Research
Research Interests
Machine learning, Computer Vision, and Network Science.
Machine Learning
Tracking of trajectories of mutually interacted collectively moving agents such as fish, birds, insects, and even humans is an active field in computer vision. However, the trajectories produced by multi-object tracking methods might consist of unconstructed segments of trajectories due to natural phenomena such as occlusion, change of illumination, etc., which require robust tracking methods. Some tracking methods employ computationally expensive approximation schemes to connect these segments. We utilize mutual interactions and dependencies between the agents to reconstruct the missing segments of the trajectories. We utilize machine learning techniques to reconstruct incomplete trajectories. We apply this approach to real-life robot swarms and to representative self-propelled particle swarms, simulated by the classic Vicsek model.
Computer Vision
With the sophisticated modern technology in the camera industry, the demand for accurate and visually pleasing images is increasing. However, the quality of images captured by cameras is inevitably degraded by noise. Thus, some processing of images is required to filter out the noise without losing vital image features such as edges, corners, etc. Even though the current literature offers a variety of denoising methods, the fidelity and efficiency of their denoising are sometimes uncertain. We develop computationally efficient image denoising methods that are capable of producing accurate outputs. Some of these methods input patches partitioned from the image rather than pixels that are well known for preserving image smoothness. We perform denoising on the manifold underlying the patch-space rather than that in the image domain to better preserve the features across the whole image.
Network Science
Extracting connectivity information in massive social networks is important for many applications. Algorithms developed for undirected networks cannot be used with social networks characterized by directed edges. We develop methods to extract the network topology from a small sample of distance measures without the need for exhaustive measurements. Real-world directed social networks such as Twitter and US election blogs have hop-distance matrices that are low-rank. Low-rank matrix completion techniques are thus used to recover the complete topology from a relatively small set of measurements. Evaluation of the proposed technique using metrics such as distance distribution, degree distribution, and hop distances show that the proposed technique is effective even when only a small fraction of distance entries are available. For many important network types, physical coordinate systems and physical distances are either difficult to discern or inapplicable. Accordingly, coordinate systems and characterizations based on hop-distance measurements, such as Topology Preserving Maps (TPMs) and Virtual-Coordinate (VC) systems are attractive alternatives to geographic coordinates for many network algorithms. We develop methods to recover the geometric and topological properties of a network with a small set of distance measurements. These methods are sometimes a combination of shortest-path recovery concepts and low-rank matrix completion.
Publications
Peer reviewed
K. Gajamannage, Y. Park, M. Muddamallappa, and S. Mathur. (2024+) Efficient Noise Filtration of Images by Low-Rank Singular Vector Approximations of Geodesics' Gramian Matrix. In review at ACM Transactions on Architecture and Code Optimization. [Preprint]
K. Gajamannage, R. Paffenroth, and A. P. Jayasumana. (2024+) A Patch-based Image Denoising Method Using Eigenvectors of the Geodesics' Gramian Matrix. In review at IEEE Access. [Preprint]
K. Gajamannage and Y. Park. (2023) Real-time Forecasting of Time Series in Financial Markets Using Sequentially Trained Dual-LSTMs. Expert Systems with Applications, 119879. [Preprint] Journal Impact Factor is 8.67
