Segmented nestedness in binary data

A binary matrix is fully nested if its columns form a chain of subsets; that is, any two columns are ordered by the subset relation, where we view each column as a subset of the rows indicated by the 1-entries. A binary matrix is k-nested if its columns can be partitioned into k pairwise disjoint blocks, each of which is fully nested. Such nested patterns are encountered, for example, in presence/absence patterns of species in ecological data. We study the automated discovery of k-nestedness on synthetic data and real ecological data. First, we show that k-nestedness can be efficiently discovered in a noisefree setting using a polynomial-time algorithm. Second, we show that it is NP-hard to find a k-nested matrix that minimizes the Hamming distance to a given dataset. Thus, it is likely that in the presence of noise no efficient algorithm exists for discovering k-nestedness in the general case. Third, we develop and evaluate multiple heuristic algorithms for discovering k-nestedness ...

• Type: Journal
• Year: 2011
• Where: SDM
• Authors: Esa Junttila, Petteri Kaski
• Keywords: Data Mining, Paleontological Data, Polynomial Time Algorithm, SDM 2011, Singular Value Decomposition