Erbo Li

Qi Qin, Erbo Li, Xingxiang Li et al.

Distributed and federated learning are important tools for high-dimensional classification of large datasets. To reduce computational costs and overcome the curse of dimensionality, feature screening plays a pivotal role in eliminating irrelevant features during data preprocessing. However, data heterogeneity, particularly label shifting across different clients, presents significant challenges for feature screening. This paper introduces a general framework that unifies existing screening methods and proposes a novel utility, label-shift robust federated feature screening (LR-FFS), along with its federated estimation procedure. The framework facilitates a uniform analysis of methods and systematically characterizes their behaviors under label shift conditions. Building upon this framework, LR-FFS leverages conditional distribution functions and expectations to address label shift without adding computational burdens and remains robust against model misspecification and outliers. Additionally, the federated procedure ensures computational efficiency and privacy protection while maintaining screening effectiveness comparable to centralized processing. We also provide a false discovery rate (FDR) control method for federated feature screening. Experimental results and theoretical analyses demonstrate LR-FFS's superior performance across diverse client environments, including those with varying class distributions, sample sizes, and missing categorical data.

Erbo Li, Hanlin Mo, Dong Xu et al.

In this paper, we propose relative projective differential invariants (RPDIs) which are invariant to general projective transformations. By using RPDIs and the structural frame of integral invariant, projective weighted moment invariants (PIs) can be constructed very easily. It is first proved that a kind of projective invariants exists in terms of weighted integration of images, with relative differential invariants as the weight functions. Then, some simple instances of PIs are given. In order to ensure the stability and discriminability of PIs, we discuss how to calculate partial derivatives of discrete images more accurately. Since the number of pixels in discrete images before and after the geometric transformation may be different, we design the method to normalize the number of pixels. These ways enhance the performance of PIs. Finally, we carry out some experiments based on synthetic and real image datasets. We choose commonly used moment invariants for comparison. The results indicate that PIs have better performance than other moment invariants in image retrieval and classification. With PIs, one can compare the similarity between images under the projective transformation without knowing the parameters of the transformation, which provides a good tool to shape analysis in image processing, computer vision and pattern recognition.