Principal component analysis for multi-spectral data

Keywords data used; sentinel 2, analysis; principal component analysis

Background

Principal Component Analysis (PCA) is a popular technique for dimensionality reduction. It can be used to explore patterns in high-dimensional data and assist unsupervised learning.

Principal components are a series of linear combinations of the original variables, among which the first principal component accounts for the greatest variance within a dataset. Each subsequent principal component accounts for the next greatest possible variance and is uncorrelated with the previously defined components.

This technique is useful for understanding Sentinel-2 data as images are captured in 12 spectral bands but only 3 variables can be visualized in a RGB composite. PCA can also be applied to timeseries data to investigate temporal evolution patterns for different land cover types.

Description

This notebook demonstrates a principal component analysis for Sentinel-2 multi-spectal data. Following steps are covered:

  1. Loading Sentinel-2 multi-spectral data.

  2. Applying PCA to transform and visualize data. ***

Getting started

To run this analysis, run all the cells in the notebook, starting with the “Load packages” cell.

Load packages

Import Python packages that are used for the analysis.

[1]:
%matplotlib inline

from sklearn.decomposition import PCA
import datacube

from deafrica_tools.datahandling import load_ard
from deafrica_tools.plotting import rgb
from deafrica_tools.classification import sklearn_flatten, sklearn_unflatten
/env/lib/python3.8/site-packages/datacube/storage/masking.py:7: DeprecationWarning: datacube.storage.masking has moved to datacube.utils.masking
  warnings.warn("datacube.storage.masking has moved to datacube.utils.masking",
/env/lib/python3.8/site-packages/geopandas/_compat.py:106: UserWarning: The Shapely GEOS version (3.8.0-CAPI-1.13.1 ) is incompatible with the GEOS version PyGEOS was compiled with (3.9.1-CAPI-1.14.2). Conversions between both will be slow.
  warnings.warn(

Connect to the datacube

Connect to the datacube so we can access DEAfrica data.

[2]:
dc = datacube.Datacube(app='pca')

Analysis parameters

This section defines the analysis parameters, including

  • center lat/lon and analysis window size for the area of interest

  • time period to be investigated

  • projection and resolution for loading data

  • acceptable range of cloud cover percentage for input Sentinel-2 granule (min_gooddata)

  • spectral bands to be explored

The default location is Betsiboka Estuary, Madagascar.

To limit overall memory usage, if a larger analysis window or higher resolution is desired, the time period should be reduced accordingly.

[3]:
# Create a query object
lat, lon = -15.92, 46.35
buffer = 0.1

query = {
    'time': ('2020-01', '2020-03'),
    'x': (lon - buffer, lon + buffer),
    'y': (lat + buffer, lat - buffer),
    'output_crs': 'epsg:6933',
    'resolution':(-20,20),
}

# use all non-overlapping 10m and 20m bands
bands = ['blue', 'green', 'red', 'red_edge_1', 'red_edge_2',
         'red_edge_3', 'nir_narrow', 'swir_1', 'swir_2']

Loading Sentinel-2 multi-spectral data

Only high probablity cloud is excluded in this example, but this can be modified for a different area.

[4]:
ds = load_ard(dc=dc,
              products=['s2_l2a'],
              measurements=bands,
              min_gooddata=0.98,
              group_by='solar_day',
              **query)

Using pixel quality parameters for Sentinel 2
Finding datasets
    s2_l2a
Counting good quality pixels for each time step
Filtering to 4 out of 18 time steps with at least 98.0% good quality pixels
Applying pixel quality/cloud mask
Loading 4 time steps
[5]:
# visualize data using selected input spectral bands
rgb(ds, bands=['swir_1','nir_narrow','red_edge_1'], index=list(range(len(ds.time))), col_wrap=4)
../../../_images/sandbox_notebooks_Frequently_used_code_Principal_component_analysis_13_0.png

Applying PCA to transform and visualize data

To perform a PCA, data is first transformed into a numpy array that can be used by sklearn.

[6]:
X = sklearn_flatten(ds)

A PCA model is generated with 3 principal components and fitted on the data.

[7]:
pca = PCA(n_components=3)
pca.fit(X)
[7]:
PCA(n_components=3)

We can investigate how much variance is accounted for in each principal component. In the default example, the first principal component accounts for a much high variance than the next two.

This step can help determine whether more principal components are needed.

[8]:
print("Relative variance in principal components:", pca.explained_variance_ratio_)
Relative variance in principal components: [0.63061713 0.21630557 0.14659838]

The input data can now be transformed into this new reference space and rearranged into a xarray dataset compatible with input data.

[9]:
predict = pca.transform(X)
[10]:
out = sklearn_unflatten(predict, ds)
out = out.to_dataset(dim=out.dims[0]).transpose('time','y','x')

Visualise PCA results

[11]:
rgb(out, bands=[2,1,0], index=list(range(len(out.time))), col_wrap=4)
../../../_images/sandbox_notebooks_Frequently_used_code_Principal_component_analysis_24_0.png

Additional information

License: The code in this notebook is licensed under the Apache License, Version 2.0. Digital Earth Africa data is licensed under the Creative Commons by Attribution 4.0 license.

Contact: If you need assistance, please post a question on the Open Data Cube Slack channel or on the GIS Stack Exchange using the open-data-cube tag (you can view previously asked questions here). If you would like to report an issue with this notebook, you can file one on Github.

Compatible datacube version:

[12]:
print(datacube.__version__)
1.8.5

Last Tested:

[13]:
from datetime import datetime
datetime.today().strftime('%Y-%m-%d')
[13]:
'2021-09-13'