  In this work, we address fusion of heterogeneous sensor data using
wavelet-based summaries of fused self-similarity information from each sensor.
The technique we develop is quite general, does not require domain specific
knowledge or physical models, and requires no training. Nonetheless, it can
perform surprisingly well at the general task of differentiating classes of
time-ordered behavior sequences which are sensed by more than one modality. As
a demonstration of our capabilities in the audio to video context, we focus on
the differentiation of speech sequences.
  Data from two or more modalities first are represented using self-similarity
matrices(SSMs) corresponding to time-ordered point clouds in feature spaces of
each of these data sources; we note that these feature spaces can be of
entirely different scale and dimensionality.
  A fused similarity template is then derived from the modality-specific SSMs
using a technique called similarity network fusion (SNF). We investigate
pipelines using SNF as both an upstream (feature-level) and a downstream
(ranking-level) fusion technique. Multiscale geometric features of this
template are then extracted using a recently-developed technique called the
scattering transform, and these features are then used to differentiate speech
sequences. This method outperforms unsupervised techniques which operate
directly on the raw data, and it also outperforms stovepiped methods which
operate on SSMs separately derived from the distinct modalities. The benefits
of this method become even more apparent as the simulated peak signal to noise
ratio decreases.
