Partial Sum Minimization of Singular Values in Robust PCA: Algorithm and Applications.

Area of Science:

• Computer Vision
• Machine Learning
• Data Science

Background:

• Robust Principal Component Analysis (RPCA) is crucial for data corrupted by sparse noise.
• Conventional RPCA methods using rank minimization do not fully leverage known target rank information in low-level vision problems.

Purpose of the Study:

• To develop an improved RPCA method that effectively utilizes a priori target rank information.
• To investigate an alternative objective function for rank minimization in RPCA.

Main Methods:

• Proposed minimizing the partial sum of singular values instead of the nuclear norm.
• This method implicitly enforces the target rank constraint during optimization.

Main Results:

• The proposed method achieves a higher success rate in low-rank data recovery when sample numbers are deficient.
• Performance is comparable to conventional methods when sample numbers are sufficient.
• Outperformed conventional nuclear norm minimization in various low-level vision applications.

Conclusions:

• Minimizing the partial sum of singular values is a more effective approach for RPCA when target rank is known.
• This method offers significant advantages in low-level vision tasks with limited data.
• The findings suggest a more efficient and accurate way to handle corrupted low-rank data.