4 papers
Generalized Image Reconstruction over T-Algebra
Liang Liao, Xuechun Zhang, Xinqiang Wang +2
Principal Component Analysis (PCA) is well known for its capability of dimension reduction and data compression. However, when using PCA for compressing/reconstructing images, imag…
General Data Analytics with Applications to Visual Information Analysis: A Provable Backward-Compatible Semisimple Paradigm over T-Algebra
Liang Liao, Stephen John Maybank
We consider a novel backward-compatible paradigm of general data analytics over a recently-reported semisimple algebra (called t-algebra). We study the abstract algebraic framework…
Intrinsic Dimension Estimation via Nearest Constrained Subspace Classifier
Liang Liao, Stephen John Maybank
We consider the problems of classification and intrinsic dimension estimation on image data. A new subspace based classifier is proposed for supervised classification or intrinsic…
Generalized Visual Information Analysis via Tensorial Algebra
Liang Liao, Stephen John Maybank
Higher order data is modeled using matrices whose entries are numerical arrays of a fixed size. These arrays, called t-scalars, form a commutative ring under the convolution produc…