Li Chu

Li Chu, Xiao Bingjia, Yuan Qiping

Recently, Transformer-base models have made significant progress in the field of time series prediction which have achieved good results and become baseline models beyond Dlinear. The paper proposes an U-Net time series prediction model (UnetTSF) with linear complexity, which adopts the U-Net architecture. We are the first to use FPN technology to extract features from time series data, replacing the method of decomposing time series data into trend and seasonal terms, while designing a fusion structure suitable for time series data. After testing on 8 open-source datasets, compared to the best linear model DLiner. Out of 32 testing projects, 31 achieved the best results. The average decrease in mse is 10.1%, while the average decrease in mae is 9.1%. Compared with the complex transformer-base PatchTST, UnetTSF obtained 9 optimal results for mse and 15 optimal results for mae in 32 testing projects.

Li Chu, Rui Wang, Xiao-Jun Wu

Collaborative representation-based classification (CRC) has demonstrated remarkable progress in the past few years because of its closed-form analytical solutions. However, the existing CRC methods are incapable of processing the nonlinear variational information directly. Recent advances illustrate that how to effectively model these nonlinear variational information and learn invariant representations is an open challenge in the community of computer vision and pattern recognition To this end, we try to design a new algorithm to handle this problem. Firstly, the second-order statistic, i.e., covariance matrix is applied to model the original image sets. Due to the space formed by a set of nonsingular covariance matrices is a well-known Symmetric Positive Definite (SPD) manifold, generalising the Euclidean collaborative representation to the SPD manifold is not an easy task. Then, we devise two strategies to cope with this issue. One attempts to embed the SPD manifold-valued data representations into an associated tangent space via the matrix logarithm map. Another is to embed them into a Reproducing Kernel Hilbert Space (RKHS) by utilizing the Riemannian kernel function. After these two treatments, CRC is applicable to the SPD manifold-valued features. The evaluations on four banchmarking datasets justify its effectiveness.