Explore model performances¶
This document presents an overview of the results from a variety of model outputs, including further modelling chip probabilities.
There are several aspects of the predictions we’d like to explore and compare across models:
Overall metrics:
[x] Kappa score: measure of how many chips the model got right, above what it would have got by pure chance
[x] Accuracy (micro-F1: general over-simplified measure of how many chips the model got right
[x] Macro-F1 averaged: mean of each class’ F1
[x] Macro-F1 weighted: weighted mean of each class’ F1
Class-based metrics:
[x] Accuracy: proportion of chips the model got right for each class
[x] Macro-F1: harmonic mean of precision and recall. Roughly, an overview of how good the model is at predicting each single class
[x] Confusion matrices: more disaggregated view on predictions. Detailed but not summarising.
Spatial metrics: compare whether the distribution of predicted labels over space resembles that of the true values
[x] Moran’s I
[x] Joint count statistics
[x] Quadrat
[x] Ripley’s G
[x] Ripley’s F
import os
import pandas
import geopandas
import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt
import tools_chip_prob_modelling as tools
from copy import deepcopy
from pysal.lib import weights
from pysal.explore import esda
ERROR 1: PROJ: proj_create_from_database: Open of /opt/conda/share/proj failed
/opt/conda/lib/python3.9/site-packages/spaghetti/network.py:36: FutureWarning: The next major release of pysal/spaghetti (2.0.0) will drop support for all ``libpysal.cg`` geometries. This change is a first step in refactoring ``spaghetti`` that is expected to result in dramatically reduced runtimes for network instantiation and operations. Users currently requiring network and point pattern input as ``libpysal.cg`` geometries should prepare for this simply by converting to ``shapely`` geometries.
warnings.warn(f"{dep_msg}", FutureWarning)
Data¶
Here we load the original chip geometries, the true labels and predictions from each model and merge everything into a single geo-table.
Geometries and true labels
gl = geopandas.read_parquet(
'/home/jovyan/data/spatial_signatures/chip_probs/model_outputs/db.pq',
columns=['label', 'train_all', 'geometry']
)
Model predictions
Grab all files with model predictions
y_preds_f = [
i for i in os.listdir(
'/home/jovyan/data/spatial_signatures/chip_probs/model_outputs/'
) if '_y_pred.pq' in i
]
y_preds_f
['logite_baseline_wx_y_pred.pq',
'RandomForestClassifier_baseline_wx_y_pred.pq',
'RandomForestClassifier_baseline_y_pred.pq',
'HistGradientBoostingClassifier_baseline_y_pred.pq',
'maxprob_baseline_y_pred.pq',
'HistGradientBoostingClassifier_baseline_wx_y_pred.pq',
'logite_baseline_y_pred.pq']
Read and store predictions and train/val label
y_preds = pandas.DataFrame(None, index=gl.index)
for f in y_preds_f:
tab = pandas.read_parquet(
os.path.join('/home/jovyan/data/spatial_signatures/chip_probs/model_outputs/', f)
).set_index(
'id'
).rename(
columns=lambda s: f.replace('_y_pred.pq', '')+'_'+s
)
y_preds = y_preds.join(tab)
Check train/val indices align across models so we can remove them:
vals = [c for c in y_preds.columns if '_Validation' in c]
for i in range(len(vals)-1):
print((y_preds[vals[i]] != y_preds[vals[i+1]]).sum())
0
0
0
0
0
0
Single table
db = gl.join(y_preds.drop(columns=vals))
db.info()
<class 'geopandas.geodataframe.GeoDataFrame'>
Int64Index: 64409 entries, 4 to 103043
Data columns (total 10 columns):
# Column Non-Null Count Dtype
--- ------ -------------- -----
0 label 64409 non-null category
1 train_all 64409 non-null bool
2 geometry 64409 non-null geometry
3 logite_baseline_wx_y_pred 64409 non-null object
4 RandomForestClassifier_baseline_wx_y_pred 64409 non-null object
5 RandomForestClassifier_baseline_y_pred 64409 non-null object
