  This paper addresses the problem of identifying a very small subset of data
points that belong to a significantly larger massive dataset (i.e., Big Data).
The small number of selected data points must adequately represent and
faithfully characterize the massive Big Data. Such identification process is
known as representative selection [19]. We propose a novel representative
selection framework by generating an l1 norm sparse graph for a given Big-Data
dataset. The Big Data is partitioned recursively into clusters using a spectral
clustering algorithm on the generated sparse graph. We consider each cluster as
one point in a Grassmann manifold, and measure the geodesic distance among
these points. The distances are further analyzed using a min-max algorithm [1]
to extract an optimal subset of clusters. Finally, by considering a sparse
subgraph of each selected cluster, we detect a representative using principal
component centrality [11]. We refer to the proposed representative selection
framework as a Sparse Graph and Grassmann Manifold (SGGM) based approach. To
validate the proposed SGGM framework, we apply it onto the problem of video
summarization where only few video frames, known as key frames, are selected
among a much longer video sequence. A comparison of the results obtained by the
proposed algorithm with the ground truth, which is agreed by multiple human
judges, and with some state-of-the-art methods clearly indicates the viability
of the SGGM framework.
