{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,2]],"date-time":"2025-04-02T14:02:53Z","timestamp":1743602573977},"reference-count":0,"publisher":"IOS Press","isbn-type":[{"value":"9781643683461","type":"print"},{"value":"9781643683478","type":"electronic"}],"license":[{"start":{"date-parts":[[2022,10,18]],"date-time":"2022-10-18T00:00:00Z","timestamp":1666051200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,10,18]]},"abstract":"<jats:p>Recently shape constrained classification has gained popularity in the machine learning literature in order to exploit extra model information besides raw data features. In this paper, we present a new Lattice Linear Discriminant Analysis (Lattice-LDA) classifier, which allows to take shape constraints of data inputs, such as monotonicity and convexity\/concavity. Lattice-LDA constructs a nonparametric nonlinear discriminant hyperplane for classification, using an additive format of 1-D lattice functions (piecewise linear functions). Moreover, the new classifier features in taking complex shape constraints including combinations of shapes or S-shape. We optimize the model parameters using the Adaptive Moment Estimation (Adam) algorithm embedding stepwise projections which guarantee feasibility of the shape constraints. Through simulation and real-world examples, we demonstrate that the new classifier could accurately recover the nonlinear marginal effect functions and improve classification accuracy when additional shape information is present.<\/jats:p>","DOI":"10.3233\/faia220373","type":"book-chapter","created":{"date-parts":[[2022,10,31]],"date-time":"2022-10-31T09:31:45Z","timestamp":1667208705000},"source":"Crossref","is-referenced-by-count":1,"title":["Lattice Linear Discriminant Analysis for Shape Constrained Classification"],"prefix":"10.3233","author":[{"given":"Geng","family":"Deng","sequence":"first","affiliation":[{"name":"Corporate Model Risk, Wells Fargo"}]},{"given":"Yaoguo","family":"Xie","sequence":"additional","affiliation":[{"name":"Corporate Model Risk, Wells Fargo"}]},{"given":"Xindong","family":"Wang","sequence":"additional","affiliation":[{"name":"Corporate Model Risk, Wells Fargo"}]},{"given":"Qiang","family":"Fu","sequence":"additional","affiliation":[{"name":"Corporate Model Risk, Wells Fargo"}]}],"member":"7437","container-title":["Frontiers in Artificial Intelligence and Applications","Fuzzy Systems and Data Mining VIII"],"original-title":[],"link":[{"URL":"https:\/\/ebooks.iospress.nl\/pdf\/doi\/10.3233\/FAIA220373","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,31]],"date-time":"2022-10-31T09:32:16Z","timestamp":1667208736000},"score":1,"resource":{"primary":{"URL":"https:\/\/ebooks.iospress.nl\/doi\/10.3233\/FAIA220373"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,18]]},"ISBN":["9781643683461","9781643683478"],"references-count":0,"URL":"https:\/\/doi.org\/10.3233\/faia220373","relation":{},"ISSN":["0922-6389","1879-8314"],"issn-type":[{"value":"0922-6389","type":"print"},{"value":"1879-8314","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,10,18]]}}}