What are the main categories of dimensionality reduction techniques?

Feature selection is a process in which a subset of relevant, informative, or predictive features is chosen from the original set. This selection is based on criteria like correlation, mutual information, or statistical significance, which are used to rank and filter the features. By doing this, feature selection effectively reduces the dimensionality of the data, maintaining the integrity of the original values without adding new ones. This technique streamlines the data for analysis and modeling while preserving essential information.

Feature selection is all about doing more with less. In production datasets with thousands of features, not all of them are useful for specific ML use cases. Selecting the least amount of features while keeping the quality of the system the same is crucial from various perspectives: the models don't need to have a high memory footprint, they train faster, use fewer resources, have faster inference times, and are easier to explain and interpret. The methods for feature selection can be split into filter, wrapper, and embedded, and can range from very simple statistical, correlation-based methods, to very complex attention based mechanisms, where the ML model learns what features are important

feature selection is akin to honing in on the essence of a problem. It's about distilling the noise and focusing on the most impactful aspects of the data. Much like a skilled chef selects the finest ingredients for a recipe, feature selection allows data scientists to highlight the key factors driving their models. It not only streamlines computation but also enhances interpretability, providing a clearer narrative about the data's crucial elements. In my experience, a judicious approach to feature selection can significantly improve model efficiency and efficacy.

Feature extraction involves transforming the original features into a lower-dimensional space. This transformation retains the essential information while reducing the dimensionality. Techniques under feature extraction include: Principal Component Analysis (PCA): PCA identifies the directions (principal components) in which the data varies the most and projects the data onto these components, reducing the dimensionality while preserving the variance. Linear Discriminant Analysis (LDA): Unlike PCA, LDA aims to find the feature space that maximizes class separability. It projects data points to a lower-dimensional space while maximizing class differences.

Feature extraction is the next layer of feature selection in a machine learning pipeline. While features are important individually, sometimes combinations of features create more predictive power than just using plain features. Usually, some knowledge of the business problem helps, since analysts know what features drive the best predictive power. However, in huge datasets this is often impractical, thus mechanisms like PCA and LDA create higher order features based on statistical measures. As the research field has developed in the last years, we've seen more advanced methods to extract features, such as attention embeddings, or models that learn how to extract features, without requiring human input.

Feature embedding is not only heavily used in NLP but also in computer vision and recommender system as well. ML algos learn relationships through mathematical operations. All data is represented in numeric form. How effective a model is depends on how good that numeric representation is. Eg, in 1 hot encoding, all unique classes are orthogonal to each other. Words like good, best represent a similar kind of meaning but in 1 hot encoding they all have independent representations. In feature embedding, we create a dense numerical representation of features with relationships encoded in vector space. Similar concepts are grouped together. Popular algorithms are: Word2Vec, BERT for that matter any supervised model can be used for this.

Feature embedding is a technique that represents original features as vectors in a high-dimensional space, where these vectors' distances or similarities indicate the relationships between features. This method employs various techniques like word2vec, GloVe, or BERT, which utilize context, semantics, or syntax to enhance the representation of features. Although feature embedding can increase the data's dimensionality, it makes the data more apt for downstream tasks like classification or clustering, as it enriches the feature set with more nuanced and contextual information.

When using features in isolation, machine learning models can perform well. However, to further elevate their performance, some tricks have to be used when it comes to feature processing. For example, some features might only have predictive power when paired with othets. In this case, attention layers can be used to automatically learn the links between various features. Let's say a machine learning project involves predicting a metric from numbers, images, and text. Those 3 data types don't go together well in a model. However, if the images and sentences are embedded, and passed to the model as numbers, the learning process can continue smoothly. In cases like this one, feature embedding is not only a nice to have, it's a must.

feature learning is like empowering machines to uncover hidden gems within the data. It's akin to giving them the ability to recognize patterns and relationships that might elude human intuition. Utilizing sophisticated algorithms like neural networks, machines can autonomously distill intricate features, providing a deeper understanding of the data's nuances. This process, while complex, often proves invaluable in tasks where manual feature engineering might fall short. Embracing feature learning aligns with the evolving landscape of AI, where machines autonomously adapt to the intricacies of the data they encounter. My experience emphasizes transformative potential of feature learning in unlocking richer insights from complex datasets.

The main goal of feature hashing is to convert a large number of features into a smaller, fixed-size space using a hash function. A hash function maps each feature to a number in a fixed range (the hash table size). This process is deterministic, meaning the same input feature will always produce the same hash value. Feature hashing enhances computational efficiency by eliminating the need to store a large dictionary of features, making it suitable for online learning and large-scale datasets. A potential issue with feature hashing is collisions, where different features get mapped to the same hash value. However, in practice, especially with a suitably large hash space, the impact of collisions on model performance is often minimal.

feature engineering is the artisanal touch in data science, where human expertise blends with machine analysis. It involves leveraging a deep understanding of the domain to craft features that might elude automated methods. While algorithms are powerful, human intuition can illuminate subtle relationships or nuances in the data. Feature engineering is akin to sculpting the raw material of data into a more refined form, enhancing its representational power. The interplay between technical prowess and domain knowledge in feature engineering often plays a pivotal role in extracting meaningful insights. My experience underscores the importance of this hands-on approach, where creativity meets data to unveil richer dimensions.