Scalable Robust Principal Component Analysis Using Grassmann Averages.

Area of Science:

• Data Science
• Computer Vision
• Machine Learning

Background:

• Manual data verification is infeasible for large datasets, which tend to contain more outliers.
• Principal Component Analysis (PCA) is effective for dimensionality reduction but sensitive to outliers.
• Existing robust PCA methods lack scalability for large-scale applications.

Purpose of the Study:

• To develop a scalable and robust method for principal component analysis (PCA) suitable for large datasets with outliers.
• To introduce a novel algorithm based on Grassmann manifolds for robust data analysis.
• To demonstrate the effectiveness of the proposed method in computer vision applications.

Main Methods:

• Introduced the concept of Grassmann Average (GA) for subspace estimation from zero-mean data.
• Developed a robust averaging technique on the Grassmann manifold.
• Formulated the Trimmed Grassmann Average (TGA) as a robust PCA method with linear computational complexity and minimal memory requirements.

Main Results:

• The Grassmann Average (GA) provides a subspace estimate less sensitive to outliers than traditional PCA for general distributions.
• The Trimmed Grassmann Average (TGA) demonstrates robustness to pixel outliers, making it suitable for computer vision.
• TGA was successfully applied to background modeling, video restoration, and shadow removal.
• Scalability was proven by applying TGA to robust PCA on an entire feature-length film.

Conclusions:

• The Trimmed Grassmann Average (TGA) offers a scalable and robust solution for PCA in large datasets with outliers.
• TGA significantly advances the capabilities of robust PCA, particularly for computer vision tasks.
• The method's efficiency and effectiveness are validated through practical applications and large-scale demonstrations.