{"type":"ScholarlyArticle","title":"Continuous nonlinear dimensionality reduction by kernel Eigenmaps","authors":[{"name":"Matthew Brand","slug":"matthew-brand","given":"Matthew","family":"Brand","affiliation":""}],"abstract":"We equate nonlinear dimensionality reduction (NLDR) to graph embedding with side information about the vertices, and derive a solution to either problem in the form of a kernel-based mixture of affine maps from the ambient space to the target space. Unlike most spectral NLDR methods, the central eigenproblem can be made relatively small, and the result is a continuous mapping defined over the entire space, not just the datapoints. A demonstration is made to visualizing the distribution of word usages (as a proxy to word meanings) in a sample of the machine learning literature.","doi":null,"url":"https://ijcai.org/proceedings/2003/81","pdf":"https://ijcai.org/proceedings/2003/0081.pdf","markdown":"https://ijcai.org/proceedings/2003/81.md","bibtex":"https://ijcai.org/proceedings/2003/bibtex/81","volume":{"slug":"2003","title":"Proceedings of the Eighteenth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2003","url":"https://ijcai.org/proceedings/2003/","year":2003,"location":"Acapulco, Mexico","dates":"","editors":"Georg Gottlob","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":81,"pages":{"first":547,"last":553},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}