Dimensionality Reduction

Dimensionality reduction refers to the process of reducing the number of input variables in a dataset. In high-dimensional datasets, it can be very difficult to visualize the relationships between variables or even to understand the dataset itself. Dimensionality reduction techniques can help handle this 'curse of dimensionality' by translating high-dimensional data into a lower-dimensional space.

How Dimensionality Reduction works

Dimensionality reduction works by identifying and removing redundant or irrelevant features, or by creating new composite features that effectively capture the most important information from the original set. This process can be carried out using various methods.

Feature Selection is a straightforward method that involves choosing a subset of the original features without any transformation. It can be done using techniques like backward elimination, forward selection, and random forests.

Feature Extraction, on the other hand, transforms the data in the high-dimensional space to a space of fewer dimensions. Techniques used include Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), and Generalized Discriminant Analysis (GDA).

PCA, for example, works by identifying the hyperplane that lies closest to the data and then it projects the data onto it. The axes on this plane are called principal components. The first principal component is the axis that explains the largest amount of variance in the data. The second principal component is orthogonal to the first and explains the second highest amount of variance, and so on.

In summary, dimensionality reduction helps in reducing computational complexity, improving model performance, and dealing with multicollinearity in data.