Y. Park, K. Gajamannage, D. Jayathilake, and E. Bollt. (2023) Recurrent Neural Networks for Chaotic Systems: Applications to Ordinary Differential Equations, Collective Motion, and Hydrological Modeling. Chaos: An Interdisciplinary Journal of Nonlinear Science. 33(1), 013109. [Journal][Preprint]
K. Gajamannage, Y. Park, and A. Sadovski. (2023) Geodesic Gramian Denoising Applied to the Images Contaminated With Noise Sampled From Diverse Probability Distributions. IET Image Processing. 17, pp. 114-156 [Journal] [Preprint]
M. Isangediok and K. Gajamannage. (2022) Fraud Detection Using Optimized Machine Learning Tools Under Imbalance Classes. In 2022 IEEE International Conference on Big Data, pp. 4275-4284. IEEE, December 2022. [Journal][Preprint]
K. Gajamannage, Y. Park, R. Paffenroth, and A. P. Jayasumana. (2022) Reconstruction of Fragmented Trajectories of Collective Motion using Hadamard Deep Autoencoders. Pattern Recognition. 131, pp. 108891 [Journal] [Preprint] Journal Impact Factor is 8.52
K. Gajamannage and R. Paffenroth. (2021) Bounded Manifold Completion. Pattern Recognition, 111, pp. 107661. [Preprint] [Journal] Journal Impact Factor is 8.52
K. Gajamannage and R. Paffenroth. (2019) Reconstruction of Agents’ Corrupted Trajectories of Collective Motion Using Low-rank Matrix Completion. In 2019 IEEE International Conference on Big Data (Big Data), pp. 2826-2834. IEEE, 2019. [Journal]
N. Bahadur, R. Paffenroth, and K. Gajamannage. (2019) Dimension Estimation of Equity Markets. In 3-rd International Workshop on Big Data for Financial News and Data, pp. 5491-5498. IEEE, 2019. [Journal]
G. Mahindre, A. P. Jayasumana, K. Gajamannage, and R. Paffenroth. (2019) On Sampling and Recovery of Topology of Directed Social Networks a Low-rank Matrix Completion Based Approach. In 2019 IEEE 44-th Conference on Local Computer Networks (LCN), pp. 324-331. IEEE, 2019. [Journal]
A. P. Jayasumana, R. Paffenroth, G. Mahindre, S. Ramasamy, and K. Gajamannage. (2019) Network Topology Mapping From Partial Virtual Coordinates and Graph Geodesics. IEEE/ACM Transactions on Networking, 27(6), pp. 2405-2417. [Preprint] [Journal]
K. Gajamannage, R. Paffenroth, and E. Bollt. (2019) A Nonlinear Dimensionality Reduction Framework Using Smooth Geodesics. Pattern Recognition, 87, pp. 226-236. [Preprint] [Journal] Journal Impact Factor is 8.52
K. Gajamannage and E. M. Bollt. (2017). Detecting phase Transitions in Collective Motion Using Manifold's Curvature. Mathematical Biosciences and Engineering, 14(2), pp. 437-453. [Preprint] [Journal]
K. Gajamannage, E. M. Bollt, M. A. Porter, and M. S. Dawkins. (2017). Modeling the Lowest-cost Splitting of a Herd of Cows by Optimizing a Cost Function. Chaos: An Interdisciplinary Journal of Nonlinear Science, 27(6), pp. 063114. [Preprint] [Journal]
K. Gajamannage, S. Butail, M. Porfiri, and E. M. Bollt. (2015). Dimensionality Reduction of Collective Motion by Principal Manifolds. Physica D: Nonlinear Phenomena, 291, pp. 62-73. [Preprint] [Journal]
K. Gajamannage, S. Butail, M. Porfiri, and E. M. Bollt. (2015). Identifying Manifolds Underlying Group Motion in Vicsek Agents. European Physical Journal Special Topics, 224, pp. 3245-3256. [Preprint] [Journal]
K. Gajamannage, S. Butail, M. Porfiri, and E. M. Bollt. (2014). Model Reduction of Collective Motion by Principal Manifolds. In Proceedings of the 17-th U.S. National Congress of Theoretical and Applied Mechanics, Michigan State University, MI, USA.
K. Gajamannage and U.N.B. Dissanayake. (2007). An Econometric Model for Hyperinflation. In Proceedings of the Peradeniya University Research Sessions (PURSE) 2007, Sri Lanka, 12(2), pp. 286-287. [Journal]
In preparation
R. Paffenroth, G. Mahindre, K. Gajamannage, and A. P. Jayasumana. A Low Complex Technique to Capture and Characterize Social Network Topology. To be submitted to ACM Transactions on Social Computing.
K. Gajamannage at el. Real-time Prognostic Health Management Using One-to-many Long Short-Term Memory. To be submitted to Expert Systems with Applications.
