Searching for Topological Symmetry in Data Haystack
Finding interesting symmetrical topological structures in high-dimensional systems is an important problem in statistical machine learning. Limited amount of available high-dimensional data and its sensitivity to noise pose computational challenges to find symmetry. Our paper presents a new method to find local symmetries in a low-dimensional 2-D grid structure which is embedded in high-dimensional 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 2-D 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.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Machine-learned metrics for predicting the likelihood of success in materials discovery
Materials discovery is often compared to the challenge of finding a needle in a haystack. While much work has focused on accurately predicting the properties of candidate materials with machine learning (ML), which amoun…
Re-thinking Temporal Search for Long-Form Video Understanding
Efficient understanding of long-form videos remains a significant challenge in computer vision. In this work, we revisit temporal search paradigms for long-form video understanding, studying a fundamental issue pertainin…
Computational EfficiencyFormVideo UnderstandingVisual LocalizationBig data searching using words
Big data analytics is one of the most promising areas of new research and development in computer science, enterprises, e-commerce, and defense. For many organizations, big data is regarded as one of their most important…
Topological Data AnalysisHyperSpacetime: Complex Algebro-Geometric Analysis of Intelligence Quantum Entanglement Convergent Evolution (Extended Abstract)
Far from the Madding Cloud When groups of ants in haystack as agents Descending gudied by curvatures instead of gradients No powerful enough in changing their environments Being inferior adapters instead of equal game…
Learning Chern Numbers of Topological Insulators with Gauge Equivariant Neural Networks
Equivariant network architectures are a well-established tool for predicting invariant or equivariant quantities. However, almost all learning problems considered in this context feature a global symmetry, i.e. each poin…