Matches in SemOpenAlex for { <https://semopenalex.org/work/W4293551267> ?p ?o ?g. }
Showing items 1 to 75 of
75
with 100 items per page.
- W4293551267 abstract "This paper studies the explanation problem for tree- and linearly-ordered array data, a problem motivated by database applications and recently solved for the one-dimensional tree-ordered case. In this paper, one is given a matrix A whose rows and columns have semantics: special subsets of the rows and special subsets of the columns are meaningful, others are not. A submatrix in A is said to be meaningful if and only if it is the cross product of a meaningful row subset and a meaningful column subset, in which case we call it an allowed rectangle. The goal is to explain A as a sparse sum of weighted allowed rectangles. Specifically, we wish to find as few weighted allowed rectangles as possible such that, for all i,j, a_{ij} equals the sum of the weights of all rectangles which include cell (i,j). In this paper we consider the natural cases in which the matrix dimensions are tree-ordered or linearly-ordered. In the tree-ordered case, we are given a rooted tree T1 whose leaves are the rows of A and another, T2, whose leaves are the columns. Nodes of the trees correspond in an obvious way to the sets of their leaf descendants. In the linearly-ordered case, a set of rows or columns is meaningful if and only if it is contiguous. For tree-ordered data, we prove the explanation problem NP-Hard and give a randomized 2-approximation algorithm for it. For linearly-ordered data, we prove the explanation problem NP-Hard and give a 2.56-approximation algorithm. To our knowledge, these are the first results for the problem of sparsely and exactly representing matrices by weighted rectangles." @default.
- W4293551267 created "2022-08-30" @default.
- W4293551267 creator A5010842984 @default.
- W4293551267 creator A5033681881 @default.
- W4293551267 creator A5044332105 @default.
- W4293551267 creator A5087578885 @default.
- W4293551267 date "2011-01-10" @default.
- W4293551267 modified "2023-09-28" @default.
- W4293551267 title "On Parsimonious Explanations for 2-D Tree- and Linearly-Ordered Data" @default.
- W4293551267 doi "https://doi.org/10.48550/arxiv.1101.1941" @default.
- W4293551267 hasPublicationYear "2011" @default.
- W4293551267 type Work @default.
- W4293551267 citedByCount "0" @default.
- W4293551267 crossrefType "posted-content" @default.
- W4293551267 hasAuthorship W4293551267A5010842984 @default.
- W4293551267 hasAuthorship W4293551267A5033681881 @default.
- W4293551267 hasAuthorship W4293551267A5044332105 @default.
- W4293551267 hasAuthorship W4293551267A5087578885 @default.
- W4293551267 hasBestOaLocation W42935512671 @default.
- W4293551267 hasConcept C104140500 @default.
- W4293551267 hasConcept C106487976 @default.
- W4293551267 hasConcept C113174947 @default.
- W4293551267 hasConcept C114614502 @default.
- W4293551267 hasConcept C118615104 @default.
- W4293551267 hasConcept C13355873 @default.
- W4293551267 hasConcept C135598885 @default.
- W4293551267 hasConcept C144901957 @default.
- W4293551267 hasConcept C159985019 @default.
- W4293551267 hasConcept C177264268 @default.
- W4293551267 hasConcept C180645754 @default.
- W4293551267 hasConcept C192562407 @default.
- W4293551267 hasConcept C199360897 @default.
- W4293551267 hasConcept C2524010 @default.
- W4293551267 hasConcept C2780551164 @default.
- W4293551267 hasConcept C2781302577 @default.
- W4293551267 hasConcept C33923547 @default.
- W4293551267 hasConcept C41008148 @default.
- W4293551267 hasConcept C77088390 @default.
- W4293551267 hasConceptScore W4293551267C104140500 @default.
- W4293551267 hasConceptScore W4293551267C106487976 @default.
- W4293551267 hasConceptScore W4293551267C113174947 @default.
- W4293551267 hasConceptScore W4293551267C114614502 @default.
- W4293551267 hasConceptScore W4293551267C118615104 @default.
- W4293551267 hasConceptScore W4293551267C13355873 @default.
- W4293551267 hasConceptScore W4293551267C135598885 @default.
- W4293551267 hasConceptScore W4293551267C144901957 @default.
- W4293551267 hasConceptScore W4293551267C159985019 @default.
- W4293551267 hasConceptScore W4293551267C177264268 @default.
- W4293551267 hasConceptScore W4293551267C180645754 @default.
- W4293551267 hasConceptScore W4293551267C192562407 @default.
- W4293551267 hasConceptScore W4293551267C199360897 @default.
- W4293551267 hasConceptScore W4293551267C2524010 @default.
- W4293551267 hasConceptScore W4293551267C2780551164 @default.
- W4293551267 hasConceptScore W4293551267C2781302577 @default.
- W4293551267 hasConceptScore W4293551267C33923547 @default.
- W4293551267 hasConceptScore W4293551267C41008148 @default.
- W4293551267 hasConceptScore W4293551267C77088390 @default.
- W4293551267 hasLocation W42935512671 @default.
- W4293551267 hasLocation W42935512672 @default.
- W4293551267 hasLocation W42935512673 @default.
- W4293551267 hasOpenAccess W4293551267 @default.
- W4293551267 hasPrimaryLocation W42935512671 @default.
- W4293551267 hasRelatedWork W1495827583 @default.
- W4293551267 hasRelatedWork W1566754092 @default.
- W4293551267 hasRelatedWork W1635682890 @default.
- W4293551267 hasRelatedWork W1984138874 @default.
- W4293551267 hasRelatedWork W2076005816 @default.
- W4293551267 hasRelatedWork W2392826917 @default.
- W4293551267 hasRelatedWork W2591708697 @default.
- W4293551267 hasRelatedWork W3121299875 @default.
- W4293551267 hasRelatedWork W3123744736 @default.
- W4293551267 hasRelatedWork W4293551267 @default.
- W4293551267 isParatext "false" @default.
- W4293551267 isRetracted "false" @default.
- W4293551267 workType "article" @default.