3 research outputs found
Geometric Fusion via Joint Delay Embeddings
We introduce geometric and topological methods to develop a new framework for
fusing multi-sensor time series. This framework consists of two steps: (1) a
joint delay embedding, which reconstructs a high-dimensional state space in
which our sensors correspond to observation functions, and (2) a simple
orthogonalization scheme, which accounts for tangencies between such
observation functions, and produces a more diversified geometry on the
embedding space. We conclude with some synthetic and real-world experiments
demonstrating that our framework outperforms traditional metric fusion methods
Graph Spectral Embedding for Parsimonious Transmission of Multivariate Time Series
We propose a graph spectral representation of time series data that 1) is
parsimoniously encoded to user-demanded resolution; 2) is unsupervised and
performant in data-constrained scenarios; 3) captures event and
event-transition structure within the time series; and 4) has near-linear
computational complexity in both signal length and ambient dimension. This
representation, which we call Laplacian Events Signal Segmentation (LESS), can
be computed on time series of arbitrary dimension and originating from sensors
of arbitrary type. Hence, time series originating from sensors of heterogeneous
type can be compressed to levels demanded by constrained-communication
environments, before being fused at a common center.
Temporal dynamics of the data is summarized without explicit partitioning or
probabilistic modeling. As a proof-of-principle, we apply this technique on
high dimensional wavelet coefficients computed from the Free Spoken Digit
Dataset to generate a memory efficient representation that is interpretable.
Due to its unsupervised and non-parametric nature, LESS representations remain
performant in the digit classification task despite the absence of labels and
limited data
High-Dimensional Data Fusion via Joint Manifold Learning
The emergence of low-cost sensing architectures for diverse modalities has made it possible to deploy sensor networks that acquire large amounts of very high-dimensional data. To cope with such a data deluge, manifold models are often developed that provide a powerful theoretical and algorithmic framework for capturing the intrinsic structure of data governed by a low-dimensional set of parameters.However, these models do not typically take into account dependencies among multiple sensors. We thus propose a new joint manifold framework for data ensembles that exploits such dependencies. We show that joint manifold structure can lead to improved performance for manifold learning. Additionally, we leverage recent results concerning random projections of manifolds to formulate a universal, network-scalable dimensionality reduction scheme that efficiently fuses the data from all sensors