City University of Hong Kong

Professor Hong Yan is going to talk about; 'Efficient Machine Learning Methods Based on Matrix and Tensor CUR Decomposition'

The training of large deep neural networks can be very expensive in term of long computing time, which requires costly equipment and high energy consumption. Vector, matrix and tensor multiplications are among the most time-consuming tasks. In this talk, a CUR decomposition-based method will be presented to reduce the computational complexity. Our basic strategy is to approximate a large low-rank matrix as a product of three much smaller matrices. Then multiplications with these matrices become very efficient. This can increase the speed of the self-attention operations in transformers significantly. Another reason for the long computing time in neural network training is that a large training dataset is needed. Our research group has recently studied a pattern matching method that requires only a small number of training samples. To achieve high accuracy and reliability, we use high-order pattern matching based on hypergraph and tensor models. A difficulty with this approach is that the high-order compatibility tensor is very large. Employing tensor CUR decomposition, we have tackled this problem and proposed an efficient pattern matching algorithm. Based on pattern matching, we have recently developed an intelligent indoor positioning and navigation system, which will be demonstrated in this talk.

Although a multidimensional data array can be very large, it may contain coherence patterns much smaller in size. For example, we may need to detect a subset of genes that co-express under a subset of conditions. In this presentation, we discuss our recently developed co-clustering algorithms for the extraction and analysis of coherent patterns in big datasets. In our method, a co-cluster, corresponding to a coherent pattern, is represented as a low-rank tensor and it can be detected from the intersection of hyperplanes in a high dimensional data space. Our method has been used successfully for DNA and protein data analysis, disease diagnosis, drug therapeutic effect assessment, and feature selection in human facial expression classification. Our method can also be useful for many other real-world data mining, image processing and pattern recognition applications.

We will talk about our recent results on the uniqueness of regular reflection solutions for the potential flow equation in a natural class of self-similar solutions. The approach is based on a nonlinear version of method of continuity. An important property of solutions for the proof of uniqueness is the convexity of the free boundary.

After a brief review on the classical Prandtl system, we introduce our recent work on the well-posedness and high Reynolds numbers limit for the MHD boundary layer that shows the tangential magnetic field stabilizes the boundary layer. And then we will discuss some instability phenomena of the shear flow for both the classical Prandtl and MHD boundary layer systems. The talk includes some recent joint works with Chengjie Liu, Yaguang Wang on the classical Prandtl equation, and with Chengjie Liu and Feng Xie on the magnetohydrodynamic boundary layer.