Summary of Robust Svd Made Easy: a Fast and Reliable Algorithm For Large-scale Data Analysis, by Sangil Han et al.
Robust SVD Made Easy: A fast and reliable algorithm for large-scale data analysis
by Sangil Han, Kyoowon Kim, Sungkyu Jung
First submitted to arxiv on: 15 Feb 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Statistics Theory (math.ST)
GrooveSquid.com Paper Summaries
GrooveSquid.com’s goal is to make artificial intelligence research accessible by summarizing AI papers in simpler terms. Each summary below covers the same AI paper, written at different levels of difficulty. The medium difficulty and low difficulty versions are original summaries written by GrooveSquid.com, while the high difficulty version is the paper’s original abstract. Feel free to learn from the version that suits you best!
| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper introduces an efficient algorithm called Spherically Normalized SVD (SNSVD) for robust singular value decomposition (SVD). The traditional SVD is sensitive to outliers, which can lead to inaccurate results. Existing robust SVD algorithms often trade off speed for accuracy or fail in the presence of only a few outliers. In contrast, SNSVD is highly insensitive to outliers, computationally scalable, and provides accurate approximations of singular vectors. It achieves remarkable speed by using only two applications of a standard reduced-rank SVD algorithm on appropriately scaled data, outperforming competing algorithms in computation times. The proposed algorithm also includes new notions of breakdown points for matrix-valued input, such as row-wise, column-wise, and block-wise breakdown points, to assess the robustness of the approximated singular vectors and their subspaces against data contamination. Theoretical and empirical analyses demonstrate that SNSVD exhibits higher breakdown points compared to standard SVD and its modifications. Empirical validation demonstrates the effectiveness of SNSVD in applications such as robust low-rank approximation and robust principal component analysis of high-dimensional microarray datasets. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary SVD is an important tool in machine learning, but it’s not good at dealing with outliers in data. This paper makes a new algorithm that can handle outliers better, called Spherically Normalized SVD (SNSVD). It’s fast and works well even when there are only a few bad data points. The algorithm also helps us understand how well the results will hold up if our data is messed up. |
Keywords
* Artificial intelligence * Machine learning * Principal component analysis
