{"id":189687,"date":"2013-07-26T00:00:00","date_gmt":"2013-07-30T12:09:04","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/parallel-coordinates-visual-multidimensional-geometry-and-its-applications\/"},"modified":"2016-08-02T06:11:42","modified_gmt":"2016-08-02T13:11:42","slug":"parallel-coordinates-visual-multidimensional-geometry-and-its-applications","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/parallel-coordinates-visual-multidimensional-geometry-and-its-applications\/","title":{"rendered":"Parallel Coordinates: Visual Multidimensional Geometry and its Applications"},"content":{"rendered":"<div class=\"asset-content\">\n<p>With parallel coordinates the perceptual barrier imposed by our 3-dimensional habitation is breached enabling the visualization of multidimensional problems. A powerful knowledge discovery process is illustrated on real multivariate datasets and an efficient classifier finds the minimal set of variables needed (features) to characterize a selected subset.<\/p>\n<p>Hypersurfaces in N-space are represented by (N \u22121) linked planar regions (patterns). This is equivalent to describing the hypersurface by its normal vectors, rather than projections as in standard surface descriptions. These patterns reveal surface characteristics i.e. developable, convexity, non-convexities (i.e. folds, concavities). Non-orientable surfaces (i.e. like the M\u00a8obius strip) yield stunning patterns unlocking new geometrical insights. This representation is preferable for some applications (like ray-tracing) even in 3-D. With this methodology our 3-dimensional experience serves as a laboratory for visually discovering properties, in the spirit of Geometry, from the patterns of 3-D surfaces and then prove their generalization for N-dimensions. The patterns persist in the presence of errors which is good news for the applications including visualization for BIG DATA.<\/p>\n<p>The parallel coordinates methodology is used in collision avoidance and conflict resolution algorithms for air traffic control (3 USA patents), computer vision (USA patent), data mining (USA patent), multi-objective optimization, intelligent process control and elsewhere.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>With parallel coordinates the perceptual barrier imposed by our 3-dimensional habitation is breached enabling the visualization of multidimensional problems. A powerful knowledge discovery process is illustrated on real multivariate datasets and an efficient classifier finds the minimal set of variables needed (features) to characterize a selected subset. Hypersurfaces in N-space are represented by (N \u22121) [&hellip;]<\/p>\n","protected":false},"featured_media":197777,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"footnotes":""},"research-area":[],"msr-video-type":[206954],"msr-locale":[268875],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-189687","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-video-type-microsoft-research-talks","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/aTkzWEB14Lo\/","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/189687"}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":0,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/189687\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/197777"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=189687"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=189687"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=189687"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=189687"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=189687"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=189687"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}