Incomplete-Data Oriented Multiview Dimension Reduction via Sparse Low-Rank Representation.

Area of Science:

• Machine Learning
• Data Science
• Computer Vision

Background:

• Traditional dimension reduction methods assume complete data across all views, which is often not true in real-world scenarios.
• Missing values in multiview data due to noise or equipment failure render most existing methods ineffective.
• Developing robust dimension reduction techniques for incomplete multiview data is crucial for practical applications.

Purpose of the Study:

• To develop a novel framework for dimension reduction on incomplete multiview data.
• To mathematically formulate the problem as sparse low-rank representation through multiview subspace (SRRS) learning.
• To propose three new methods for handling missing values and performing dimension reduction in multiview datasets.

Main Methods:

• Introduced Sparse Low-Rank Representation through Multiview Subspace (SRRS) learning to jointly impute missing values and reduce dimensions.
• Developed three novel methods: multiview subspace learning via graph embedding, structured sparsity, and sparse multiview feature selection via rank minimization.
• Elaborated objective functions and optimization algorithms for each proposed method.

Main Results:

• Extensive experiments on toy and real-world datasets (face images, news, activity, neuroimaging) demonstrate superior performance.
• The proposed SRRS-based methods significantly outperform state-of-the-art comparable methods in data recovery, clustering, and classification.
• Integrating sparsity and low-rankness provides a clear advantage over using either property individually.

Conclusions:

• The proposed SRRS framework effectively handles dimension reduction for incomplete multiview data by imputing missing values.
• The developed methods offer robust solutions for various downstream tasks, including clustering and classification.
• The study highlights the importance of addressing data incompleteness in multiview learning and demonstrates the efficacy of the proposed approach.