What is dimensionality reduction, and how does it relate to embeddings?

Dimensionality reduction is the process of simplifying high-dimensional data into a lower-dimensional form while preserving its essential structure. High-dimensional data, such as images or text, often contains redundant or noisy features that make analysis computationally expensive and less intuitive. Techniques like Principal Component Analysis (PCA) or t-Distributed Stochastic Neighbor Embedding (t-SNE) identify patterns or relationships in the data and project it onto fewer dimensions. For example, PCA transforms data by finding axes (principal components) that capture the most variance, enabling tasks like visualizing multi-feature datasets in 2D/3D. This simplification helps reduce memory usage, speed up algorithms, and improve model performance by focusing on meaningful information.

Embeddings are dense, low-dimensional vector representations of data that capture semantic or contextual relationships. They are widely used in machine learning to convert discrete or complex inputs (like words or images) into continuous vectors. For instance, Word2Vec embeds words into vectors where similar words (e.g., “king” and “queen”) cluster closer in space. Similarly, image embeddings generated by convolutional neural networks (CNNs) represent images as compact vectors, preserving visual features. Unlike raw data, embeddings encode meaningful patterns, making them easier for models to process. They are often learned through training, such as neural networks optimizing vectors to predict context (in NLP) or classify images (in computer vision).

Dimensionality reduction and embeddings are closely linked because embeddings inherently reduce dimensions. While traditional techniques like PCA explicitly optimize for variance, embeddings often achieve reduction implicitly by learning task-specific representations. For example, autoencoders use neural networks to compress input data into a latent space (embedding) and reconstruct it, effectively performing nonlinear dimensionality reduction. Similarly, recommendation systems use matrix factorization to embed users and items into lower dimensions, capturing preferences without raw interaction data. Both approaches aim to retain critical information in fewer dimensions, but embeddings often prioritize semantic relationships over statistical properties. This makes embeddings particularly useful for downstream tasks like clustering or similarity search, where preserving contextual meaning matters more than mere variance.