{"type":"ScholarlyArticle","title":"Neighborhood MinMax Projections","authors":[{"name":"Feiping Nie","slug":"feiping-nie","given":"Feiping","family":"Nie","affiliation":""},{"name":"Shiming Xiang","slug":"shiming-xiang","given":"Shiming","family":"Xiang","affiliation":""},{"name":"Changshui Zhang","slug":"changshui-zhang","given":"Changshui","family":"Zhang","affiliation":""}],"abstract":"A new algorithm, Neighborhood MinMax Projections(NMMP), is proposed for supervised dimensionality reduction in this paper. The algorithm aims at learning a linear transformation, and focuses only on the pairwise points where the two points are neighbors of each other. After the transformation, the considered pairwise points within the same class are as close as possible, while those between different classes are as far as possible. We formulate this problem as a constrained optimization problem, in which the global optimum can be effectively and efficiently obtained. Compared with the popular supervised method, Linear Discriminant Analysis(LDA), our method has three significant advantages. First, it is able to extract more discriminative features. Second, it can deal with the case where the class distributions are more complex than Gaussian. Third, the singularity problem existing in LDA does not occur naturally. The performance on several data sets demonstrates the effectiveness of the proposed method.","doi":null,"url":"https://ijcai.org/proceedings/2007/160","pdf":"https://ijcai.org/proceedings/2007/0160.pdf","markdown":"https://ijcai.org/proceedings/2007/160.md","bibtex":"https://ijcai.org/proceedings/2007/bibtex/160","volume":{"slug":"2007","title":"Proceedings of the Twentieth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2007","url":"https://ijcai.org/proceedings/2007/","year":2007,"location":"Hyderabad, India","dates":"","editors":"Ramon López de Mántaras","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":160,"pages":{"first":993,"last":997},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}