Tensor Computing and Multidimensional Data Analysis

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.