Quantifying the Conceptual Error in Dimensionality Reduction

Autor:	Johannes Hirth, Tom Hanika
Rok vydání:	2021
Předmět:	Set (abstract data type) Reduction (complexity) Theoretical computer science Computer science Dimensionality reduction Formal concept analysis Conceptual structure Standard problem Matrix decomposition Variety (cybernetics)
Zdroj:	Graph-Based Representation and Reasoning ISBN: 9783030869816 ICCS
DOI:	10.1007/978-3-030-86982-3_8
Popis:	Dimension reduction of data sets is a standard problem in the realm of machine learning and knowledge reasoning. They affect patterns in and dependencies on data dimensions and ultimately influence any decision-making processes. Therefore, a wide variety of reduction procedures are in use, each pursuing different objectives. A so far not considered criterion is the conceptual continuity of the reduction mapping, i.e., the preservation of the conceptual structure with respect to the original data set. Based on the notion scale-measure from formal concept analysis we present in this work a) the theoretical foundations to detect and quantify conceptual errors in data scalings; b) an experimental investigation of our approach on eleven data sets that were respectively treated with a variant of non-negative matrix factorization.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::4a8d064c4c8071255e11e213769a9a74 https://doi.org/10.1007/978-3-030-86982-3_8 Zobrazit plný text záznamu