To train sophisticated machine learning models one usually needs many
training samples. Especially in healthcare settings these samples can be very
expensive, meaning that one institution alone usually does not have enough on
its own. Merging privacy-sensitive data from different sources is usually
restricted by data security and data protection measures. This can lead to
approaches that reduce data quality by putting noise onto the variables (e.g.,
in $\epsilon$-differential privacy) or omitting certain values (e.g., for
$k$-anonymity). Other measures based on cryptographic methods can lead to very
time-consuming computations, which is especially problematic for larger
multi-omics data. We address this problem by introducing ESCAPED, which stands
for Efficient SeCure And PrivatE Dot product framework, enabling the
computation of the dot product of vectors from multiple sources on a
third-party, which later trains kernel-based machine learning algorithms, while
neither sacrificing privacy nor adding noise. We evaluated our framework on
drug resistance prediction for HIV-infected people and multi-omics
dimensionality reduction and clustering problems in precision medicine. In
terms of execution time, our framework significantly outperforms the
best-fitting existing approaches without sacrificing the performance of the
algorithm. Even though we only show the benefit for kernel-based algorithms,
our framework can open up new research opportunities for further machine
learning models that require the dot product of vectors from multiple sources.

ESCAPPED 是一种高效安全的点积框架，允许训练核心机器学习算法，同时不牺牲隐私，也不添加噪声。在评估上，相对于现有的最佳方法，我们的框架在执行时间上表现得更好，同时不会影响算法的性能。

面向医疗应用的基于核的机器学习算法高效安全私密点乘框架

ESCAPED: Efficient Secure and Private Dot Product Framework for  Kernel-based Machine Learning Algorithms with Applications in Healthcare

We propose a framework for 2D shape analysis using positive definite kernels
defined on Kendall's shape manifold. Different representations of 2D shapes are
known to generate different nonlinear spaces. Due to the nonlinearity of these
spaces, most existing shape classification algorithms resort to nearest
neighbor methods and to learning distances on shape spaces. Here, we propose to
map shapes on Kendall's shape manifold to a high dimensional Hilbert space
where Euclidean geometry applies. To this end, we introduce a kernel on this
manifold that permits such a mapping, and prove its positive definiteness. This
kernel lets us extend kernel-based algorithms developed for Euclidean spaces,
such as SVM, MKL and kernel PCA, to the shape manifold. We demonstrate the
benefits of our approach over the state-of-the-art methods on shape
classification, clustering and retrieval.

使用 Kendall 形状流形上的正定内核提出了一个 2D 形状分析框架，该内核允许我们将形状映射到一个高维希尔伯特空间中，从而使我们能够扩展内核方法并进行形状分类、聚类和检索。

基于希尔伯特空间嵌入的形状分析框架

A Framework for Shape Analysis via Hilbert Space Embedding

Symmetric Positive Definite (SPD) matrices have become popular to encode
image information. Accounting for the geometry of the Riemannian manifold of
SPD matrices has proven key to the success of many algorithms. However, most
existing methods only approximate the true shape of the manifold locally by its
tangent plane. In this paper, inspired by kernel methods, we propose to map SPD
matrices to a high dimensional Hilbert space where Euclidean geometry applies.
To encode the geometry of the manifold in the mapping, we introduce a family of
provably positive definite kernels on the Riemannian manifold of SPD matrices.
These kernels are derived from the Gaussian ker- nel, but exploit different
metrics on the manifold. This lets us extend kernel-based algorithms developed
for Euclidean spaces, such as SVM and kernel PCA, to the Riemannian manifold of
SPD matrices. We demonstrate the benefits of our approach on the problems of
pedestrian detection, ob- ject categorization, texture analysis, 2D motion
segmentation and Diffusion Tensor Imaging (DTI) segmentation.

该文提出了一种针对 Riemann 流形的 SPD 矩阵进行高维映射的方法，使用一组可证明的正定核函数来扩展基于核方法的算法，进而在人行检测、物体分类、纹理分析、2D 运动分割以及扩散张量成像分割等问题上取得了良好的效果。