Dimension reduction is increasingly applied to high-dimensional biomedical
data to improve its interpretability. When datasets are reduced to two
dimensions, each observation is assigned an x and y coordinates and is
represented as a point on a scatter plot. A significant challenge lies in
interpreting the meaning of the x and y axes due to the complexities inherent
in dimension reduction. This study addresses this challenge by using the x and
y coordinates derived from dimension reduction to calculate class and feature
centroids, which can be overlaid onto the scatter plots. This method connects
the low-dimension space to the original high-dimensional space. We illustrate
the utility of this approach with data derived from the phenotypes of three
neurogenetic diseases and demonstrate how the addition of class and feature
centroids increases the interpretability of scatter plots.

通过使用由降维得到的 x 和 y 坐标来计算类别质心和特征质心并将其叠加在散点图上，本研究解决了将 x 和 y 轴的含义解释复杂性的问题，展示了这种方法在三种神经遗传疾病表型数据中的应用及类别质心和特征质心的添加如何增加散点图的可解释性。

利用类别和特征质心增强降维散点图

Enhancing Dimension-Reduced Scatter Plots with Class and Feature  Centroids

We propose a method that substantially improves the efficiency of deep
distance metric learning based on the optimization of the triplet loss
function. One epoch of such training process based on a naive optimization of
the triplet loss function has a run-time complexity O(N^3), where N is the
number of training samples. Such optimization scales poorly, and the most
common approach proposed to address this high complexity issue is based on
sub-sampling the set of triplets needed for the training process. Another
approach explored in the field relies on an ad-hoc linearization (in terms of
N) of the triplet loss that introduces class centroids, which must be optimized
using the whole training set for each mini-batch - this means that a naive
implementation of this approach has run-time complexity O(N^2). This complexity
issue is usually mitigated with poor, but computationally cheap, approximate
centroid optimization methods. In this paper, we first propose a solid theory
on the linearization of the triplet loss with the use of class centroids, where
the main conclusion is that our new linear loss represents a tight upper-bound
to the triplet loss. Furthermore, based on the theory above, we propose a
training algorithm that no longer requires the centroid optimization step,
which means that our approach is the first in the field with a guaranteed
linear run-time complexity. We show that the training of deep distance metric
learning methods using the proposed upper-bound is substantially faster than
triplet-based methods, while producing competitive retrieval accuracy results
on benchmark datasets (CUB-200-2011 and CAR196).

本文提出了一种新的线性损失函数来优化深度距离度量学习中的三元组损失函数，无需使用类别中心点最优化步骤，并有了实际运行时间复杂度为线性的算法。该方法在基准数据集上达到了竞争性的检索准确性结果。