Name
Abstract | ||
|---|---|---|
A technique for adjusting a minimum volume set of covering ellipsoids technique is elaborated. Solutions to this problem have potential application in one-class classification and clustering problems. Its main original features are: 1) It avoids the direct evaluation of determinants by using diagonalization properties of the involved matrices, 2) it identifies and removes outliers from the estimation process, 3) it avoids binary variables resulting from the combinatorial character of the assignment problem that are replaced by continuous variables in the range [0,1], 4) the problem can be solved by a bilevel algorithm that in its first level determines the ellipsoids and in its second level reassigns the data points to ellipsoids and identifies outliers based on an algorithm that forces the Karush-Kuhn-Tucker conditions to be satisfied. Two theorems provide rigorous bases for the proposed methods. Finally, a set of examples of application in different fields is given to illustrate the power of the method and its practical performance. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1109/TPAMI.2013.94 | IEEE Trans. Pattern Anal. Mach. Intell. |
Keywords | Field | DocType |
covering approach,binary variable,ellipsoids technique,combinatorial character,potential application,bilevel algorithm,karush-kuhn-tucker condition,continuous variable,data point,minimum volume,clustering problem,assignment problem,data clustering,determinants,karush kuhn tucker conditions,one class classification,data handling,computational geometry,data models,ellipsoids,matrices,classification | One-class classification,Computer science,Computational geometry,Artificial intelligence,Cluster analysis,Karush–Kuhn–Tucker conditions,Data point,Mathematical optimization,Ellipsoid,Pattern recognition,Outlier,Algorithm,Assignment problem | Journal |
Volume | Issue | ISSN |
35 | 12 | 1939-3539 |
Citations | PageRank | References |
2 | 0.39 | 19 |
Authors | ||
7 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| David Martínez-Rego | 1 | 2 | 0.39 |
| Enrique Castillo | 2 | 555 | 59.86 |
| Oscar Fontenla-Romero | 3 | 337 | 39.49 |
| Amparo Alonso-Betanzos | 4 | 885 | 76.98 |
| Martinez-Rego, D. | 5 | 2 | 0.39 |
| Fontenla-Romero, O. | 6 | 2 | 0.39 |
| Alonso-Betanzos, A. | 7 | 2 | 0.39 |