Adjacency Simplicial Complex Module¶

You can try out spatial-tda by using the cloud-computing platforms below without having to install anything on your computer:

Installation¶

To install spatial_tda, use:

In [1]:

# !pip install -U spatial-tda

# !pip install -U spatial-tda

Import Libraries¶

In [2]:

import geopandas as gpd
import matplotlib.pyplot as plt

import geopandas as gpd import matplotlib.pyplot as plt

Import Geospatial Data for the Analysis¶

In [4]:

arlington_svi.head(2)

arlington_svi.head(2)

Out[4]:

	FIPS	EP_POV	EP_UNEMP	EP_PCI	EP_NOHSDP	EP_UNINSUR	EP_AGE65	EP_AGE17	EP_DISABL	EP_SNGPNT	EP_LIMENG	EP_MINRTY	EP_MUNIT	EP_MOBILE	EP_CROWD	EP_NOVEH	EP_GROUPQ	geometry
0	51013100100	1.2	2.1	76748.0	1.4	1.9	13.6	29.6	5.7	6.4	2.3	23.4	0.5	0.0	0.0	0.6	0.2	POLYGON ((-77.16811 38.89652, -77.16421 38.899...
1	51013100200	1.5	2.0	94706.0	0.1	1.9	15.9	29.9	4.9	2.3	2.5	14.4	0.7	0.0	0.0	2.0	0.1	POLYGON ((-77.15968 38.90315, -77.15454 38.907...

In [5]:

# plot the data for EP_POV in a geopandas plot
arlington_svi.plot(column='EP_POV', legend=True)
plt.show()

# plot the data for EP_POV in a geopandas plot arlington_svi.plot(column='EP_POV', legend=True) plt.show()

Adjacency Simplicial Complex Module¶

The adjacency module provides tools for constructing adjacency-based simplicial complexes and extracting relevant topological summaries.

Key Features¶

• Constructing adjacency-based simplicial complexes
• Extracting topological summaries
• Visualizing simplicial complexes (Under development)

In [6]:

# import the library
import spatial_tda as tda

# import the library import spatial_tda as tda

Create the Adjacency Simplicial Complex Object from the Geospatial Data¶

In [7]:

adjacency_simplex = tda.AdjacencySimplex(geo_dataframe=arlington_svi, variable = "EP_POV", threshold=None, filter_method='up')

adjacency_simplex = tda.AdjacencySimplex(geo_dataframe=arlington_svi, variable = "EP_POV", threshold=None, filter_method='up')

Filter and sort the Variable¶

In [8]:

adjacency_simplex.filter_sort_gdf()

adjacency_simplex.filter_sort_gdf()

Calculate the Adjacent Counties/Census Tracts¶

In [9]:

adjacency_simplex.calculate_adjacent_countries()

adjacency_simplex.calculate_adjacent_countries()

Create the Simplicial Complex using the Adjacency Matrix¶

In [10]:

adjacency_simplex.form_simplicial_complex()

adjacency_simplex.form_simplicial_complex()

Calculate the Persistent Homology and get the TDA summary for the study area(Arlington County, VA)¶

In [11]:

summaries = adjacency_simplex.compute_persistence()

summaries = adjacency_simplex.compute_persistence()

In [12]:

print(summaries)

print(summaries)

{'H0': 57, 'TL': 435.9000000000001, 'AL': 7.647368421052633, 'TML': 217.95000000000005, 'AML': 3.8236842105263165}

Plot(GIF) the Simplicial Complex that generated from Adjacency Simplex Method¶

In [ ]:

adjacency_simplex.plot_simplicial_complex()

adjacency_simplex.plot_simplicial_complex()