  In today's information systems, the availability of massive amounts of data
necessitates the development of fast and accurate algorithms to summarize these
data and represent them in a succinct format. One crucial problem in big data
analytics is the selection of representative instances from large and
massively-distributed data, which is formally known as the Column Subset
Selection (CSS) problem. The solution to this problem enables data analysts to
understand the insights of the data and explore its hidden structure. The
selected instances can also be used for data preprocessing tasks such as
learning a low-dimensional embedding of the data points or computing a low-rank
approximation of the corresponding matrix. This paper presents a fast and
accurate greedy algorithm for large-scale column subset selection. The
algorithm minimizes an objective function which measures the reconstruction
error of the data matrix based on the subset of selected columns. The paper
first presents a centralized greedy algorithm for column subset selection which
depends on a novel recursive formula for calculating the reconstruction error
of the data matrix. The paper then presents a MapReduce algorithm which selects
a few representative columns from a matrix whose columns are massively
distributed across several commodity machines. The algorithm first learns a
concise representation of all columns using random projection, and it then
solves a generalized column subset selection problem at each machine in which a
subset of columns are selected from the sub-matrix on that machine such that
the reconstruction error of the concise representation is minimized. The paper
demonstrates the effectiveness and efficiency of the proposed algorithm through
an empirical evaluation on benchmark data sets.
