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r"""
Ordination methods (:mod:`skbio.stats.ordination`)
==================================================
.. currentmodule:: skbio.stats.ordination
This module contains several ordination methods, including Principal
Coordinate Analysis, Correspondence Analysis, Redundancy Analysis and
Canonical Correspondence Analysis.
Ordination Functions
--------------------
.. autosummary::
:toctree:
ca
pcoa
pcoa_biplot
cca
rda
Classes
-------
.. autosummary::
:toctree:
OrdinationResults
Utility Functions
-----------------
.. autosummary::
:toctree:
mean_and_std
corr
scale
svd_rank
e_matrix
f_matrix
Examples
--------
This is an artificial dataset (table 11.3 in [1]_) that represents fish
abundance in different sites (`Y`, the response variables) and
environmental variables (`X`, the explanatory variables).
>>> import numpy as np
>>> import pandas as pd
First we need to construct our explanatory variable dataset `X`.
>>> X = np.array([[1.0, 0.0, 1.0, 0.0],
... [2.0, 0.0, 1.0, 0.0],
... [3.0, 0.0, 1.0, 0.0],
... [4.0, 0.0, 0.0, 1.0],
... [5.0, 1.0, 0.0, 0.0],
... [6.0, 0.0, 0.0, 1.0],
... [7.0, 1.0, 0.0, 0.0],
... [8.0, 0.0, 0.0, 1.0],
... [9.0, 1.0, 0.0, 0.0],
... [10.0, 0.0, 0.0, 1.0]])
>>> transects = ['depth', 'substrate_coral', 'substrate_sand',
... 'substrate_other']
>>> sites = ['site1', 'site2', 'site3', 'site4', 'site5', 'site6', 'site7',
... 'site8', 'site9', 'site10']
>>> X = pd.DataFrame(X, sites, transects)
Then we need to create a dataframe with the information about the species
observed at different sites.
>>> species = ['specie1', 'specie2', 'specie3', 'specie4', 'specie5',
... 'specie6', 'specie7', 'specie8', 'specie9']
>>> Y = np.array([[1, 0, 0, 0, 0, 0, 2, 4, 4],
... [0, 0, 0, 0, 0, 0, 5, 6, 1],
... [0, 1, 0, 0, 0, 0, 0, 2, 3],
... [11, 4, 0, 0, 8, 1, 6, 2, 0],
... [11, 5, 17, 7, 0, 0, 6, 6, 2],
... [9, 6, 0, 0, 6, 2, 10, 1, 4],
... [9, 7, 13, 10, 0, 0, 4, 5, 4],
... [7, 8, 0, 0, 4, 3, 6, 6, 4],
... [7, 9, 10, 13, 0, 0, 6, 2, 0],
... [5, 10, 0, 0, 2, 4, 0, 1, 3]])
>>> Y = pd.DataFrame(Y, sites, species)
We can now perform canonical correspondence analysis. Matrix `X` contains a
continuous variable (depth) and a categorical one (substrate type) encoded
using a one-hot encoding.
>>> from skbio.stats.ordination import cca
We explicitly need to avoid perfect collinearity, so we'll drop one of the
substrate types (the last column of `X`).
>>> del X['substrate_other']
>>> ordination_result = cca(Y, X, scaling=2)
Exploring the results we see that the first three axes explain about
80% of all the variance.
>>> ordination_result.proportion_explained
CCA1 0.466911
CCA2 0.238327
CCA3 0.100548
CCA4 0.104937
CCA5 0.044805
CCA6 0.029747
CCA7 0.012631
CCA8 0.001562
CCA9 0.000532
dtype: float64
References
----------
.. [1] Legendre P. and Legendre L. 1998. Numerical Ecology. Elsevier,
Amsterdam.
"""
# ----------------------------------------------------------------------------
# Copyright (c) 2013--, scikit-bio development team.
#
# Distributed under the terms of the Modified BSD License.
#
# The full license is in the file COPYING.txt, distributed with this software.
# ----------------------------------------------------------------------------
from ._redundancy_analysis import rda
from ._correspondence_analysis import ca
from ._canonical_correspondence_analysis import cca
from ._principal_coordinate_analysis import pcoa, pcoa_biplot
from ._ordination_results import OrdinationResults
from ._utils import (mean_and_std, scale, svd_rank, corr, e_matrix, f_matrix,
center_distance_matrix)
__all__ = ['ca', 'rda', 'cca', 'pcoa', 'pcoa_biplot', 'OrdinationResults',
'mean_and_std', 'scale', 'svd_rank', 'corr',
'e_matrix', 'f_matrix', 'center_distance_matrix']
|
