HUMAP is a novel hierarchical dimensionality reduction technique that effectively preserves both global and local structures in the low-dimensional representation of high-dimensional datasets, while maintaining the mental map across hierarchy levels.
A novel nonlinear dynamical system is proposed for dimensionality reduction, inspired by the formation control of mobile agents. The system combines local and global geometric constraints to preserve the intrinsic structure of high-dimensional data.
The authors present a unifying framework for computing robust principal directions of Euclidean and non-Euclidean data using flag manifolds. This framework enables the development of novel dimensionality reduction algorithms by modifying the flag type or altering the norms used in the optimization.
This paper presents two novel algorithms, Shift-NMF and Nearly-NMF, that can handle noisy data with negative values in non-negative matrix factorization (NMF) while maintaining the non-negativity constraints on the templates and coefficients.