Topological and statistical behavior classifiers for tracking applications

Bendich, Paul; Chin, Sang; Clark, J.L.; DeSena, Jonathan T.; Harer, John; Munch, Elizabeth; Newman, Andrew; Porter, David W.; Rouse, David B.; Strawn, Nate; Watkins, Adam

doi:10.1109/taes.2016.160405

Cited by 20 publications

(32 citation statements)

References 22 publications

(18 reference statements)

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“…Other approaches to the same problem include analyzing the diagram as an image, as in Bendich et al (2014), or basing features on more sophisticated algebraic geometry, as advocated in Adcock, Carlsson and Carlsson (2013).…”

Section: Detailed Analysis Of Brain Artery Datamentioning

confidence: 99%

Persistent homology analysis of brain artery trees

Bendich¹,

Marron²,

Miller³

et al. 2016

Ann. Appl. Stat.

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235

227

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New representations of tree-structured data objects, using ideas from topological data analysis, enable improved statistical analyses of a population of brain artery trees. A number of representations of each data tree arise from persistence diagrams that quantify branching and looping of vessels at multiple scales. Novel approaches to the statistical analysis, through various summaries of the persistence diagrams, lead to heightened correlations with covariates such as age and sex, relative to earlier analyses of this data set. The correlation with age continues to be significant even after controlling for correlations from earlier significant summaries.

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Section: Detailed Analysis Of Brain Artery Datamentioning

confidence: 99%

Persistent homology analysis of brain artery trees

Bendich¹,

Marron²,

Miller³

et al. 2016

Ann. Appl. Stat.

Self Cite

235

227

View full text Add to dashboard Cite

show abstract

“…We also generated point sets with an iterated function system. For this a discrete distribution is defined on values (0, 1,2,3,4) with corresponding probabilities 1 3 , 1 6 , 1 6 , 1 6 , 1 6 . We denote this distribution by IFS.…”

Section: Iterated Function System (Ifs)mentioning

confidence: 99%

Metrics and Stabilization in One Parameter Persistence

Chachólski¹,

Riihimäki²

2020

SIAM J. Appl. Algebra Geometry

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We propose the use of persistent homology in a supervised way. We believe homological persistence is fundamentally not about decomposition theorems but a central role is played by a choice of metrics. Choosing a pseudometric between persistent vector spaces leads to a model. Fitting this model is what we believe supervised homological persistence is. We develop theory behind constructing such models and we give evidence of the usefulness of this approach in concrete data analysis tasks.

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“…tests( [3], [22]). This work analyzed motion primitives directly from imagery (in this case, WAMI) modalities.…”

Section: Multiple Hypothesis Trackingmentioning

confidence: 99%

Geometric cross-modal comparison of heterogeneous sensor data

Tralie¹,

Smith

Borggren

et al. 2018

2018 IEEE Aerospace Conference

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In this work, we address the problem of cross-modal comparison of aerial data streams. A variety of simulated automobile trajectories are sensed using two different modalities: full-motion video, and radio-frequency (RF) signals received by detectors at various locations. The information represented by the two modalities is compared 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. Several metrics for comparing SSMs are explored, including a cutting-edge time-warping technique that can simultaneously handle local time warping and partial matches, while also controlling for the change in geometry between feature spaces of the two modalities. We note that this technique is quite general, and does not depend on the choice of modalities. In this particular setting, we demonstrate that the cross-modal distance between SSMs corresponding to the same trajectory type is smaller than the cross-modal distance between SSMs corresponding to distinct trajectory types, and we formalize this observation via precision-recall metrics in experiments. Finally, we comment on promising implications of these ideas for future integration into multiple-hypothesis tracking systems.

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Topological and statistical behavior classifiers for tracking applications

Cited by 20 publications

References 22 publications

Persistent homology analysis of brain artery trees

Persistent homology analysis of brain artery trees

Metrics and Stabilization in One Parameter Persistence

Geometric cross-modal comparison of heterogeneous sensor data

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