Differences Between Keyword, Sparse and Dense Vector Indexes

Aspect Sparse Vector Index Dense Vector Index Keyword Index
Storage Principle Only non-zero elements are stored. All elements are stored, including zeros. Keywords or terms are stored, often as a mapping to their data locations.
Space Efficiency High, due to storage of only non-zero values. Lower, all values including zeroes take up space. Varies, depends on the number of unique keywords and their storage method.
Data Representation Represents data with many zeroes (e.g., document-term matrices). Represents data with few or no zeroes (e.g., image pixels). Represents text data through specific terms used for retrieval.
Lookup Speed Slower, indirect lookup through index mappings. Faster, direct access due to continuous memory allocation. Fast for text searches, depends on the efficiency of the indexing algorithm.
Ideal Use Case High-dimensional data with sparsity, like text data in NLP. Data with dense representations, like colored images in graphics. Text retrieval systems, like search engines and database searches.
Index Complexity More complex due to the need for mapping structures. Simpler, as it uses sequential storage. Complexity depends on the indexing algorithm and the data structure used (e.g., hash tables, inverted indexes).
Examples Text vectorization with TF-IDF, one-hot encoding for categorical data. RGB values in images, continuous sensor data. Inverted indexes in full-text search engines, keyword-based queries in databases.

Factor Sparse Vector Index Dense Vector Index
Storage Stores only non-zero elements Stores all elements, including zeros
Space Efficiency High, as it only records non-zero elements Lower, as it records all elements
Access Time Slower, as it requires mapping to find an element Faster, as elements are in a continuous block
Update Time Can be slower if changing the sparsity structure Typically faster for updates
Use Case Ideal for data with many zeros Ideal for data with few zeros
Complexity More complex data structure Simpler data structure
Examples Text frequency in documents, adjacency matrices in graphs Image data, audio signal processing
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