# Principal component analysis for multi-spectral data

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**Compatibility:**Notebook currently compatible with both the`NCI`

and`DEA Sandbox`

environments**Products used:**ga_s2am_ard_3, ga_s2bm_ard_3

## 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:

Loading Sentinel-2 multi-spectral data.

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
import datacube
from sklearn.decomposition import PCA
import sys
sys.path.insert(1, '../Tools/')
from dea_tools.datahandling import load_ard
from dea_tools.plotting import rgb
from dea_tools.classification import sklearn_flatten, sklearn_unflatten
```

### Connect to the datacube

Connect to the datacube so we can access DEA data.

```
[2]:
```

```
dc = datacube.Datacube(app='Principal_component_analysis')
```

### Analysis parameters

This section defines the analysis parameters, including

`lat, lon`

: center lat/lon for the area of interest`buffer`

: the window size around the centre lat/lon for the area of interest`time_range`

: time period to be investigated`min_gooddata`

: minimum fraction of good-data in the image before it while be returned`bands`

: spectral bands to be explored

The default location is the Norman River, Qld.

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

```
[3]:
```

```
lat, lon = -17.5687, 140.9653
buffer = 0.05
time_range = ('2019-12', '2020-03')
bands = [
'nbart_blue', 'nbart_green', 'nbart_red', 'nbart_red_edge_1', 'nbart_red_edge_2',
'nbart_red_edge_3', 'nbart_nir_2', 'nbart_swir_2', 'nbart_swir_3'
]
min_gooddata = 0.99
```

## Loading cloud-masked Sentinel-2 multi-spectral data

```
[4]:
```

```
# Define the query dict
query = {
'time': time_range,
'x': (lon - buffer, lon + buffer),
'y': (lat + buffer, lat - buffer),
'output_crs': 'epsg:3577',
'resolution': (-20, 20),
'group_by': 'solar_day',
'measurements': bands
}
```

```
[5]:
```

```
# Load the data
ds = load_ard(dc=dc,
products=['ga_s2am_ard_3', 'ga_s2bm_ard_3'],
min_gooddata=min_gooddata,
mask_pixel_quality=False,
**query)
```

```
Finding datasets
ga_s2am_ard_3
ga_s2bm_ard_3
Counting good quality pixels for each time step using fmask
Filtering to 6 out of 24 time steps with at least 99.0% good quality pixels
Loading 6 time steps
```

```
[6]:
```

```
# Visualize data using selected input spectral bands
rgb(ds,
bands=['nbart_swir_2', 'nbart_nir_2', 'nbart_red_edge_1'],
col='time',
col_wrap=3)
```

## 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 using the DEA function `sklearn_flatten`

.

```
[7]:
```

```
x = sklearn_flatten(ds)
```

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

```
[8]:
```

```
pca = PCA(n_components=3)
pca.fit(x)
```

```
[8]:
```

PCA(n_components=3)

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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.

```
[9]:
```

```
print('Relative variance in principal components:',
pca.explained_variance_ratio_)
```

```
Relative variance in principal components: [0.86241157 0.07656634 0.05398086]
```

The input data can now be transformed into this new reference space and rearranged into an `xarray.Dataset`

compatible with our input data.

```
[10]:
```

```
predict = pca.transform(x)
```

```
[11]:
```

```
out = sklearn_unflatten(predict, ds)
out = out.to_dataset(dim=out.dims[0]).transpose('time', 'y', 'x')
```

### Visualise PCA results

```
[12]:
```

```
# Plot PCA bands
rgb(out,
bands=[2, 1, 0],
col='time',
col_wrap=3,
percentile_stretch=[0.2, 0.90])
```

## Additional information

**License:** The code in this notebook is licensed under the Apache License, Version 2.0. Digital Earth Australia 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.

**Last modified:** April 2023

**Compatible datacube version:**

```
[13]:
```

```
print(datacube.__version__)
```

```
1.8.12
```

## Tags

**Tags**: sandbox compatible, NCI compatible, sentinel 2, rgb, sklearn_flatten, sklearn_unflatten, principal component analysis, statistics