sparses

Sparses is not a standard term in mathematics or computer science. It is sometimes used informally as a plural noun to refer to sparse structures or datasets—instances where most entries are zero or missing. In formal literature, the adjective sparse is preferred, with phrases such as sparse matrices, sparse representations, or sparse signals. When used, sparses function as a shorthand for the collection of sparse components across a system.

Sparses encompass sparse matrices, vectors, tensors, graphs, and signals. Common representations store only nonzero elements and their indices, using formats such as Compressed Sparse Row (CSR), Compressed Sparse Column (CSC), Coordinate (COO), or specialized sparse tensor formats. These approaches reduce memory usage and accelerate operations like sparse matrix–vector multiplication, since many computations can skip zero entries. The concept of sparsity also appears in graph structures (sparse graphs), where edge density is low.

Applications include machine learning with high-dimensional, sparse feature spaces such as text data, recommender systems, scientific computing, and compressed sensing. Challenges include maintaining sparsity under transformations, handling dynamic sparsity in streaming data, and preserving numerical stability. The term sparses remains informal and context-dependent; when precision is required, it is better to refer to the specific sparse structure or storage format in use. See also sparse representation, sparse matrix, and sparse graph.