6 HistGradientBoostingClassifier_baseline_y_pred 64409 non-null object
7 maxprob_baseline_y_pred 64409 non-null object
8 HistGradientBoostingClassifier_baseline_wx_y_pred 64409 non-null object
9 logite_baseline_y_pred 64409 non-null object
dtypes: bool(1), category(1), geometry(1), object(7)
memory usage: 6.6+ MB
Metrics¶
Set intuitive order of models
model_names = [
'maxprob_baseline_y_pred',
'logite_baseline_y_pred',
'logite_baseline_wx_y_pred',
'RandomForestClassifier_baseline_y_pred',
'RandomForestClassifier_baseline_wx_y_pred',
'HistGradientBoostingClassifier_baseline_y_pred',
'HistGradientBoostingClassifier_baseline_wx_y_pred'
]
model_names_short = [
'maxprob_baseline',
'logite',
'logite_wx',
'RF',
'RF_wx',
'HBGB',
'HBGB_wx'
]
Calculate all metrics by model
metrics = {}
train = db.query('train_all')
val = db.query('~train_all')
for model in model_names:
meta = tools.build_perf(
train['label'],
train[model],
val['label'],
val[model],
tools.class_names
)
metrics[model] = deepcopy(meta)
Global¶
Single scores¶
global_scores = []
for model in metrics:
global_scores.append(pandas.Series(
{i.replace('perf_', '').replace('_val', ''): metrics[model][i] for i in [
'perf_kappa_val',
'perf_model_accuracy_val',
'perf_macro_f1_avg_val',
'perf_macro_f1_w_val'
]},
name=model
))
global_scores = pandas.concat(
global_scores, axis=1
)[
model_names
].rename(
columns=lambda s: s.replace('_y_pred', '')
).T
global_scores
| kappa | model_accuracy | macro_f1_avg | macro_f1_w | |
|---|---|---|---|---|
| maxprob_baseline | 0.082029 | 0.240624 | 0.152201 | 0.257502 |
| logite_baseline | 0.156026 | 0.418220 | 0.148086 | 0.403382 |
| logite_baseline_wx | 0.188568 | 0.426946 | 0.163392 | 0.421285 |
| RandomForestClassifier_baseline | 0.170341 | 0.484825 | 0.167571 | 0.455233 |
| RandomForestClassifier_baseline_wx | 0.262610 | 0.530728 | 0.259750 | 0.505413 |
| HistGradientBoostingClassifier_baseline | 0.182966 | 0.490841 | 0.209516 | 0.465232 |
| HistGradientBoostingClassifier_baseline_wx | 0.238086 | 0.503143 | 0.231285 | 0.491264 |
Confusion matrices¶
Standard version with counts of occurrences as values (left panels) and row standardised (right panels):
f, axs = plt.subplots(4, 4, figsize=(12, 12))
model_loc = [
(0, 0), # Maxprob
(1, 0), # Logite
(1, 1), # Logite Wx
(2, 0), # RF
(2, 1), # RF Wx
(3, 0), # HGBD
(3, 1) # HGBD Wx
]
# Raw counts #
maxcount = max([np.array(metrics[model]['perf_confusion_val']).max()])
for i, model in enumerate(model_names):
ax = tools.build_cm_plot(
metrics[model]['perf_confusion_val'],
maxcount=maxcount,
ax=axs[model_loc[i]]
)
ax.set_title(model_names_short[i])
axs[0, 1].set_axis_off()
# Std #
for i, model in enumerate(model_names):
xy = model_loc[i]
ax = tools.build_cm_plot(
metrics[model]['perf_confusion_val'],
maxcount=maxcount,
std=True,
ax=axs[xy[0], xy[1]+2]
)
ax.set_title(model_names_short[i])
axs[0, 3].set_axis_off()
plt.tight_layout()
Class-based¶
Accuracy¶
wca = []
for i, model in enumerate(model_names):
wca.append(pandas.Series(
metrics[model]['perf_within_class_accuracy_val'],
metrics[model]['meta_class_names'],
name=model_names_short[i]
))
wca = pandas.concat(
wca, axis=1
)[model_names_short].T
wca
| urbanity | dense_urban_neighbourhoods | dense_residential_neighbourhoods | connected_residential_neighbourhoods | gridded_residential_quarters | accessible_suburbia | disconnected_suburbia | open_sprawl | warehouse_park_land | urban_buffer | countryside_agriculture | wild_countryside | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| maxprob_baseline | 0.6 | 0.263889 | 0.190476 | 0.082192 | 0.223529 | 0.370526 | 0.000000 | 0.195699 | 0.293907 | 0.120669 | 0.303030 | 0.732816 |
| logite | 0.0 | 0.000000 | 0.000000 | 0.000000 | 0.129412 | 0.528421 | 0.000000 | 0.371326 | 0.184588 | 0.300146 | 0.632074 | 0.005543 |
