1 / 15

Brief Overview of Research October 10, 2001 Debasis Mitra Florida Institute of Technology

This research provides a brief overview of theoretical, application, and experimental plans and works in qualitative spatio-temporal reasoning from October 10, 2001. Topics include composition tables, symmetries, complexity checking, maximal tractable algebra, and domain-theoretic algorithms. Generalized star ontology and qualitative reasoning in uncertain spaces are explored, along with applications in robotics, bioinformatics, and computer arts. Experimental plans involve statistical studies, identifying problem structures, and developing stochastic algorithms.

canales
Download Presentation

Brief Overview of Research October 10, 2001 Debasis Mitra Florida Institute of Technology

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Brief Overview of Research October 10, 2001 Debasis Mitra Florida Institute of Technology

  2. Mutiple directions • => Theoretical thrusts • Application plans / works • Experimental plans /works

  3. Reasoning Problem Input: B {Northeast | Southwest} A, C {South} B, D {North, East, Northeast} A, C {South, Southeast, East, Northwest} A Question: (1) Are they consistent?, (2) Find one/all consistent solution Representation: A D B C

  4. Star Ontology

  5. Some Observations  basic relations r and l, (1) r.r = r (2) r,r = r.r = either T, when r is a two dimensional region, or {r, 0, r-inverse}, when r is one-dimensional region, with ris the inverse of r (3) r.l = l.r (commutative) (4) r.l = inverse(r. l), where inverse of a set comprises of inverse of the elements in the original set

  6. Star Ontology-6 (Tasks) • Develop Composition table • Study symmetries in the composition table (e.g., a.a =a) • Complexity of consistency checking (NP-hard for sure!) • Find maximal tractable algebra (by observing symmetries) • Develop domain-theoretic algorithms (geometrical algorithms as opposed to algebraic algorithms with the axiomatic Composition-table) • Write papers!!!

  7. Generalized Star Ontology-Alpha • Space divided with 360/alpha, for some integer alpha, starting with ‘East’ • Previous one was star-ontology(6), Cardinal ontology was star ontology(4) • For odd alpha there is no algebra! • All previous questions revisited

  8. Generalized Spatio-temporal reasoning • An ontology-independent framework: • Basic relations w.r.t. a reference object (B) • Connectivity/topology of the basic relations (a qualitative space) • Property of the basic relations (e.g., dimensionality) • What criteria determines complexity (NP-hardness vs tractability) • Domain-theoretic study, algorithms (geometrical) • Specialize to known+unknown ontologies (benefit to applications)

  9. A Qualitative space

  10. Uncertainty-based Spatio-temporal reasoning With Peter Haddawy, U of Wisconsin. Millwaukee: Preference structure elicitation for user modeling (e-commerce), using Knowledge-based ANN, extend KBANN with STR

  11. Application Plans / Works • Robotics (Swedish support from UAV project??): • Direction-interval algebra of Renz • Star algebra(alpha) • Occlusion algebra (Qualitative algebra for objects hiding behind each other) • Bio-informatics: (1) identify qualitative reasoning problems and (2) find out the underlying ontologies • “Geometrical modeling” and qualitative reasoning!! Computer and arts: Picasso/cartoon

  12. Experimental Plans / Works: Background • Big-Oh notation is a big hoax!! (Sorry) • It only provides a very vague (agreed – genuine) idea on a problem’s inherent complexity wrt some canonical parameter (‘size’) • Number of problem instances is infinite, problems have more complex structures than just one parameter (wake up computer “scientists”) • We need to do statistical study, identify structures, develop more stochastic algorithms (which are ‘hot’ algorithms? which areas are succeeding most?)

  13. Experimental Plans / Works • Phase transitions: e.g., Hamiltonian Ckt problem is hardest at ~4.5 arcs/node, 3-SAT is hardest at 4.3 literals per clause • Studied Allen’s algorithm, identified some problem structures using stat-tools (significance studies) • Study star algebra empirically • Develop stochastic algorithms for the generalized algebra

  14. Class-project level to Ph.D. level problems • N-Queens “hybrid” algorithm: implementation, generalize to other CSP areas • Island-based search algorithm: a “practical” add-on heuristic, implement • Multi-dimensional datamodel for numerical data: theoretical study + implement • Deploy AI planning for Component-oriented programming • Visualize spatio-temporal information: [HisViz, Spying-info, etc.]  [Backend database issue, Reasoning algorithms and Data structures issue, GUI issue, etc.]

More Related