Name
Abstract | ||
|---|---|---|
A square symmetric matrix is a Robinson similarity matrix if entries in its rows and columns are nondecreasing when moving toward the diagonal. A Robinson similarity matrix can be viewed as the affinity matrix between objects arranged in linear order, where objects closer together have higher affinity. We define a new parameter, Gamma(1), which measures how badly a given matrix fails to be Robinson similarity. Namely, a matrix is Robinson similarity precisely when its Gamma(1) attains zero, and a matrix with small Gamma(1) is close (in the normalized l(1)-norm) to a Robinson similarity matrix. Moreover, both Gamma(1) and the Robinson similarity approximation can be computed in polynomial time. Thus, our parameter recognizes Robinson similarity matrices which are perturbed by noise and can therefore be a useful tool in the problem of seriation of noisy data. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1137/18M1174544 | SIAM JOURNAL ON DISCRETE MATHEMATICS |
Keywords | Field | DocType |
Robinson similarity matrices,Robinsonian matrices,unit interval graphs,seriation,linear embeddings of graphs | Diagonal,Row and column spaces,Discrete mathematics,Noisy data,Combinatorics,Unit interval graphs,Symmetric matrix,Mathematics,Similarity matrix,Seriation (archaeology) | Journal |
Volume | Issue | ISSN |
33 | 2 | 0895-4801 |
Citations | PageRank | References |
0 | 0.34 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mahya Ghandehari | 1 | 21 | 3.43 |
| Jeannette Janssen | 2 | 295 | 32.23 |