Hierarchical Uniform Manifold Approximation and Projection (HUMAP): A Novel Dimensionality Reduction Technique for Preserving Global and Local Structures across Hierarchy Levels
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.
Formation-Controlled Dimensionality Reduction: A Novel Dynamical System Approach for Manifold Learning
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.
Robust and Flexible Principal Directions via Flag Manifolds
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.
Algorithms for Handling Noisy Data with Negative Values in Non-Negative Matrix Factorization
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.
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