For a smooth stationary Gaussian field on R d and level ℓ ∈ R, we consider the number of connected components of the excursion set {f ≥ ℓ} (or level set {f = ℓ}) contained in large domains. The mean of this quantity is known to scale like the volume of the domain under general assumptions on the field. We prove that, assuming sufficient decay of correlations (e.g. the Bargmann-Fock field), a central limit theorem holds with volume-order scaling. Previously such a result had only been established for 'additive' geometric functionals of the excursion/level sets (e.g. the volume or Euler characteristic) using Hermite expansions. Our approach, based on a martingale analysis, is more robust and can be generalised to a wider class of topological functionals. A major ingredient in the proof is a third moment bound on critical points, which is of independent interest.
The Planetary Data System (PDS) maintains archives of data collected by
NASA missions that explore our solar system. The PDS Cartography and
Imaging Sciences Node (Imaging Node) provides access to millions of
images of planets, moons, and other bodies. Given the large and
continually growing volume of data, there is a need for tools that
enable users to quickly search for images of interest. Each image
archived at the PDS Imaging Node is described by a rich set of
searchable metadata properties, such as the time it was collected and
the instrument used. However, users often wish to search on the content
of the image to find those images most relevant to their scientific
investigation or individual curiosity.
To enable the content-based search of the large image archives, we
utilized machine learning techniques to create convolution neural
network (CNN) classification models. The initial CNN classification
results for rover missions (i.e., Mars Science Laboratory and Mars
Exploration Rover) and orbiter missions (i.e., Mars Reconnaissance
Orbiter, Cassini, and Galileo) were deployed at the PDS Image Atlas
(https://pds-imaging.jpl.nasa.gov/search) in 2017. With the
content-based search capability, users of the PDS Image Atlas can search
using a list of pre-defined classes and quickly find relevant images.
For example, users can search “Impact ejecta” and find the images
containing impact ejecta from the archive of the Mars Reconnaissance
Orbiter mission.
All of the CNN classification models were trained using the transfer
learning approach, in which we adapted a CNN model pretrained on Earth
images to classify planetary images. Over the past several years, we
employed the following three techniques to improve the efficiency of
collecting labeled data sets, the accuracy of the models, and the
interpretability of the classification results:
· First, we used the marginal-probability based active learning
(MP-AL) algorithm to improve the efficiency of collecting labeled data
sets.
· Second, we used the classifier chain and ensemble approaches to
improve the accuracy of the classification results.
· Third, we incorporated the prototypical part network (ProtoPNet)
architecture to improve the interpretability of the classification
results.
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