Sparsity
SparsityIt is the premise of compressed sensing, mainly referring to the situation where the proportion of empty elements is large. It is usually calculated by dividing the number of elements set to 0 in a vector or matrix by the total number of entries in the vector or matrix.
In a matrix, if the number of elements with a value of 0 is much greater than the number of non-zero elements, the matrix is called a sparse matrix. Correspondingly, if the number of non-zero elements accounts for the majority, the matrix is called a dense matrix.
If the signal is sparse, it means that there are many zero elements in the signal. In this case, the information can be compressed and the problem can be solved by simply finding non-zero elements. However, in reality, the signal itself is not sparse. After a transformation, it is mostly sparse on a set of bases, that is, a sparse representation of the signal.
In addition, there are two types of sparsity: feature sparsity and model sparsity. Feature sparsity refers to the sparsity of feature vectors, while model sparsity refers to the sparsity of model weights.