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Module « scipy.spatial »

Fonction procrustes - module scipy.spatial

Signature de la fonction procrustes

def procrustes(data1, data2) 

Description

help(scipy.spatial.procrustes)

Procrustes analysis, a similarity test for two data sets.

Each input matrix is a set of points or vectors (the rows of the matrix).
The dimension of the space is the number of columns of each matrix. Given
two identically sized matrices, procrustes standardizes both such that:

- :math:`tr(AA^{T}) = 1`.

- Both sets of points are centered around the origin.

Procrustes ([1]_, [2]_) then applies the optimal transform to the second
matrix (including scaling/dilation, rotations, and reflections) to minimize
:math:`M^{2}=\sum(data1-data2)^{2}`, or the sum of the squares of the
pointwise differences between the two input datasets.

This function was not designed to handle datasets with different numbers of
datapoints (rows).  If two data sets have different dimensionality
(different number of columns), simply add columns of zeros to the smaller
of the two.

Parameters
----------
data1 : array_like
    Matrix, n rows represent points in k (columns) space `data1` is the
    reference data, after it is standardised, the data from `data2` will be
    transformed to fit the pattern in `data1` (must have >1 unique points).
data2 : array_like
    n rows of data in k space to be fit to `data1`.  Must be the  same
    shape ``(numrows, numcols)`` as data1 (must have >1 unique points).

Returns
-------
mtx1 : array_like
    A standardized version of `data1`.
mtx2 : array_like
    The orientation of `data2` that best fits `data1`. Centered, but not
    necessarily :math:`tr(AA^{T}) = 1`.
disparity : float
    :math:`M^{2}` as defined above.

Raises
------
ValueError
    If the input arrays are not two-dimensional.
    If the shape of the input arrays is different.
    If the input arrays have zero columns or zero rows.

See Also
--------
scipy.linalg.orthogonal_procrustes
scipy.spatial.distance.directed_hausdorff : Another similarity test
  for two data sets

Notes
-----
- The disparity should not depend on the order of the input matrices, but
  the output matrices will, as only the first output matrix is guaranteed
  to be scaled such that :math:`tr(AA^{T}) = 1`.

- Duplicate data points are generally ok, duplicating a data point will
  increase its effect on the procrustes fit.

- The disparity scales as the number of points per input matrix.

References
----------
.. [1] Krzanowski, W. J. (2000). "Principles of Multivariate analysis".
.. [2] Gower, J. C. (1975). "Generalized procrustes analysis".

Examples
--------
>>> import numpy as np
>>> from scipy.spatial import procrustes

The matrix ``b`` is a rotated, shifted, scaled and mirrored version of
``a`` here:

>>> a = np.array([[1, 3], [1, 2], [1, 1], [2, 1]], 'd')
>>> b = np.array([[4, -2], [4, -4], [4, -6], [2, -6]], 'd')
>>> mtx1, mtx2, disparity = procrustes(a, b)
>>> round(disparity)
0

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