Search results for: GEOMETRIC ANALOGUE

• Geometric analogue of holographic reduced representation

  Publication

  • D. Aerts
  • M. Czachor
  • M. B. De

  - Journal of Mathematical Psychology - Year 2009

  Holographic reduced representations (HRRs) are distributed representations of cognitive structuresbased on superpositions of convolution-bound n-tuples. Restricting HRRs to n-tuples consisting of 1,one reinterprets the variable binding as a representation of the additive group of binary n-tupleswith addition modulo 2. Since convolutions are not defined for vectors, the HRRs cannot be directlyassociated with geometric structures....

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• A comparison of geometric analogues of holographic reduced representations, original holographic reduced representations and binary spatter codes

  Publication

  • -. Ł. A. Patyk
  • M. Czachor
  • D. Aerts

  - Year 2011

  Geometric Analogues of Holographic Reduced Representations (GA HRR) employ role-filler binding based on geometric products. Atomic objects are real-valued vectors in n-dimensional Euclidean space and complex statements belong to a hierarchy of multivectors. The paper reports a battery of tests aimed at comparison of GA HRR with Holographic Reduced Representation (HRR) and Binary Spatter Codes (BSC). Firstly, we perform a test of...

• Distributed Representations Based on Geometric Algebra: the Continuous Model

  Publication

  • A. Patyk-Łońska
  • M. Czachor
  • D. Aerts

  - Informatica - Year 2011

  Authors revise the concept of a distributed representation of data as well as two previously developed models: Holographic Reduced Representation (HRR) and Binary Spatter Codes (BSC). A Geometric Analogue (GAc - ''c'' stands for continuous as opposed to its discrete version) of HRR is introduced - it employs role-filler binding based on geometric products. Atomic objects are real-valued vectors in n-dimensional Euclidean space...

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