Dimensionality Reduction

Dimensionality reduction is an important task in machine learning which facilities analysis, compression and visualization of high dimensional data. The problem is that most of the times the machine learning algorithms (e.g. methos for clustering, classification, regression, etc.) don't need to use all the features from the dataset to get great results; in fact, some cases they work better with a reduced dataset. It has a long history as a method for data visualization and for extracting low dimensional features.

The primary objective of dimensionality reduction, as the name implies, is to reduce the number of features in the data while retaining as much relevant information as possible. This type of technique is useful in various scenarios:

• Data and Model Interpretation: Dimensionality reduction methods can help simplify the data and model for users and stakeholders. By reducing the quantity of variables, we can focus on the key factors that influence the outcomes. This makes it easier to understand and interpret the model's behavior, as well as communicate the results to non-technical audiences.

• Decrease Training Time: Dimensionality reduction can contribute to reducing the training time of machine learning models. When working with high-dimensional datasets, the training process can become computationally expensive and time-consuming. By removing irrelevant or redundant information and features, we reduce the complexity of the data and the model, which improves the speed of the training process. This is particularly beneficial when working real-time applications, where efficiency is crucial.

• Variance Reduction: Dimensionality reduction techniques can reinforce the generalization of machine learning models by reducing the variance. High-dimensional datasets often contain noise and irrelevant features that can lead to overfitting, this occurs when the model memorizes the data instead of learning patterns. By focusing on the most informative and discriminative features, we improve the model's ability to generalize well to unseen data. In this way, the machine learning model can perform more robust and reliable predictions.

• Data Compression: Dimensionality reduction methods can be applied to compress the data in situations where storage or computational resources are limited. By reducing the number of features, we also reduce the memory footprint required to store the data and the computational resources needed to process it. This compression is beneficial in scenarios such as big data analysis, where efficient storage and processing are critical for scalability and performance.

There are two different techniques in dimensionality reduction: feature selection and feature extraction. 

• Feature Selection: It focuses on selecting a subset of the original features that are most relevant and informative for the given task. Instead of creating new features, feature selection aims to identify the most discriminative features from the original dataset. These methods can be based on various criteria, such as statistical measures like correlation analysis and mutual information scores, or machine learning algorithms.

• Feature extraction: On the other hand, feature extraction involves transforming the original features into a new set of features with reduced dimensionality. Rather than selecting a subset from the original features, feature extraction techniques create new features that capture the most important information from the original data.

It's important to note that not all dimensionality reduction methods works equal for all the problems, the choice of technique depends on the specific characteristics of the dataset and the objectives of the analysis. Experimentation and evaluation of different dimensionality reduction methods are necessary to find the most suitable approach for a given task.