Vector embeddings are a technique used to represent high-dimensional data in a lower-dimensional space while preserving its essential features and relationships. They are particularly useful in handling sparse data, which is characterized by many missing values or a limited number of non-zero entries. Instead of trying to deal with this sparsity directly, vector embeddings transform the data into a more compact, dense format where similar items or features are positioned closer together in the vector space. This representation allows models to capture relationships and similarities that may not be apparent in the original sparse data.
For instance, consider a text dataset where each document is represented by a bag of words. This method creates a sparse matrix where most entries are zero because many terms will not appear in every document. By using word embeddings like Word2Vec or GloVe, each word can be represented as a dense vector based on its context in the dataset. Thus, instead of dealing with a large matrix filled with zeros, continuous-valued vectors can summarize information in a more compact way. This compactness helps in reducing computational requirements and improves the performance of downstream tasks like classification or clustering.
Furthermore, vector embeddings can generalize well by capturing semantic relationships between items, making them invaluable in applications such as recommendation systems and natural language processing. For example, in a recommendation system, user preferences and product characteristics can be embedded into the same vector space. When a user interacts with a few products, their vector representation can guide the system to recommend similar products based on the distance between their respective vectors. This way, embeddings can effectively manage the challenges of sparse data by highlighting relationships that might be hidden in its original form.