Summary of From Explained Variance Of Correlated Components to Pca Without Orthogonality Constraints, by Marie Chavent (imb) et al.
From explained variance of correlated components to PCA without orthogonality constraints
by Marie Chavent, Guy Chavent
First submitted to arxiv on: 7 Feb 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG)
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| 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 addresses the challenge of designing sparse Principal Component Analysis (PCA) by relaxing the orthogonality constraint on loadings. The authors introduce new objective functions, expvar(Y), which measure the variance explained by correlated components Y = AZ. They conduct a comprehensive study of mathematical and numerical properties for six definitions of expvar(Y), concluding that only two are suitable for use in block PCA formulations. The proposed approach enables the design of sparse PCA models without requiring orthogonal loadings. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper helps us better understand how to analyze big data sets by making a change to an old technique called Principal Component Analysis (PCA). Normally, this method requires all the different pieces of information to be separate and not connected. But in this case, we’re going to allow some connections between these pieces, which will make it easier to find important patterns in the data. |
Keywords
* Artificial intelligence * Pca * Principal component analysis
