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Tutorial - Prof. Alfred Inselberg

Last modified 2014-07-04 17:37

Multidimensional Detective - the Blessings of Dimensionality
Prof. Alfred Inselberg
School of Mathematical Sciences, Tel Aviv University, Israel
Senior Fellow, San Diego Supercomputing Center
Inventor of the multidimensional system of Parallel Coordinates and author of textbook "Parallel Coordinates: VISUAL Multidimensional Geometry", (praised by Stephen Hawking among others.)
www.cs.tau.ac.il/~aiisreal/

Date: July 22, 2014 - 5:45pm
Location: Ballroom 1


Abstract

    Searching a dataset with M items for interesting, depending on the objectives, properties is inherently hard. There are 2M possible subsets anyone of which may satisfy the objectives. The visual cues, our eyes can pick from a good data display, help navigate through this combinatorial explosion. How this is done is part of the story.
    For the visualization of multivariate problems numerous mappings encoding multidimensional information visually into 2-D or 3-D have been invented to augment our perception, which is limited by our 3-dimensional habitation. Wonderful successes like Minard’s “Napoleon’s March to Moscow”, Snow’s “dot map” and others are ad hoc (i.e. one-of-a-kind) and exceptional. Succinct multivariate relations are rarely apparent from static displays; interactivity is essential. In turn, this raises the issues of effective GUI – Graphic User Interface, queries, exploration strategies and information preserving displays. These issues are presented and explained in the tutorial..

    We postulate that a display of datasets with N variables suitable for exploration satisfy the following requirements:
    • should preserve information – the dataset can be completely reconstructed from the picture,
    • has low representational complexity – the computational cost of constructing the displaylow,
    • works for any N – not limited by the dimension
    • treats every variable uniformly,
    • reveals multivariate relations in the dataset – most important and controversial criterion,
    • is based on a rigorous mathematical and algorithmic methodology – to eliminate ambiguity in the results. Also dataset can be recognized after rotations, translations, scalings and perspective transformations. These and additional issues comprising the discovery process are better appreciated via the exploration of real datasets.

    We will show how these are splendidly satisfied using Parallel Coordinates displays armed with well designed queries. Specifically there are three (3) atomic queries which can be combined via Boolean operators to produce complex queries easily controlled by the user. Guidelines and strategies for knowledge discovery are illustrated on several real datasets (financial, process control, credit-score and one with hundreds of variables) with stunning results. A geometric classification algorithm, having low computational complexity, provides the classification rule explicitly and visually. The minimal set of variables, features, required to state the rules is found and ordered by their predictive value. Multivariate relations can be modeled as hypersurfaces and used for decision support. A model of a (real) country’s economy reveals sensitivities, impact of constraints, trade-offs and economic sectors unknowingly competing for the same resources. A smart display for Intensive Care Units determines the patient’s state by the interaction of many variables. An overview of the methodology provides foundational understanding; learning the patterns corresponding to various multivariate relations. These patterns are robust in the presence of errors and that is good news for the applications. A topology of proximity emerges opening the way for visualization in Big Data. For a fun example showing the methodologies power, a 4-D animated visualization for Special Relativity explaining Time Dilation and other “strange” phenomena is presented.

Biography

    Al received a Ph.D. in Mathematics and Physics from the University of Illinois (UICU). He was graduate assistant at the Biological Computer Lab (BCL), where research on Brain Function, Cognition and Learning was carried out (coupled to McCulloch’s Lab at MIT), and continued as Research Asst. Prof. From 1966-1995 he was IBM researcher (reaching a rank just below Fellow) at the Los Angeles Scientific Center and later Yorktown Labs. He developed a Mathematical Model of the (Inner) Ear (TIME, Newsweek 1974) concurrently teaching at UCLA and USC. He joined the Technion’s faculty 1971-73, Ben Gurion University 1977-83, and is at Tel Aviv University since 1995. AI was elected Senior Fellow in Visualization at the San Diego Supercomputing Center (1996), Distinguished Visiting Professor at the Korea University (2008) and National University of Singapore (2011). He invented the multidimensional visualization methodology of Parallel Coordinates which has become widely accepted and applied (Air Traffic Control, Data Mining etc). His textbook on the subject, published by Springer, was praised by Stephen Hawking among others.
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