise correlation information, which is represented through the higher-order correlation tensor. We propose novel semi-symmetric correlation tensor decomposition method which effectively captures the informative spatial patterns of pixel-wise correlations to facilitate cancer diagnosis. We establish the theoretical properties for recovering structure and for classification consistency. In addition, we develop an efficient algorithm to achieve computational scalability. Our simulation studies and an application on breast cancer imaging data all indicate that the proposed method outperforms other competing methods in terms of pattern recognition and prediction accuracy. In the second part, we propose an active metric learning method for clustering with pairwise constraints. The proposed method actively queries the label of informative instance pairs, while estimating underlying metrics by incorporating unlabeled instance pairs, which leads to a more accurate and efficient clustering process. In particular, we augment the queried constraints by generating more pairwise labels to provide additional information in learning a metric to enhance clustering performance. Furthermore, we increase the robustness of metric learning by updating the learned metric sequentially and penalizing the irrelevant features adaptively. In addition, we propose a novel active query strategy that evaluates the information gain of instance pairs more accurately by incorporating the neighborhood structure, which improves clustering efficiency without extra labeling cost. In theory, we provide a tighter error bound of the proposed metric learning method utilizing augmented queries compared with methods using existing constraints only. Furthermore, we also investigate the improvement using the active query strategy instead of random selection. Numerical studies on simulation settings and real datasets indicate that the proposed method is especially advantageous when the signal-to-noise ratio between significant features and irrelevant features is low.

Graduation Semester

2021-08

Type of Resource

Thesis

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http://hdl.handle.net/2142/112986

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Copyright 2021 by Yujia Deng. All rights reserved.

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