| logite_wx | 0.0 | 0.000000 | 0.000000 | 0.000000 | 0.200000 | 0.698947 | 0.000000 | 0.409319 | 0.297491 | 0.320324 | 0.602740 | 0.025499 |
| RF | 0.0 | 0.000000 | 0.000000 | 0.000000 | 0.117647 | 0.406316 | 0.000000 | 0.156272 | 0.050179 | 0.587946 | 0.562889 | 0.000000 |
| RF_wx | 0.0 | 0.083333 | 0.114286 | 0.000000 | 0.352941 | 0.526316 | 0.000000 | 0.253047 | 0.363799 | 0.488384 | 0.727411 | 0.003326 |
| HBGB | 0.0 | 0.013889 | 0.019048 | 0.027397 | 0.200000 | 0.456842 | 0.000000 | 0.128315 | 0.250896 | 0.571618 | 0.578525 | 0.013304 |
| HBGB_wx | 0.0 | 0.222222 | 0.133333 | 0.095890 | 0.317647 | 0.309474 | 0.227273 | 0.177061 | 0.354839 | 0.474977 | 0.687976 | 0.080931 |
h = sns.heatmap(wca, vmin=0, vmax=1, cmap='viridis')
h.set_xticklabels(h.get_xticklabels(), rotation = 45, ha="right")
h.set_title('Within-class Accuracy');
Macro F1¶
f1 = []
for i, model in enumerate(model_names):
f1.append(pandas.Series(
metrics[model]['perf_f1_val'],
metrics[model]['meta_class_names'],
name=model_names_short[i]
))
f1 = pandas.concat(
f1, axis=1
)[model_names_short].T
f1
| urbanity | dense_urban_neighbourhoods | dense_residential_neighbourhoods | connected_residential_neighbourhoods | gridded_residential_quarters | accessible_suburbia | disconnected_suburbia | open_sprawl | warehouse_park_land | urban_buffer | countryside_agriculture | wild_countryside | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| maxprob_baseline | 0.304762 | 0.078431 | 0.358752 | 0.098765 | 0.085202 | 0.000000 | 0.168889 | 0.193823 | 0.195253 | 0.026316 | 0.143044 | 0.173173 |
| logite | 0.288009 | 0.000000 | 0.555819 | 0.000000 | 0.000000 | 0.000000 | 0.128655 | 0.274583 | 0.372212 | 0.000000 | 0.147248 | 0.010504 |
| logite_wx | 0.304029 | 0.000000 | 0.568372 | 0.000000 | 0.000000 | 0.000000 | 0.145923 | 0.299974 | 0.389539 | 0.000000 | 0.208805 | 0.044061 |
| RF | 0.456805 | 0.000000 | 0.533333 | 0.000000 | 0.000000 | 0.000000 | 0.196078 | 0.210120 | 0.527011 | 0.000000 | 0.087500 | 0.000000 |
| RF_wx | 0.514403 | 0.000000 | 0.613705 | 0.167832 | 0.102564 | 0.000000 | 0.437956 | 0.317732 | 0.516315 | 0.000000 | 0.439870 | 0.006623 |
| HBGB | 0.490950 | 0.052632 | 0.537680 | 0.036697 | 0.025641 | 0.000000 | 0.276423 | 0.190223 | 0.523844 | 0.000000 | 0.354430 | 0.025668 |
| HBGB_wx | 0.371212 | 0.064815 | 0.601901 | 0.108527 | 0.114695 | 0.047847 | 0.189474 | 0.249874 | 0.505653 | 0.000000 | 0.380769 | 0.140655 |
h = sns.heatmap(f1, cmap='viridis')
h.set_xticklabels(h.get_xticklabels(), rotation = 45, ha="right")
h.set_title('F1 Score');
Spatial¶
The goal in this section is to capture how well a set of predictions reproduces the spatial pattern of the original labels. Our first step for this is to consider the labels for a given class. We take those and calculate measures of spatial concentration, either by considering lattice data or a point pattern. In the former case, we compute measures of degree of clustering that treat our data as both continuous (i.e., probability of class occurrence) and discrete. For the latter, we treat instances of a class as a point pattern that is distribtuted across the geography of interest. We then characterise this pattern spatially with a series of explicitly spatial metrics, and calculate those also for the set of predictions from each model we run. Since both the scores for the labels and the predictions is based on the same set of potential locations (i.e. the underlying set of places where a chip can take 1 or 0), the two can be compared directly. Our metrics of interest are thus the difference between the value of a given spatial statistic for the labels, and that for a set of predictions. Smaller quantities will represent greater affinity between the spatial structure of the original labels and that of our predictions. We operationalise this using the validation set.
