giotto-ph 0.2.4

Point clouds

Persistence diagram of a random point cloud of 100 points in 3D Euclidean space, up to homology dimension 2, using all available threads:

pc = np.random.random((100, 3))
dgm = ripser_parallel(pc, maxdim=2, n_threads=-1)

Distance matrices and graphs

You can also work with distance matrices by passing metric="precomputed":

from scipy.spatial.distance import pdist, squareform

# A distance matrix
dm = squareform(pdist(pc))
dgm = ripser_parallel(pc, metric="precomputed", maxdim=2, n_threads=-1)

More generally, you can work with dense or sparse adjacency matrices of weighted graphs. Here is a dense square matrix interpreted as the adjacency matrix of a fully connected weighted graph with 100 vertices:

# Entries can be negative. The only constraint is that, for every i and j, dm[i, j] ≥ max(dm[i, i], dm[j, j])
# With dense input, the lower diagonal is ignored
adj_dense = np.random.random((100, 100))
np.fill_diagonal(adj_dense, 0)
dgm = ripser_parallel(adj_dense, metric="precomputed", maxdim=2, n_threads=-1)

And here is a sparse adjacency matrix:

# See API reference for treatment of entries below the diagonal
from scipy.sparse import random
adj_sparse = random(100, 100, density=0.1)
dgm = ripser_parallel(adj_sparse, metric="precomputed", maxdim=2, n_threads=-1)

Edge Collapser

Push the computation to higher homology dimensions and larger point clouds/distance matrices/adjacency matrices using edge collapses:

dgm_higher = ripser_parallel(pc, maxdim=5, collapse_edges=True, n_threads=-1)

(Note: not all datasets and configurations will benefit from edge collapses. For more details, see our paper below.)

Weighted Rips Filtrations

Use the weights and weight_params parameters to constructed a weighted Rips filtration as defined in this paper. weights can either be a custom 1D array of vertex weights, or the string "DTM" for distance-to-measure reweighting:

dgm_dtm = ripser_parallel(pc, weights="DTM", n_threads=-1)

Dependencies

The latest stable version of giotto-ph requires:

• Python (>= 3.7)

• NumPy (>= 1.19.1)

• SciPy (>= 1.5.0)

• scikit-learn (>= 0.23.1)

User installation

The simplest way to install giotto-ph is using pip

python -m pip install -U giotto-ph

If necessary, this will also automatically install all the above dependencies. Note: we recommend upgrading pip to a recent version as the above may fail on very old versions.

Developer installation

Please consult the dedicated page for detailed instructions on how to build giotto-ph from sources across different platforms.

Testing

After installation, you can launch the test suite from inside the source directory

pytest gph