This page shows selected topics of our recent research work on tensor computing and multidimensional data analysis. Click the title to read the related paper. A list of more publications can be found here.
Tensor and Hypergraph Models
- Hypergraph matching based on constrained optimization: The matching method does not require any training data.
- Redundancy removal in the compatibility tensor for hypergraphy matching based on CUR decomposition: The matching method does not require any training data and can accommodate non-rigid body motion and large dataset size. This is the first known attempt to use CUR decomposition in pattern matching.
- Computation of HOSVD based on random projections: The algorithms are suitable for implementation on parallel processors.
Co-clustering
- Geometric biclustering method (co-clustering for 2D data) based on the Hough Transform: Patent granted: X. Gan, A. Liew, and H. Yan, "Representation and extraction of biclusters from data arrays," United States Patent 7,849,088, 2010.
- Co-cluster detection in the singular vector spaces: This method can be used for finding coherent co-cluster patterns in tensor data with an arbitrary number of modes.
- Summary of hyperplane based methods for co-clustering: A large dataset may contain only small coherent patterns, which can be detected using co-clustering.
- Co-clustering for facial expression feature selection and recognition: This is the first known attempt to use co-clustering for feature selection.
Hardware Accelerators
- FPGA based parallel processors for non-negative tensor decomposition: The algorithms can also be implemented on GPU to speed up the computation.
- FPGA based parallel processors for singular spectrum analysis of Hankel tensors: This is an example of collaborations between mathematicians and computer engineers. A speed-up from 172 to 1004 is achieved compared with the CPU implementation.
Machine Learning Algorithms
- Online spatio-temporal tensor learning: In video analysis, SVD can be updated continuously. The method works effectively for face tracking and facial expression recognition.
- Unsupervised domain adaptation based on manifold learning: Collecting training data is time-consuming and costly to train a classifier. This work makes it possible to use information from a labeled source domain in an unlabeled target domain.
Multidimensional Data Analysis in Imaging, Biology, and Medicine
- Tensor feature for night-time vehicle detection: This method can detect and classify cars, taxis, buses, and mini-buses.
- Dynamic background removal in videos: A novel method, principal mode component analysis (PMCA), is developed to solve the challenging problem of subtracting the moving background from video data.
- 4D cell data analysis: An automated system, CShaper, is developed for cell segmentation, tracking, and visualization from microscopic images.
- Tensor features of gait dynamics data in Parkinson's disease: Discriminating characteristics are discovered from multisensor time series of gait force between Parkinson's disease and healthy control cohorts.
- Tensor decomposition for cancer drug sensitivity analysis: Protein-ligand interaction fingerprints from tensor data provide powerful features for the sensitivity prediction of lung cancer drugs.
