Measuring the Data
This addresses the challenge of dimensionality reduction for big data analysis, but appears incremental as it combines existing methods without clear novel breakthroughs.
The paper tackled the problem of identifying the intrinsic manifold in big data by using Optimal Transport to generate tangent spaces and reveal intrinsic dimensions, followed by Koopman Dimensionality Reduction for nonlinear transformation, resulting in encouraging but unspecified outcomes.
Measuring the Data analytically finds the intrinsic manifold in big data. First, Optimal Transport generates the tangent space at each data point from which the intrinsic dimension is revealed. Then, the Koopman Dimensionality Reduction procedure derives a nonlinear transformation from the data to the intrinsic manifold. Measuring the data procedure is presented here, backed up with encouraging results.