What we are going to try to do is characterise the degree of clustering of the predictions for each class. For the set of original labels, these are the maps:
f, axs = plt.subplots(4, 3, figsize=(12, 12))
axs = axs.flatten()
for i, c in enumerate(
metrics['maxprob_baseline_y_pred']['meta_class_names']
):
ax = axs[i]
sp_db.assign(v=sp_db['label'] == c).plot(
'v', categorical=True, legend=True, cmap='viridis_r', edgecolor='none', ax=ax
)
ax.set_title(c)
ax.set_axis_off()
We start with only the validation set, as that is the pattern we are interested in characterising.
sp_db = db.query(
'train_all == False'
)
Spatial structure (w and coords)¶
For lattice metrics, we conceptualise space in a topological way, for which we build a spatial weights matrix. We work with two different types of topology: a distance band and nearest neighbors.
For the distance band, we ensure every polygon is linked to at least one neighbor by calculating the minimum band we need to apply:
min_thr = weights.min_threshold_distance(
np.array([sp_db.centroid.x, sp_db.centroid.y]).T
)
min_thr
2437.0473938764508
We then build the weights matrix based on that distance:
w_thr = weights.DistanceBand.from_dataframe(sp_db, min_thr)
This produces a set of cardinalities we can explore with an eye to match similarly with the \(k\)-nearest neighbors weights later.
pandas.Series(w_thr.cardinalities).plot.hist(bins=68, figsize=(9, 3));
We then use \(k=35\) to build the nearest neighbor weights:
w_knn = weights.KNN.from_dataframe(sp_db, k=35)
The point coordinates of each chip are a more straightforward task. We store them as a ndarray as that’s how we’ll need them later:
xys = sp_db.centroid
xys = np.array([xys.x, xys.y]).T
Metric computation¶
To accelerate computations across different cores, we set it up in Dask:
from dask import bag as dbag
from dask.distributed import Client, LocalCluster
client = Client(LocalCluster(n_workers=8))
Numba: Attempted to fork from a non-main thread, the TBB library may be in an invalid state in the child process. Numba: Attempted to fork from a non-main thread, the TBB library may be in an invalid state in the child process. Numba: Attempted to fork from a non-main thread, the TBB library may be in an invalid state in the child process. Numba: Attempted to fork from a non-main thread, the TBB library may be in an invalid state in the child process. Numba: Attempted to fork from a non-main thread, the TBB library may be in an invalid state in the child process. Numba: Attempted to fork from a non-main thread, the TBB library may be in an invalid state in the child process. Numba: Attempted to fork from a non-main thread, the TBB library may be in an invalid state in the child process. Numba: Attempted to fork from a non-main thread, the TBB library may be in an invalid state in the child process. Numba: Attempted to fork from a non-main thread, the TBB library may be in an invalid state in the child process. 2022-08-07 14:07:35,668 - distributed.diskutils - INFO - Found stale lock file and directory '/home/jovyan/work/code/signature_ai/ai_experiments/dask-worker-space/worker-uep79n9d', purging 2022-08-07 14:07:35,668 - distributed.diskutils - INFO - Found stale lock file and directory '/home/jovyan/work/code/signature_ai/ai_experiments/dask-worker-space/worker-63ansyiy', purging 2022-08-07 14:07:35,668 - distributed.diskutils - INFO - Found stale lock file and directory '/home/jovyan/work/code/signature_ai/ai_experiments/dask-worker-space/worker-b38pqrvd', purging
client.restart()
And span the computations of all the statistics across different cores:
from importlib import reload
reload(tools);
%%time
wd = {'thr': w_thr, 'knn': w_knn}
tasks = [(
# y w xys Name
sp_db[model], wd, xys, model
) for model in model_names+['label']]
sp_metrics = pandas.concat(dbag.from_sequence(tasks).map(
tools.spatial_perf
).compute())
