A New Surrogating Algorithm by the Complex Graph Fourier Transform (CGFT)

Belda, Jordi; Vergara, Luis; Safont, Gonzalo; Salazar, Addisson; Parcheta, Zuzanna

doi:10.3390/e21080759

Cited by 20 publications

(8 citation statements)

References 57 publications

(73 reference statements)

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“…Additionally, utilizing the graph structure, especially through approaches, like the graph Fourier transform as discussed in ref. [28], can be adopted to improve tracking capabilities, offering a richer representation of data relationships. Moreover, efforts to expand the training dataset with a more diverse range of event camera data could be undertaken.…”

Section: Discussionmentioning

confidence: 99%

Exploring the Potential of Event Camera Imaging for Advancing Remote Pupil-Tracking Techniques

Kang,

Lee,

Jeong

2023

Applied Sciences

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Pupil tracking plays a crucial role in various applications, including human–computer interactions, biometric identification, and Autostereoscopic three-dimensional (3D) displays, such as augmented reality (AR) 3D head-up displays (HUDs). This study aims to explore and compare advancements in pupil-tracking techniques using event camera imaging. Event cameras, also known as neuromorphic cameras, offer unique benefits, such as high temporal resolution and low latency, making them well-suited for capturing fast eye movements. For our research, we selected fast classical machine-learning-based computer vision techniques to develop our remote pupil tracking using event camera images. Our proposed pupil tracker combines local binary-pattern-features-based eye–nose detection with the supervised-descent-method-based eye-nose alignment. We evaluate the performance of event-camera-based techniques in comparison to traditional frame-based approaches to assess their accuracy, robustness, and potential for real-time applications. Consequently, our event-camera-based pupil-tracking method achieved a detection accuracy of 98.1% and a tracking accuracy (pupil precision < 10 mm) of 80.9%. The findings of this study contribute to the field of pupil tracking by providing insights into the strengths and limitations of event camera imaging for accurate and efficient eye tracking.

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Section: Discussionmentioning

confidence: 99%

Exploring the Potential of Event Camera Imaging for Advancing Remote Pupil-Tracking Techniques

Kang,

Lee,

Jeong

2023

Applied Sciences

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“…This approach leads to a slight bias in the distribution of graphs that are generated but benefits from a predictable execution time. Alternatively, recent development of Complex Graph Fourier Transform for surrogating graph data [ 13 ] could possibly be used to generate the synthetic graphs needed for experiments, given that controlling the second smallest eigenvalue of the graph Laplacian guarantees that the generated graph will consist of a single connected component.…”

Section: Methodsmentioning

confidence: 99%

An Information-Theoretic Bound on p-Values for Detecting Communities Shared between Weighted Labeled Graphs

Obradovic

Kovačević

et al. 2022

Entropy

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Extraction of subsets of highly connected nodes (“communities” or modules) is a standard step in the analysis of complex social and biological networks. We here consider the problem of finding a relatively small set of nodes in two labeled weighted graphs that is highly connected in both. While many scoring functions and algorithms tackle the problem, the typically high computational cost of permutation testing required to establish the p-value for the observed pattern presents a major practical obstacle. To address this problem, we here extend the recently proposed CTD (“Connect the Dots”) approach to establish information-theoretic upper bounds on the p-values and lower bounds on the size and connectedness of communities that are detectable. This is an innovation on the applicability of CTD, broadening its use to pairs of graphs.

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“…For future work, we will explore how to gain knowledge of the distribution with even less prior information, so that the current framework can be applied. Complex graph Fourier transform and the more general GGSP have been proposed [12], [50]. It may bring new insights by synergizing these frameworks with our probabilistic approach.…”

Section: Network Infection Spreading: Base Changementioning

confidence: 99%

Graph Signal Processing Over a Probability Space of Shift Operators

Tay

Ortega

2023

IEEE Trans. Signal Process.

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Graph signal processing (GSP) uses a shift operator to define a Fourier basis for the set of graph signals. The shift operator is often chosen to capture the graph topology. However, in many applications, the graph topology may be unknown a priori, its structure uncertain, or generated randomly from a predefined set for each observation. Each graph topology gives rise to a different shift operator. In this paper, we develop a GSP framework over a probability space of shift operators. We develop the corresponding notions of Fourier transform, MFC filters, and band-pass filters, which subsumes classical GSP theory as the special case where the probability space consists of a single shift operator. We show that an MFC filter under this framework is the expectation of random convolution filters in classical GSP, while the notion of bandlimitedness requires additional wiggle room from being simply a fixed point of a band-pass filter. We develop a mechanism that facilitates mapping from one space of shift operators to another, which allows our framework to be applied to a rich set of scenarios. We demonstrate how the theory can be applied by using both synthetic and real datasets.

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A New Surrogating Algorithm by the Complex Graph Fourier Transform (CGFT)

Cited by 20 publications

References 57 publications

Exploring the Potential of Event Camera Imaging for Advancing Remote Pupil-Tracking Techniques

Exploring the Potential of Event Camera Imaging for Advancing Remote Pupil-Tracking Techniques

An Information-Theoretic Bound on p-Values for Detecting Communities Shared between Weighted Labeled Graphs

Graph Signal Processing Over a Probability Space of Shift Operators

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