{"@type": "dcat:Dataset", "accessLevel": "public", "accrualPeriodicity": "irregular", "bureauCode": ["026:00"], "contactPoint": {"@type": "vcard:Contact", "fn": "Elizabeth Foughty", "hasEmail": "mailto:elizabeth.a.foughty@nasa.gov"}, "description": "OPTIMAL PARTITIONS OF DATA IN HIGHER DIMENSIONS\r\n\r\nBRADLEY W. JACKSON*, JEFFREY D. SCARGLE**, AND CHRIS CUSANZA, DAVID BARNES, DENNIS\r\nKANYGIN, RUSSELL SARMIENTO, SOWMYA SUBRAMANIAM, TZU-WANG CHUANG***\r\n\r\nAbstract. Consider piece-wise constant approximations to a function of several parameters, and\r\nthe problem of finding the best such approximation from measurements at a set of points in the\r\nparameter space. We find good approximate solutions to this problem in two steps: (1) partition\r\nthe parameter space into cells, one for each of the N data points, and (2) collect these cells into\r\nblocks, such that within each block the function is constant to within measurement uncertainty.\r\nWe describe a branch-and-bound algorithm for finding the optimal partition into connected blocks,\r\nas well as an O(N2) dynamic programming algorithm that finds the exact global optimum over this\r\nexponentially large search space, in a data space of any dimension. This second solution relaxes\r\nthe connectivity constraint, and requires additivity and convexity conditions on the block fitness\r\nfunction, but in practice none of these items cause problems. From the wide variety of intelligent\r\ndata understanding applications (including cluster analysis, classification, and anomaly detection)\r\nwe demonstrate two: partitioning of the State of California (2D) and the Universe (3D).", "distribution": [{"@type": "dcat:Distribution", "description": "OPTIMAL PARTITIONS OF DATA IN HIGHER DIMENSIONS", "downloadURL": "https://c3.nasa.gov/dashlink/static/media/publication/Paper_8_.pdf", "format": "PDF", "mediaType": "application/pdf", "title": "Paper 8 .pdf"}], "identifier": "DASHLINK_230", "issued": "2010-10-13", "keyword": ["ames", "dashlink", "nasa"], "landingPage": "https://c3.nasa.gov/dashlink/resources/230/", "modified": "2025-03-31", "programCode": ["026:029"], "publisher": {"@type": "org:Organization", "name": "Dashlink"}, "title": "OPTIMAL PARTITIONS OF DATA IN HIGHER DIMENSIONS"}