In this study, we consider the realm of covariance matrices in machine
learning, particularly focusing on computing Fr\'echet means on the manifold of
symmetric positive definite matrices, commonly referred to as Karcher or
geometric means. Such means are leveraged in numerous machine-learning tasks.
Relying on advanced statistical tools, we introduce a random matrix
theory-based method that estimates Fr\'echet means, which is particularly
beneficial when dealing with low sample support and a high number of matrices
to average. Our experimental evaluation, involving both synthetic and
real-world EEG and hyperspectral datasets, shows that we largely outperform
state-of-the-art methods.

使用随机矩阵理论的方法估计协方差矩阵中的 Fréchet 均值，在处理低样本支持和大量需要平均的矩阵时表现优于现有方法。

随机矩阵理论改进的对称正定矩阵的弗雷歇均值

Random matrix theory improved Fréchet mean of symmetric positive  definite matrices

The extraction of consensus segmentations from several binary or
probabilistic masks is important to solve various tasks such as the analysis of
inter-rater variability or the fusion of several neural network outputs. One of
the most widely used methods to obtain such a consensus segmentation is the
STAPLE algorithm. In this paper, we first demonstrate that the output of that
algorithm is heavily impacted by the background size of images and the choice
of the prior. We then propose a new method to construct a binary or a
probabilistic consensus segmentation based on the Fr\'{e}chet means of
carefully chosen distances which makes it totally independent of the image
background size. We provide a heuristic approach to optimize this criterion
such that a voxel's class is fully determined by its voxel-wise distance to the
different masks, the connected component it belongs to and the group of raters
who segmented it. We compared extensively our method on several datasets with
the STAPLE method and the naive segmentation averaging method, showing that it
leads to binary consensus masks of intermediate size between Majority Voting
and STAPLE and to different posterior probabilities than Mask Averaging and
STAPLE methods. Our code is available at
this https URL .

提出了一种基于 Fréchet 平均的方法，用于从多个二进制或概率掩模中提取一致的分割，从而完全独立于图像背景大小，并生成与 STAPLE 方法和朴素分割平均方法不同的二进制一致掩模和后验概率。