Closed-Form, Provable, and Robust PCA via Leverage Statistics and Innovation Search

Mostafa Rahmani, Ping Li

Research output: Contribution to journalArticlepeer-review


The idea of Innovation Search, which was initially proposed for data clustering, was recently used for outlier detection. In the application of Innovation Search for outlier detection, the directions of innovation were utilized to measure the innovation of the data points. We study the Innovation Values computed by the Innovation Search algorithm under a quadratic cost function and it is proved that Innovation Values with the new cost function are equivalent to Leverage Scores. This interesting connection is utilized to establish several theoretical guarantees for a Leverage Score based robust PCA method and to design a new robust PCA method. The theoretical results include performance guarantees with different models for the distribution of outliers and the distribution of inliers. In addition, we demonstrate the robustness of the algorithms against the presence of noise. The numerical and theoretical studies indicate that while the presented approach is fast and closed-form, it can outperform most of the existing algorithms.

Original languageEnglish (US)
Article number9429896
Pages (from-to)3132-3144
Number of pages13
JournalIEEE Transactions on Signal Processing
StatePublished - 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Electrical and Electronic Engineering


  • Innovation Search
  • Leverage Statistics
  • Robust PCA
  • outlier detection
  • unsupervised learning


Dive into the research topics of 'Closed-Form, Provable, and Robust PCA via Leverage Statistics and Innovation Search'. Together they form a unique fingerprint.

Cite this