  Analysis of big data has become an increasingly relevant area of research,
with data often represented on discrete networks both constructed and organic.
While for structured domains, there exist intuitive definitions of signals and
frequencies, the definitions are much less obvious for data sets associated
with a given network. Often, the eigenvectors of an induced graph Laplacian are
used to construct an orthogonal set of low-frequency vectors. For larger
graphs, however, the computational cost of creating such structures becomes
untenable, and the quality of the approximation is adequate only for signals
near the span of the set. We propose a construction of a full basis of
frequencies with computational complexity that is near-linear in time and
linear in storage. Using this frequency domain, we can compress data sets on
unstructured graphs more robustly and accurately than spectral-based
constructions.
