Searching for Topological Symmetry in Data Haystack
Abstract
Finding interesting symmetrical topological structures in highdimensional systems is an important problem in statistical machine learning. Limited amount of available highdimensional data and its sensitivity to noise pose computational challenges to find symmetry. Our paper presents a new method to find local symmetries in a lowdimensional 2D grid structure which is embedded in highdimensional structure. To compute the symmetry in a grid structure, we introduce three legal grid moves (i) Commutation (ii) Cyclic Permutation (iii) Stabilization on sets of local grid squares, grid blocks. The three grid moves are legal transformations as they preserve the statistical distribution of hamming distances in each grid block. We propose and coin the term of grid symmetry of data on the 2D data grid as the invariance of statistical distributions of hamming distance are preserved after a sequence of grid moves. We have computed and analyzed the grid symmetry of data on multivariate Gaussian distributions and Gamma distributions with noise.
 Publication:

arXiv eprints
 Pub Date:
 March 2016
 DOI:
 10.48550/arXiv.1603.03703
 arXiv:
 arXiv:1603.03703
 Bibcode:
 2016arXiv160303703R
 Keywords:

 Computer Science  Machine Learning