In this chapter, we learned that dimensionality reduction is the process of transferring data that has a higher dimension into a new representation of data with a lower dimension. It is used to reduce the number of correlated features in a dataset and extract the most informative features. Such a transformation can help increase the performance of other algorithms, reduce computational complexity, and make human-readable visualizations.
We learned that there are two different approaches to solve this task. One is feature selection, which doesn't create new features, while the second one is dimensionality reduction algorithms, which make new feature sets. We also learned that dimensionality reduction algorithms are linear and non-linear and that we should select either type, depending on our data. We saw that there are a lot of different algorithms with different properties and computational complexity and that it makes sense to try different ones to see which are the best solution for particular tasks. Note that different libraries have different implementations for identical algorithms, so their results can differ, even for the same data.
The area of dimensionality reduction algorithms is a field that's in continual development. There is, for example, a new algorithm called Uniform Manifold Approximation and Projection (UMAP) that's based on Riemannian geometry and algebraic topology. It competes with the t-SNE algorithm in terms of visualization quality but also preserves more of the original data's global structure after the transformation is complete. It is also much more computationally effective, which makes it suitable for large-scale datasets. However, at the moment, there is no C++ implementation of it.
In the next chapter, we will discuss classification tasks and how to solve them. Usually, when we have to solve a classification task, we have to divide a group of objects into several subgroups. Objects in such subgroups share some common properties that are distinct from the properties in other subgroups.