Talus

Fast partitioning of point-cloud data (or graphs) according to a real-valued function over the points. These partitions correspond to regions that flow to some local minima or maxima - as a concrete example, if applied to topography data using elevation as the real-valued function, partitioning by local minima would correspond to watersheds. Furthermore, also computes how persistent each partition is. In the topography example, if we partitioned by maxima, then these persistence values would correspond to the topographical prominence of the peaks in a given landscape.

Example Usage

import networkx as nx
import talus_python.morse as morse

node_locs = [(0, 3), (1, -1), (2, 10), (3, 2), (4, 7)]
nodes = [
    morse.MorseNode(identifier=i, value=i, vector=list(v))
    for i, v in enumerate(node_locs)
]

G = nx.Graph()
for node in nodes:
    G.add_node(node)

G.add_edge(nodes[0], nodes[1])
G.add_edge(nodes[0], nodes[3])
G.add_edge(nodes[1], nodes[2])
G.add_edge(nodes[1], nodes[4])
G.add_edge(nodes[3], nodes[4])

ms_complex = morse.MorseSmaleComplex.from_graph(G)
result = ms_complex.morse_data

# See what local maxima each node was assigned to
print("Assignments:", result.ascending_complex.complex.complex)

# See how persistent each local maxima is
print("Persistence:", result.ascending_complex.complex.lifetimes)

# Show the node partitions at a certain timestep in the filtration
print("Partitions:", result.ascending_complex.compute_cells_at_lifetime(0))

Assignments: {0: 4, 3: 4, 1: 4, 4: 4, 2: 2}
Persistence: {1: 0.0, 3: 0.0, 2: 1.0, 0: 0.0, 4: inf}
Partitions: {2: [2], 4: [0, 3, 1, 4]}