Bounded manifold completion

Gajamannage, Kelum; Paffenroth, Randy

doi:10.1016/j.patcog.2020.107661

Cited by 7 publications

(7 citation statements)

References 18 publications

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“…Eqns. ( 19), (20), and (21) with R (t) i = [1, 0; 0, 1] for all i's and t's represent the classic Vicsek model. In Sec.…”

Section: Algorithm 2: Lmc For the Reconstruction Of Fragmented Trajectoriesmentioning

confidence: 99%

“…(30) with Eqns. ( 19), (20), and ( 21) to produce the dataset of a collective motion scenario at an obstacle. We approximate the linear rank as well as the nonlinear rank of this spiral dataset as explained in Sec.…”

Section: Collective Motion At An Obstaclementioning

confidence: 99%

“…Since the rank of a dataset can be approximated using two approaches, linear and nonlinear, we provide technical details of those two approaches here. The linear approximation for the rank of a dataset is formulated as the number of non-zero SVs of the Gramian matrix of the squared Euclidean distance matrix of the dataset [20]. For that, first, we compute the squared Euclidean distance matrix between configurations as…”

Section: Linear and Nonlinear Approximation Of Rankmentioning

confidence: 99%

“…Eqns. ( 19), (20), and ( 21) with the rotational matrix in Eqn. ( 24) provide the complete formulation of the system generating the spiral collective motion dataset.…”

Section: Spiral Collective Motionmentioning

confidence: 99%

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Reconstruction of Agents’ Corrupted Trajectories of Collective Motion Using Low-rank Matrix Completion

Gajamannage

Paffenroth

2019

2019 IEEE International Conference on Big Data (Big Data)

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Learning dynamics of collectively moving agents such as fish or humans is an active field in research. Due to natural phenomena such as occlusion and change of illumination, the multi-object methods tracking such dynamics might lose track of the agents where that might result fragmentation in the constructed trajectories. Here, we present an extended deep autoencoder (DA) that we train only on fully observed segments of the trajectories by defining its loss function as the Hadamard product of a binary indicator matrix with the absolute difference between the outputs and the labels. The trajectories of the agents practicing collective motion is low-rank due to mutual interactions and dependencies between the agents that we utilize as the underlying pattern that our Hadamard deep autoencoder (HDA) codes during its training. The performance of our HDA is compared with that of a low-rank matrix completion scheme in the context of fragmented trajectory reconstruction.

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“…Eqns. ( 19), (20), and (21) with R (t) i = [1, 0; 0, 1] for all i's and t's represent the classic Vicsek model. In Sec.…”

Section: Algorithm 2: Lmc For the Reconstruction Of Fragmented Trajectoriesmentioning

confidence: 99%

Section: Collective Motion At An Obstaclementioning

confidence: 99%

Section: Linear and Nonlinear Approximation Of Rankmentioning

confidence: 99%

“…Eqns. ( 19), (20), and ( 21) with the rotational matrix in Eqn. ( 24) provide the complete formulation of the system generating the spiral collective motion dataset.…”

Section: Spiral Collective Motionmentioning

confidence: 99%

See 2 more Smart Citations

Reconstruction of Agents’ Corrupted Trajectories of Collective Motion Using Low-rank Matrix Completion

Gajamannage

Paffenroth

2019

2019 IEEE International Conference on Big Data (Big Data)

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“…Each patch is a point in a ρ 2 -dimensional ambient space where a hidden low-dimensional manifold, describing the prominent features of the noisy image, underlies (Gajamannage et al, 2015a), (Gajamannage et al, 2015b). Revealing this hidden manifold helps to better explain the structure of the patch set and then helps to identify the features in the image (Gajamannage and Paffenroth, 2021). Revealing such a manifold is a nonlinear dimensionality reduction approach (Gajamannage et al, 2019) where the extra dimensions mostly represent noise and minor image features.…”

Section: Introductionmentioning

confidence: 99%

Geodesic Gramian Denoising Applied to the Images Contaminated With Noise Sampled From Diverse Probability Distributions

Park¹,

Gajamannage²,

Sadovski³

2022

Preprint

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As quotidian use of sophisticated cameras surges, people in modern society are more interested in capturing fine-quality images. However, the quality of the images might be inferior to people's expectations due to the noise contamination in the images. Thus, filtering out the noise while preserving vital image features is an essential requirement. Current existing denoising methods have their own assumptions on the probability distribution in which the contaminated noise is sampled for the method to attain its expected denoising performance. In this paper, we utilize our recent Gramian-based filtering scheme to remove noise sampled from five prominent probability distributions from selected images. This method preserves image smoothness by adopting patches partitioned from the image, rather than pixels, and retains vital image features by performing denoising on the manifold underlying the patch space rather than in the image domain. We validate its denoising performance, using three benchmark computer vision test images applied to two state-of-the-art denoising methods, namely BM3D and K-SVD.

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Real-time forecasting of time series in financial markets using sequentially trained dual-LSTMs

Gajamannage

Park

Jayathilake

2023

Expert Systems with Applications

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Bounded manifold completion

Cited by 7 publications

References 18 publications

Reconstruction of Agents’ Corrupted Trajectories of Collective Motion Using Low-rank Matrix Completion

Reconstruction of Agents’ Corrupted Trajectories of Collective Motion Using Low-rank Matrix Completion

Geodesic Gramian Denoising Applied to the Images Contaminated With Noise Sampled From Diverse Probability Distributions

Real-time forecasting of time series in financial markets using sequentially trained dual-LSTMs

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