ERROR 1: PROJ: proj_create_from_database: Open of /opt/conda/share/proj failed ERROR 1: PROJ: proj_create_from_database: Open of /opt/conda/share/proj failed ERROR 1: PROJ: proj_create_from_database: Open of /opt/conda/share/proj failed ERROR 1: PROJ: proj_create_from_database: Open of /opt/conda/share/proj failed ERROR 1: PROJ: proj_create_from_database: Open of /opt/conda/share/proj failed ERROR 1: PROJ: proj_create_from_database: Open of /opt/conda/share/proj failed ERROR 1: PROJ: proj_create_from_database: Open of /opt/conda/share/proj failed ERROR 1: PROJ: proj_create_from_database: Open of /opt/conda/share/proj failed /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/pointpats/random.py:60: RuntimeWarning: divide by zero encountered in double_scalars intensity = n_observations / _area(hull) /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/pointpats/random.py:60: RuntimeWarning: divide by zero encountered in double_scalars intensity = n_observations / _area(hull) /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/pointpats/distance_statistics.py:281: RuntimeWarning: invalid value encountered in true_divide fracs = numpy.cumsum(counts) / counts.sum() /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim /opt/conda/lib/python3.9/site-packages/esda/moran.py:193: RuntimeWarning: divide by zero encountered in double_scalars self.z_sim = (self.I - self.EI_sim) / self.seI_sim
CPU times: user 23.2 s, sys: 1.17 s, total: 24.4 s
Wall time: 47 s
sp_metrics.query('(model=="label") & (metric=="jc_thr")')
| signature | metric | value | model | |
|---|---|---|---|---|
| 4 | urban_buffer | jc_thr | 109045.0 | label |
| 11 | countryside_agriculture | jc_thr | 135527.0 | label |
| 18 | dense_urban_neighbourhoods | jc_thr | 244.0 | label |
| 25 | open_sprawl | jc_thr | 9375.0 | label |
| 32 | gridded_residential_quarters | jc_thr | 366.0 | label |
| 39 | accessible_suburbia | jc_thr | 2163.0 | label |
| 46 | warehouse_park_land | jc_thr | 7677.0 | label |
| 53 | connected_residential_neighbourhoods | jc_thr | 144.0 | label |
| 60 | dense_residential_neighbourhoods | jc_thr | 257.0 | label |
| 67 | disconnected_suburbia | jc_thr | 15.0 | label |
| 74 | urbanity | jc_thr | 4.0 | label |
| 81 | wild_countryside | jc_thr | 17196.0 | label |
To do:
[x] Find out why there are
NaNvalues in the table[ ] Calculate (weighted) average across classes for overall score
[x] Move
Morancomputation to adask.bag[ ] Update graphics and narrative
Lattice-based metrics¶
Moran’s I¶
Now we want to compute Moran’s I for each class present in a set of predictions, for which we write the following method:
Now we can calculate measures of distance between each model and the labels:
moran_dists = {}
for model in model_names:
for w in ['knn', 'thr']:
moran_dists[f'{model}_{w}'] = (
morans.loc[f'label_{w}', :] - morans.loc[f'{model}_{w}', :]
)
moran_dists = pandas.DataFrame(moran_dists)
To visualise which models get closer to the original labels, we focus on each class separately as there is a lot of variation in distance across classes but we really are focused on variation across models within each class. We operationalise this by dividing the scores of a giving class by its average.
h = sns.heatmap(
moran_dists.div(moran_dists.mean(axis=1), axis=0)
)
h.set_xticklabels(h.get_xticklabels(), rotation = 45, ha="right")
h.set_title("Moran's I by class by model");
IMPORANT - Note there are some NaN values in the table, these correspond to instances where a model does not predict any chip in a given class.
Joint counts¶
Here we look at joint counts and, specifically, focus on the proportion of pairs of a given class that are neighbors.
tst = tools.spatial_perf((sp_db['label'], w_knn, None))
tst
( moran jcs
urban_buffer 0.650926 104942.5
countryside_agriculture 0.761201 109258.0
dense_urban_neighbourhoods 0.281699 358.0
open_sprawl 0.464526 12172.0
gridded_residential_quarters 0.293207 440.0
accessible_suburbia 0.303767 2649.5
warehouse_park_land 0.718528 7098.5
connected_residential_neighbourhoods 0.153006 199.0
dense_residential_neighbourhoods 0.222241 414.5
disconnected_suburbia 0.037901 15.0
urbanity 0.045493 4.0
wild_countryside 0.832364 13276.5,
None)