If you want to play around with SuiteSparse:GraphBLAS using Python, try python-graphblas (https://python-graphblas.readthedocs.io/). And this is a shameless plug. I'm one of the authors of the Python wrapper.
GraphBLAS is underrated and underused IMHO. If you use e.g. scipy.sparse, NetworkX, or similar, you should check out GraphBLAS. It is really fast even compared to scipy.sparse, and more capable in many ways.
They've actually started implementing the NetworkX API
> The concept of sparsity is useful in combinatorics and application areas such as network theory and numerical analysis, which typically have a low density of significant data or connections. Large sparse matrices often appear in scientific or engineering applications when solving partial differential equations.
CuGraph has a NetworkX-like API, though only so many of the networkx algorithms are yet reimplemented with some possible CUDA-optimizations.
> cuGraph operates, at the Python layer, on GPU DataFrames, thereby allowing for seamless passing of data between ETL tasks in cuDF and machine learning tasks in cuML. Data scientists familiar with Python will quickly pick up how cuGraph integrates with the Pandas-like API of cuDF. Likewise, users familiar with NetworkX will quickly recognize the NetworkX-like API provided in cuGraph, with the goal to allow existing code to be ported with minimal effort into RAPIDS.
> While the high-level cugraph python API provides an easy-to-use and familiar interface for data scientists that's consistent with other RAPIDS libraries in their workflow, some use cases require access to lower-level graph theory concepts. For these users, we provide an additional Python API called pylibcugraph, intended for applications that require a tighter integration with cuGraph at the Python layer with fewer dependencies. Users familiar with C/C++/CUDA and graph structures can access libcugraph and libcugraph_c for low level integration outside of python.
To give an example of real world sparse matrices, power grids can have thousands and thousands of nodes, but most of those nodes only connect to a few other nodes at most that are local neighbors. Systems are highly sparse as a result
Compared to the Powerset graph that includes all possible operators and parameter values and parentheses in infix but not Reverse Polish Notation, a correlation graph is sparse: most conditional probabilities should be expected to tend toward the Central Limit Theorem, so if you subtract (or substitute) a constant noise scalar, a factor graph should be extra-sparse. https://en.wikipedia.org/wiki/Central_limit_theorem_for_dire...
What do you call a factor graph with probability distribution functions (PDFs) instead of float64s?
Are Path graphs and Path graphs with cycles extra sparse? An adjacency matrix for all possible paths through a graph is also mostly zeroes.
https://en.wikipedia.org/wiki/Path_graph
Methods of feature reduction use and affect the sparsity of a sparse matrix (that does not have elements for confounding variables). For example, from "Exploratory factor analysis (EFA) versus principal components analysis (PCA)" https://en.wikipedia.org/wiki/Factor_analysis :
> For either objective, it can be shown that the principal components are eigenvectors of the data's covariance matrix. Thus, the principal components are often computed by eigendecomposition of the data covariance matrix or singular value decomposition of the data matrix. PCA is the simplest of the true eigenvector-based multivariate analyses and is closely related to factor analysis. Factor analysis typically incorporates more domain specific assumptions about the underlying structure and solves eigenvectors of a slightly different matrix.
