Parallel Hierarchical Affinity Propagation with MapReduce

The accelerated evolution and explosion of the Internet and social media is generating voluminous quantities of data (on zettabyte scales). Paramount amongst the desires to manipulate and extract actionable intelligence from vast big data volumes is the need for scalable, performance-conscious analytics algorithms. To directly address this need, we propose a novel MapReduce implementation of the exemplar-based clustering algorithm known as Affinity Propagation. Our parallelization strategy extends to the multilevel Hierarchical Affinity Propagation algorithm and enables tiered aggregation of unstructured data with minimal free parameters, in principle requiring only a similarity measure between data points. We detail the linear run-time complexity of our approach, overcoming the limiting quadratic complexity of the original algorithm. Experimental validation of our clustering methodology on a variety of synthetic and real data sets (e.g. images and point data) demonstrates our competitiveness against other state-of-the-art MapReduce clustering techniques

Constructions of potentially eventually positive sign patterns with reducible positive part

Potentially eventually positive (PEP) sign patterns were introduced by Berman et al. (Electron. J. Linear Algebra 19 (2010), 108–120), where it was noted that a matrix is PEP if its positive part is primitive, and an example was given of a 3×3 PEP sign pattern with reducible positive part. We extend these results by constructing n×n PEP sign patterns with reducible positive part, for every n≥3.This is an article from Involve 4 (2011): 405, doi:10.2140/involve.2011.4.405. Posted with permission.</p

Potentially eventually exponentially positive sign patterns

We introduce the study of potentially eventually exponentially positive (PEEP) sign patterns and establish several results using the connections between these sign patterns and the potentially eventually positive (PEP) sign patterns. It is shown that the problem of characterizing PEEP sign patterns is not equivalent to that of characterizing PEP sign patterns. A characterization of all 2×2 and 3×3 PEEP sign patterns is given.This is an article from Involve 6 (2013): 261, doi:10.2140/involve.2013.6.261. Posted with permission.</p