How to calculate the variance of location details

Location has latitude and longitude. I am looking for a single value that will capture the variance of the location details (not separate variance for latitude and longitude). What is the best way to achieve that?

>>> pdf = pd.DataFrame({'latitude': {0: 47.0, 8: 54.0, 14: 55.0, 15: 39.0, 2: 31.0},
              'longitude': {0: 29.0, 8: 10.0, 14: 36.0, 15: -9.0, 2: 121.0}
             })

>>> pdf

  latitude  longitude

0   47.0    29.0
8   54.0    10.0
14  55.0    36.0
15  39.0    -9.0
2   31.0    121.0

As per numpy

#these points are having the same spread, but at different location
df2 = pd.DataFrame({'latitude': {0: 147.0, 8: 154.0, 14: 155.0, 15: 139.0, 2: 131.0},
                   'longitude': {0: 154.0, 8: 155.0, 14: 139.0, 15: 131.0, 2: 147.0} })
df2['new'] = (df2['latitude']-df2['latitude'].mean()).mul(df2['longitude']-df2['longitude'].mean()).div(100)
score = df2['new'].var()
df2.plot(kind='scatter', x='longitude', y='latitude')

Output score 0.4407372

#these points are further apart
df3 = pd.DataFrame({'latitude': {0: 14.0, 8: 15.0, 14: 155.0, 15: 13.0, 2: 131.0},
                   'longitude': {0: 15.0, 8: 215.0, 14: 39.0, 15: 131.0, 2: 147.0} })
df3['new'] = (df3['latitude']-df3['latitude'].mean()).mul(df3['longitude']-df3['longitude'].mean()).div(100)
score = df3['new'].var()
df3.plot(kind='scatter', x='longitude', y='latitude')

Output score 2332.5498432

CodePudding user response：

Single variance measure, converting latlong to cartesian (from recipe). Using safe divide method described here

import pandas as pd
import numpy as np

pdf = pd.DataFrame(
    {
        "latitude": {0: 47.0, 8: 54.0, 14: 55.0, 15: 39.0, 2: 31.0},
        "longitude": {0: 29.0, 8: 10.0, 14: 36.0, 15: -9.0, 2: 121.0},
    }
)


def get_cartesian(latlon):
    lat, lon = latlon
    lat, lon = np.deg2rad(lat), np.deg2rad(lon)
    R = 6371  # radius of the earth
    x = R * np.cos(lat) * np.cos(lon)
    y = R * np.cos(lat) * np.sin(lon)
    z = R * np.sin(lat)

    return (x, y, z)


pdf = pdf.assign(
    latlong=pd.Series([x for x in zip(pdf.latitude.values, pdf.longitude.values)], index=pdf.index),
    cartesian=lambda x: x["latlong"].apply(get_cartesian),
    x=lambda c: c["cartesian"].apply(lambda x: x[0]),
    y=lambda c: c["cartesian"].apply(lambda x: x[1]),
    z=lambda c: c["cartesian"].apply(lambda x: x[2]),
)

sum_means = pdf.x.mean()   pdf.y.mean()   pdf.z.mean()
variance = sum_means and sum_means / 3 or 0

result:

2910.4314471812527