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Reduced row echelon form and non-linear approximation for subspace segmentation and high-dimensional data clustering
| Content Provider | Semantic Scholar |
|---|---|
| Author | Aldroubi, Akram Sekmen, Ali |
| Copyright Year | 2014 |
| Abstract | Abstract Given a set of data W = { w 1 , … , w N } ∈ R D drawn from a union of subspaces, we focus on determining a nonlinear model of the form U = ⋃ i ∈ I S i , where { S i ⊂ R D } i ∈ I is a set of subspaces, that is nearest to W. The model is then used to classify W into clusters. Our approach is based on the binary reduced row echelon form of data matrix, combined with an iterative scheme based on a non-linear approximation method. We prove that, in absence of noise, our approach can find the number of subspaces, their dimensions, and an orthonormal basis for each subspace S i . We provide a comprehensive analysis of our theory and determine its limitations and strengths in presence of outliers and noise. |
| Starting Page | 271 |
| Ending Page | 287 |
| Page Count | 17 |
| File Format | PDF HTM / HTML |
| DOI | 10.1016/j.acha.2013.12.001 |
| Volume Number | 37 |
| Alternate Webpage(s) | http://www.tnstate.edu/computer_science/Dr.Sekmen_PDF-3.pdf |
| Alternate Webpage(s) | https://doi.org/10.1016/j.acha.2013.12.001 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