Invited talks
Low-rank data imputation using Hadamard deep autoencoders, with applications to fragmented trajectory reconstruction of collective motion. In the Department of Computer Science, University of Rhode Island, Kingston, RI, USA. (Nov. 15, 2023)
Real-time Forecasting of Time Series in Financial Markets Using Sequentially Trained Dual-LSTM. In the School of Business, University of Rhode Island, Kingston, RI, USA. (Nov. 10, 2023)
Low-rank data imputation using Hadamard deep autoencoders, with applications to fragmented trajectory reconstruction of collective motion. In the Department of Computer Science, University of Rhode Island, Kingston, RI, USA. (Oct. 13, 2023)
Low-rank data imputation using Hadamard deep autoencoders, with applications to fragmented trajectory reconstruction of collective motion. In the Department of Mathematics and Appl. Math. Science, University of Rhode Island, Kingston, RI, USA. (Sep. 18, 2023)
Low-rank data imputation using Hadamard deep autoencoders, with applications to fragmented trajectory reconstruction of collective motion. In the Department of Mathematics and Statistics, University of Memphis, Memphis, TN, USA. (Mar. 10, 2023)
Bounded Manifold Completion. In the Department of Mathematics and Statistics, American University, Washington, DC, USA. (Mar. 3, 2023)
Low-rank data imputation using Hadamard deep autoencoders, with applications to fragmented trajectory reconstruction of collective motion. In the Department of Mathematics and Statistics, Washington State University, Pulman, WA, USA. (Feb. 24, 2023)
Reconstruction of Fragmented Trajectories of Collective Motion using Hadamard Deep Autoencoders. In the Department of Mathematics and Statistics, James Madison University, Harrisonburg, VA, USA. (Feb. 17, 2023)
Interdisciplinary Approaches to Environmental Data Science. In the Department of Mathematics and Statistics, James Madison University, Harrisonburg, VA, USA. (Feb. 17, 2023)
Positive Semidefinite Matrix Completion. In the Department of Mathematics, Ohio University, Athens, OH, USA. (Feb. 15, 2023)
Introduction to Optimization. In the Department of Mathematics, Ohio University, Athens, OH, USA. (Feb. 15, 2023)
Positive Semidefinite Matrix Completion. In the Department of Mathematics and Applied Mathematical Sciences, University of Rhode Island, Kingston, RI, USA. (Feb. 01, 2023)
Introduction to Optimization. In the Department of Mathematics and Applied Mathematical Sciences, University of Rhode Island, Kingston, RI, USA. (Feb. 01, 2023)
Bounded Manifold Completion. In the Department of Mathematical Sciences, University of Memphis, Memphis, TN, USA. (Jan. 16, 2023)
Bounded Manifold Completion. In the Department of Mathematics, Rowan University, Glassboro, NJ, USA. (Dec. 13, 2022)
Introduction to Optimization. In the Department of Mathematics, Rowan University, Glassboro, NJ, USA. (Dec. 12, 2022)
Positive Semidefinite Matrix Completion. In the School of Mathematical and Statistical Sciences, Southern Illinois University, Carbondale, IL, USA. (March 10, 2022)
Bounded Manifold Completion. In the Department of Mathematics, University of Massachusetts−Boston, Boston, MA, USA. (Feb. 17, 2022)
Reconstruction of Fragmented Trajectories of Collective Motion using Hadamard Deep Autoencoders. In the Department of Mathematics and Statisstics, Texas A&M University–Corpus Christi, Corpus Christi, TX, USA. (Oct. 29, 2021)
Reconstruction of Agents’ Corrupted Trajectories of Collective Motion using Low-Rank Matrix Completion and Hadamard Autoencoders. In the Session of Advances in Collective Behavior and Self-Organization, 2021 SIAM Conference on Dynamical Systems, USA. (May 25, 2021)
Opportunities for Graduate Studies in the USA – My Journey so far. In the Department of Mathematics, Faculty of Science, University of Peradeniya, Peradeniya, Sri Lanka. (August 14, 2020)
Smooth Geodesic Embedding -- A Nonlinear Dimensionality Reduction Method. In the 2-nd Annual TSU-PVAMU Workshop on Artificial Intelligence and Machine Learning, Texas Southern University, Houston, TX, USA. (January 23, 2020)
