The Data Big Bang and the Expanding Digital Universe: High-Dimensional, Complex and Massive Data Sets in an Inflationary Epoch

Table 1

Examples of complex data types and some of the methods for their representation and processing.

Data Types	Some Astronomical Applications	Traditional Approaches to Data Representation & Processing	Advanced Approaches to Data Representation & Processing
Vector Data	(1) Multiwavelength observations.	(1) Linear dimension reduction: PCA and its modifications.	(1) Spectral methods, eigenmaps, diffusion maps, LLE, ISOMAP.
	(2) Multitemporal observations.		(2) Sampling on graphs.
	(3) VO.		(3) Methods based on nonlinear dynamics.
	(4) Spectra.		(4) Neural networks, fuzzy-C sets.
			(5) Genetic algorithms.
			(6) Scientific visualization.
			(7) Compressed sensing.
Manifold-Valued and/or Manifold-Defined	(1) Polarization measurements (CMB).	(1) Various sampling distributions on the sphere.	(1) Healpix (data on 2D sphere).
	(2) Gravitational lensing.		(2) Needlets.
	(3) Solar astrophysics.		(3) Sampling on manifolds.
			(4) Scientific visualization.