Abstract
Nonnegative Least Squares (NNLS) is a general form for many important problems. We consider a special case of NNLS where the input is nonnegative. It is called Totally Nonnegative Least Squares (TNNLS) in the literature. We show a reduction of TNNLS to a single class Support Vector Machine (SVM), thus relating the sparsity of a TNNLS solution to the sparsity of supports in a SVM. This allows us to apply any SVM solver to the TNNLS problem. We get an order of magnitude improvement in running time by first obtaining a smaller version of our original problem with the same solution using a fast approximate SVM solver. Second, we use an exact NNLS solver to obtain the solution. We present experimental evidence that this approach improves the performance of state-of-the-art NNLS solvers by applying it to both randomly generated problems as well as to real datasets, calculating radiation therapy dosages for cancer patients.
| Original language | English (US) |
|---|---|
| Title of host publication | Proceedings of the International Joint Conference on Neural Networks |
| Pages | 1922-1929 |
| Number of pages | 8 |
| DOIs | |
| State | Published - 2011 |
| Externally published | Yes |
| Event | 2011 International Joint Conference on Neural Network, IJCNN 2011 - San Jose, CA, United States Duration: Jul 31 2011 → Aug 5 2011 |
Other
| Other | 2011 International Joint Conference on Neural Network, IJCNN 2011 |
|---|---|
| Country | United States |
| City | San Jose, CA |
| Period | 7/31/11 → 8/5/11 |
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ASJC Scopus subject areas
- Software
- Artificial Intelligence
Cite this
Sparseness and a reduction from Totally Nonnegative Least Squares to SVM. / Potluru, Vamsi K.; Plis, Sergey M.; Luan, Shuang; Calhoun, Vince Daniel; Hayes, Thomas P.
Proceedings of the International Joint Conference on Neural Networks. 2011. p. 1922-1929 6033459.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Sparseness and a reduction from Totally Nonnegative Least Squares to SVM
AU - Potluru, Vamsi K.
AU - Plis, Sergey M.
AU - Luan, Shuang
AU - Calhoun, Vince Daniel
AU - Hayes, Thomas P.
PY - 2011
Y1 - 2011
N2 - Nonnegative Least Squares (NNLS) is a general form for many important problems. We consider a special case of NNLS where the input is nonnegative. It is called Totally Nonnegative Least Squares (TNNLS) in the literature. We show a reduction of TNNLS to a single class Support Vector Machine (SVM), thus relating the sparsity of a TNNLS solution to the sparsity of supports in a SVM. This allows us to apply any SVM solver to the TNNLS problem. We get an order of magnitude improvement in running time by first obtaining a smaller version of our original problem with the same solution using a fast approximate SVM solver. Second, we use an exact NNLS solver to obtain the solution. We present experimental evidence that this approach improves the performance of state-of-the-art NNLS solvers by applying it to both randomly generated problems as well as to real datasets, calculating radiation therapy dosages for cancer patients.
AB - Nonnegative Least Squares (NNLS) is a general form for many important problems. We consider a special case of NNLS where the input is nonnegative. It is called Totally Nonnegative Least Squares (TNNLS) in the literature. We show a reduction of TNNLS to a single class Support Vector Machine (SVM), thus relating the sparsity of a TNNLS solution to the sparsity of supports in a SVM. This allows us to apply any SVM solver to the TNNLS problem. We get an order of magnitude improvement in running time by first obtaining a smaller version of our original problem with the same solution using a fast approximate SVM solver. Second, we use an exact NNLS solver to obtain the solution. We present experimental evidence that this approach improves the performance of state-of-the-art NNLS solvers by applying it to both randomly generated problems as well as to real datasets, calculating radiation therapy dosages for cancer patients.
UR - http://www.scopus.com/inward/record.url?scp=80054750138&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=80054750138&partnerID=8YFLogxK
U2 - 10.1109/IJCNN.2011.6033459
DO - 10.1109/IJCNN.2011.6033459
M3 - Conference contribution
AN - SCOPUS:80054750138
SN - 9781457710865
SP - 1922
EP - 1929
BT - Proceedings of the International Joint Conference on Neural Networks
ER -