A Nonlinear Dimensionality Reduction Framework Using Smooth Geodesics. In the Department of Mathematics & Statistics, Texas A&M University–Corpus Christi, Corpus Christi, TX, USA. (October 25, 2019)
Bounded Manifold Completion. In the Department of Mathematics & Statistics, Texas A&M University–Corpus Christi, Corpus Christi, TX, USA. (April 15, 2019)
Conditional Probability, In the Department of Mathematics, DigiPen Institute of Technology, Redmond, WA, USA. (March 29, 2019)
Bounded Manifold Completion. In the Department of Mathematics, DigiPen Institute of Technology, Redmond, WA, USA. (March 29, 2019)
Scatter plots and Correlation. In the Department of Mathematics, State University of New York, Cortland, NY, USA. (March 6, 2019)
Bounded Manifold Completion. In the Department of Mathematics, State University of New York, Cortland, NY, USA. (March 6, 2019)
Central Limit Theorem. In the Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH, USA. (Feb. 15, 2019)
Bounded Manifold Completion. In the Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH, USA. (Feb. 15, 2019)
Introduction to Dimension Reduction and Its Evolution. In Denksport Lecture Series, Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA, USA. (Jan. 28, 2019)
Smoothness Preserving Nonlinear Dimensionality Reduction Using Splines. In the Department of Mathematical Sciences Colloquium, Worcester Polytechnic Institute, Worcester, MA, USA. (Sep. 01, 2017)
Manifold Learning and Dimensionality Reduction. In Clarkson University Chapter of SIAM, Clarkson University, Potsdam, NY, USA. (April 2, 2014)
Contributed talks (conference)
K. Gajamannage, R. Paffenroth, and A. P. Jayasumana. A Patch-based Image Denoising Method Using Eigenvectors of the Geodesics' Gramian Matrix. In Conference of Texas Statisticians (COTS), Corpus Christi, TX, USA. (Sep. 19, 2020)
K. Gajamannage and R. Paffenroth. Reconstruction of agents’ corrupted trajectories of collective motion using low-rank matrix completion. In IEEE Bigdata 2019, Los Angeles, CA, USA. (Dec. 9−12, 2019)
K. Gajamannage and R. Paffenroth. Generalized geodesic approach for nonlinear dimensionality reduction with the aid of matrix completion. In 2018 SIAM Annual Meeting, Portland, OR, USA. (July 9−13, 2018)
K. Gajamannage, R. Paffenroth, and E. M. Bollt. A Nonlinear dimensionality reduction framework using smooth geodesics. In 2017 SIAM Annual Meeting, Pittsburgh, PA, USA. (July 10−14, 2017)
K. Gajamannage, E. M. Bollt. Detecting phase transitions in collective motion using manifold's curvature. In SIAM Conference on Applications of Dynamical Systems 2017, Snowbird, UT, USA. (May 21−25, 2017)
K. Gajamannage, E. M. Bollt, M. A. Porter, and M. S. Dawkins. Modeling an efficient segregation of a herd of cows by minimizing the cost from synchronization. In 2016 SIAM Annual Meeting, Boston, MA, USA. (July 11−15, 2016)
K. Gajamannage, S. Butail, M. Porfiri, and E. M. Bollt. Identifying manifolds underlying group motion in Vicsek agents. In Clarkson University Graduate Research Symposium 2015, Potsdam, NY, USA. (Sep. 28−29, 2015)
K. Gajamannage, S. Butail, M. Porfiri, and E. M. Bollt. Dimensionality reduction of collective motion by principal manifolds. In SIAM Conference on Applications of Dynamical Systems 2015, Snowbird, UT, USA. (May 17−21, 2015)
Posters presentations (conference)
K. Gajamannage, S. Butail, M. Porfiri, and E. M. Bollt. Identifying manifolds underlying group motion in Vicsek agents. In Dynamics Days XXXV, Durham, NC, USA. (Jan. 7−10, 2016)
K. Gajamannage, S. Butail, M. Porfiri, and E. M. Bollt. Model reduction of collective motion by principal manifolds. In 4th New York Conference on Applied Mathematics, Cornel University, Ithaca, NY, USA. (Nov. 09, 2013)
Workshops
Teaching effectively: Engaging a variety of learners. In Teaching Effectiveness Conference 2015, State University of New York, Potsdam, NY, USA. (Oct. 24, 2015)