skbio.stats.composition.tree_basis#

skbio.stats.composition.tree_basis(tree)[source]#

Calculate the sparse representation of an ilr basis from a tree.

This computes an orthonormal basis specified from a bifurcating tree.

Parameters:

treeskbio.TreeNode: Input bifurcating tree. Must be strictly bifurcating (i.e. every internal node needs to have exactly two children). This is used to specify the ilr basis.

Returns:

scipy.sparse.coo_matrix: The ilr basis required to perform the ilr_inv transform. This is also known as the sequential binary partition. Note that this matrix is represented in clr coordinates.
list of str: List of tree node names indicating the ordering in the basis.

Raises:

ValueError: If the tree doesn’t contain two branches.

Examples

>>> from skbio import TreeNode
>>> tree = u"((b,c)a, d)root;"
>>> t = TreeNode.read([tree])
>>> basis, nodes = tree_basis(t)
>>> basis.toarray()
array([[-0.40824829, -0.40824829,  0.81649658],
       [-0.70710678,  0.70710678,  0.        ]])