A broadly successful approach to Big Data analysis involves understanding and manipulating not the raw data, but the essence of the data.
This may apply when we "capture" the data during measurements, as in compressed sensing, sampling or streaming algorithms. Not all data is captured, but only a representation suitable for subsequent analyses: in many applications, this representation is succinct—far smaller than the original data—and adequate at least for approximate analyses.
It may also apply when we "store and transport" data, as in compression, distributed sensing and data fusion: a succinct summary of the data might well suffice and save significantly on communication between multiple sites.
Finally, it may apply when we store, analyze and mine data, as in signal analysis, statistical analyses, complex query processing, machine learning or optimization: even sophisticated algorithms may be able to be executed fast and with sufficient accuracy given a succinct representation of the data, saving computing time and space.
Thus succinct representations of data, be they for capture, storage, transportation or analysis, not only make dealing with Big Data more efficient, but in some cases even bring a formidable Big Data task into the realm of the feasible. Succinct representations are possible because of the underlying principles of sparsity in nature.
In this workshop, we will cast a broad net and include many of the perspectives on data reduction that have been developed in various fields, including computer science, statistics, applied mathematics and signal processing. We will also highlight the many applications of such techniques in science and engineering. The workshop, which takes place early in the program, will set the stage for the semester-long activity in in the general area of resource-constrained Big Data analysis.
These presentations were supported in part by an award from the Simons Foundation.