Dimensionality reduction methods are employed to decrease data
dimensionality, either to enhance machine learning performance or to facilitate
data visualization in two or three-dimensional spaces. These methods typically
fall into two categories: feature selection and feature transformation. Feature
selection retains significant features, while feature transformation projects
data into a lower-dimensional space, with linear and nonlinear methods. While
nonlinear methods excel in preserving local structures and capturing nonlinear
relationships, they may struggle with interpreting global structures and can be
computationally intensive. Recent algorithms, such as the t-SNE, UMAP, TriMap,
and PaCMAP prioritize preserving local structures, often at the expense of
accurately representing global structures, leading to clusters being spread out
more in lower-dimensional spaces. Moreover, these methods heavily rely on
hyperparameters, making their results sensitive to parameter settings. To
address these limitations, this study introduces a clustering-based approach,
namely CBMAP (Clustering-Based Manifold Approximation and Projection), for
dimensionality reduction. CBMAP aims to preserve both global and local
structures, ensuring that clusters in lower-dimensional spaces closely resemble
those in high-dimensional spaces. Experimental evaluations on benchmark
datasets demonstrate CBMAP's efficacy, offering speed, scalability, and minimal
reliance on hyperparameters. Importantly, CBMAP enables low-dimensional
projection of test data, addressing a critical need in machine learning
applications. CBMAP is made freely available at
this https URL and can be installed from the Python Package
Directory (PyPI) software repository with the command pip install cbmap.

介绍了一种基于聚类的降维方法 CBMAP，旨在同时保留全局和局部结构，提供速度、可扩展性和对超参数依赖较小的解决方案，满足机器学习应用中对测试数据的低维投影的需求。