14,496 research outputs found
Spectral partitioning of time-varying networks with unobserved edges
We discuss a variant of `blind' community detection, in which we aim to
partition an unobserved network from the observation of a (dynamical) graph
signal defined on the network. We consider a scenario where our observed graph
signals are obtained by filtering white noise input, and the underlying network
is different for every observation. In this fashion, the filtered graph signals
can be interpreted as defined on a time-varying network. We model each of the
underlying network realizations as generated by an independent draw from a
latent stochastic blockmodel (SBM). To infer the partition of the latent SBM,
we propose a simple spectral algorithm for which we provide a theoretical
analysis and establish consistency guarantees for the recovery. We illustrate
our results using numerical experiments on synthetic and real data,
highlighting the efficacy of our approach.Comment: 5 pages, 2 figure
Scaling by 5 on a 1/4-Cantor Measure
Each Cantor measure (\mu) with scaling factor 1/(2n) has at least one
associated orthonormal basis of exponential functions (ONB) for L^2(\mu). In
the particular case where the scaling constant for the Cantor measure is 1/4
and two specific ONBs are selected for L^2(\mu), there is a unitary operator U
defined by mapping one ONB to the other. This paper focuses on the case in
which one ONB (\Gamma) is the original Jorgensen-Pedersen ONB for the Cantor
measure (\mu) and the other ONB is is 5\Gamma. The main theorem of the paper
states that the corresponding operator U is ergodic in the sense that only the
constant functions are fixed by U.Comment: 34 page
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