In this article, I am going to show you how to choose the number of principal components when using principal component analysis for dimensionality reduction.
In the first section, I am going to give you a short answer for those of you who are in a hurry and want to get something working. Later, I am going to provide a more extended explanation for those of you who are interested in understanding PCA.
At the very beginning of the tutorial, I’ll explain the dimensionality of a dataset, what dimensionality reduction means, the main approaches to dimensionality reduction, the reasons for dimensionality reduction and what PCA means. Then, I will go deeper into the topic of PCA by implementing the PCA algorithm with the Scikit-learn machine learning library. This will help you to easily apply PCA to a real-world dataset and get results very fast.
Uniform Manifold Approximation and Projection (UMAP) is a dimension reduction technique that can be used for visualisation similarly to t-SNE, but also for general non-linear dimension reduction. The algorithm is founded on three assumptions about the data
The data is uniformly distributed on Riemannian manifold;
The Riemannian metric is locally constant (or can be approximated as such);
The manifold is locally connected.
From these assumptions it is possible to model the manifold with a fuzzy topological structure. The embedding is found by searching for a low dimensional projection of the data that has the closest possible equivalent fuzzy topological structure.