Maximum Covariance Analysis in Python
Project description
xMCA | Maximum Covariance Analysis in Python
The aim of this package is to provide a flexible tool for the climate science community to perform Maximum Covariance Analysis (MCA) in a simple and consistent way. Given the huge popularity of xarray
in the climate science community, xmca
supports xarray.DataArray
as well as numpy.ndarray
as input formats.
Mode 2 of complex rotated Maximum Covariance Analysis showing the shared dynamics of SST and continental precipitation associated to ENSO between 1980 and 2020.
What is MCA?
MCA maximises the temporal covariance between two different data fields and is closely related to Principal Component Analysis (PCA) / Empirical Orthogonal Function analysis (EOF analysis). While EOF analysis maximises the variance within a single data field, MCA allows to extract the dominant co-varying patterns between two different data fields. When the two input fields are the same, MCA reduces to standard EOF analysis.
For the mathematical understanding please have a look at e.g. Bretherton et al. or the lecture material written by C. Bretherton.
New in release 1.0.x
- method
predict
allows to project new, unseen data to obtain the corresponding PCs (works for standard, rotation and complex) - more efficient storing/loading of files; Unfortunately, this and the point above made it necessary to change the code considerably. As a consequence, loading models which were performed and saved using an older package version (0.x.y) is not supported.
- add method to summarize performed analysis (
summary
) - add method to return input fields
- improve docs
- correct and consistent use of definition of loadings
- some bugfixes (e.g. hom/het patterns)
Core Features
Standard | Rotated | Complex | Complex Rotated | |
---|---|---|---|---|
EOF analysis | :heavy_check_mark: | :heavy_check_mark: | :heavy_check_mark: | :heavy_check_mark: |
MCA | :heavy_check_mark: | :heavy_check_mark: | :heavy_check_mark: | :heavy_check_mark: |
* click on check marks for reference
** A paper featuring complex (rotated) MCA has been submitted and is currently under review. However, you can already check a pre-print on arXiv.
Installation
Installation is simply done by:
pip install xmca
Quickstart
Import the package
from xmca.array import MCA # use with np.ndarray
from xmca.xarray import xMCA # use with xr.DataArray
As an example, we take North American surface temperatures shipped with
xarray
. Note: only works with xr.DataArray
, not xr.Dataset
.
import xarray as xr # only needed to obtain test data
# split data arbitrarily into west and east coast
data = xr.tutorial.open_dataset('air_temperature').air
west = data.sel(lon=slice(200, 260))
east = data.sel(lon=slice(260, 360))
PCA / EOF analysis
Construct a model with only one field and solve it to perform standard PCA / EOF analysis.
pca = xMCA(west) # PCA of west coast
pca.solve(complexfify=False) # True for complex PCA
eigenvalues = pca.singular_values() # singular vales = eigenvalues for PCA
expvar = pca.explained_variance() # explained variance
pcs = pca.pcs() # Principal component scores (PCs)
eofs = pca.eofs() # spatial patterns (EOFs)
Obtaining a Varimax/Promax-rotated solution can be achieved by rotating
the model choosing the number of EOFs to be rotated (n_rot
) as well as the
Promax parameter (power
). Here, power=1
equals a Varimax-rotated solution.
pca.rotate(n_rot=10, power=1)
expvar_rot = pca.explained_variance() # explained variance
pcs_rot = pca.pcs() # Principal component scores (PCs)
eofs_rot = pca.eofs() # spatial patterns (EOFs)
MCA
Same as for PCA / EOF analysis, but with two input fields instead of one.
mca = xMCA(west, east) # MCA of field A and B
mca.solve(complexfify=False) # True for complex MCA
eigenvalues = mca.singular_values() # singular vales
pcs = mca.pcs() # expansion coefficient (PCs)
eofs = mca.eofs() # spatial patterns (EOFs)
Saving/loading an analysis
mca.save_analysis('my_analysis') # this will save the data and a respective
# info file. The files will be stored in a
# special directory
mca2 = xMCA() # create a new, empty instance
mca2.load_analysis('my_analysis/info.xmca') # analysis can be
# loaded via specifying the path to the
# info file created earlier
Quickly inspect your results visually
The package provides a method to plot individual modes.
mca2.set_field_names('West', 'East')
pkwargs = {'orientation' : 'vertical'}
mca2.plot(mode=1, **pkwargs)
Result of default plot method after performing MCA on T2m of North American west and east coast showing mode 1.
You may want to modify the plot for some better optics:
from cartopy.crs import EqualEarth # for different map projections
# map projections for "left" and "right" field
projections = {
'left': EqualEarth(),
'right': EqualEarth()
}
pkwargs = {
"figsize" : (8, 5),
"orientation" : 'vertical',
'cmap_eof' : 'BrBG', # colormap amplitude
"projection" : projections,
}
mca2.plot(mode=3, **pkwargs)
You can save the plot to your local disk as a .png
file via
skwargs={'dpi':200}
mca2.save_plot(mode=3, plot_kwargs=pkwargs, save_kwargs=skwargs)
Documentation
Please have a look at the documentation page for instructions on how to install and some examples to get started.
Please cite
I am just starting my career as a scientist. Feedback on my scientific work is therefore important to me in order to assess which of my work advances the scientific community. As such, if you use the package for your own research and find it helpful, I would appreciate feedback here on Github, via email, or as a citation:
Niclas Rieger, 2021: nicrie/xmca: version x.y.z. doi:10.5281/zenodo.4749830.
Credits
Kudos to the developers and contributors of the following Github projects which I initially used myself and used as an inspiration:
And of course credits to the developers of the extremely useful packages
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