Name
Title | ||
|---|---|---|
Multidimensional partitioning and bi-partitioning: analysis and application to gene expression data sets |
Abstract | ||
|---|---|---|
Eigenvectors and, more generally, singular vectors, have proved to be useful tools for data mining and dimension reduction. Spectral clustering and reordering algorithms have been designed and implemented in many disciplines, and they can be motivated from several different standpoints. Here we give a general, unified derivation from an applied linear algebra perspective. We use a variational approach that has the benefit of (a) naturally introducing an appropriate scaling, (b) allowing for a solution in any desired dimension, and (c) dealing with both the clustering and bi-clustering issues in the same framework. The motivation and analysis is then backed up with examples involving two large data sets from modern, high-throughput, experimental cell biology. Here, the objects of interest are genes and tissue samples, and the experimental data represents gene activity. We show that looking beyond the dominant, or Fiedler, direction reveals important information. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1080/00207160701210158 | Int. J. Comput. Math. |
Keywords | Field | DocType |
appropriate scaling,data mining,multidimensional partitioning,dimension reduction,large data set,spectral clustering,gene expression data set,bi-clustering issue,different standpoint,gene activity,experimental cell biology,experimental data,microarray,graph laplacian,high throughput,feature selection,mathematics,linear algebra,singular value decomposition,cell biology,eigenvectors | Singular value decomposition,Linear algebra,Spectral clustering,Mathematical optimization,Dimensionality reduction,Feature selection,Mathematical analysis,Algebraic connectivity,Cluster analysis,Eigenvalues and eigenvectors,Mathematics | Journal |
Volume | Issue | ISSN |
85 | 3-4 | 0020-7160 |
Citations | PageRank | References |
1 | 0.40 | 10 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Gabriela Kalna | 1 | 13 | 2.17 |
| J. Keith Vass | 2 | 28 | 1.47 |
| Desmond J. Higham | 3 | 1304 | 209.01 |