How do I create a radial cluster like the following code-example in Python?

I have studied this issue a little bit more and it seems now to be best to create a new function for plotting radial cluster directly from the linkage output (rather than hacking the plotted one). I may cook up eventually something, but nothing very soon.

I'm assuming that your data naturally admit this kind of radial embedding. Have you verified that? Does there exists a suitable method in the linkage for your purposes?

It seems that for any method linkage will return a binary-tree structure. In your examples you have more general tree. You need some extra knowledge how to consolidate tree nodes. This all ready invalidates the idea of hacking the original dendrogram.

Update:
Would this naive example plot be a reasonable similar enough for your purposes? If so, I'll be able to post some really simple code to achieve it.

Update 2:

Here is the code:

radial_demo.py:

from numpy import r_, ones, pi, sortfrom numpy.random import randfrom radial_grouper import tree, pre_order, post_orderfrom radial_visualizer import simple_linkfrom pylab import axis, figure, plot, subplot# ToDo: create proper documentationdef _s(sp, t, o):    subplot(sp)    t.traverse(simple_link, order= o)    axis('equal')def demo1(n):    p= r_[2* pi* rand(1, n)- pi, ones((1, n))]    t= tree(p)    f= figure()    _s(221, t, pre_order)    _s(222, t, post_order)    t= tree(p, tols= sort(2e0* rand(9)))    _s(223, t, pre_order)    _s(224, t, post_order)    f.show()    # f.savefig('test.png')# ToDO: implement more demosif __name__ == '__main__':    demo1(123)

radial_grouper.py:

"""All grouping functionality is collected here."""from collections import namedtuplefrom numpy import r_, arange, argsort, array, ones, pi, wherefrom numpy import logical_and as landfrom radial_support import from_polar__all__= ['tree', 'pre_order', 'post_order']Node= namedtuple('Node', 'ndx lnk')# ToDo: enhance documentationdef _groub_by(p, tol, r):    g, gm, gp= [], [], p- p[0]    while True:        if gp[-1]< 0: break        ndx= where(land(0.<= gp, gp< tol))[0]        if 0< len(ndx):            g.append(ndx)            gm.append(p[ndx].mean())        gp-= tol    return g, array([gm, [r]* len(gm)])def _leafs(p):    return argsort(p[0])def _create_leaf_nodes(ndx):    nodes= []    for k in xrange(len(ndx)):        nodes.append(Node(ndx[k], []))    return nodesdef _link_and_create_nodes(_n, n_, cn, groups):    nodes, n0= [], 0    for k in xrange(len(groups)):        nodes.append(Node(n_+ n0, [cn[m] for m in groups[k]]))        n0+= 1    return n_, n_+ n0, nodesdef _process_level(nodes, polar, p, tol, scale, _n, n_):    groups, p= _groub_by(p, tol, scale* polar[1, _n])    _n, n_, nodes= _link_and_create_nodes(_n, n_, nodes, groups)    polar[:, _n: n_]= p    return nodes, polar, _n, n_def _create_tree(p, r0, scale, tols):    if None is tols:        tols= .3* pi/ 2** arange(5)[::-1]    _n, n_= 0, p.shape[1]    polar= ones((2, (len(tols)+ 2)* n_))    polar[0, :n_], polar[1, :n_]= p[0], r0    # leafs    nodes= _create_leaf_nodes(_leafs(p))    nodes, polar, _n, n_= _process_level(    nodes, polar, polar[0, _leafs(p)], tols[0], scale, _n, n_)    # links    for tol in tols[1:]:        nodes, polar, _n, n_= _process_level(        nodes, polar, polar[0, _n: n_], tol, scale, _n, n_)    # root    polar[:, n_]= [0., 0.]    return Node(n_, nodes), polar[:, :n_+ 1]def _simplify(self):    # ToDo: combine single linkages    return self._rootdef _call(self, node0, node1, f, level):    f(self, [node0.ndx, node1.ndx], level)def pre_order(self, node0, f, level= 0):    for node1 in node0.lnk:        _call(self, node0, node1, f, level)        pre_order(self, node1, f, level+ 1)def post_order(self, node0, f, level= 0):    for node1 in node0.lnk:        post_order(self, node1, f, level+ 1)        _call(self, node0, node1, f, level)class tree(object):    def __init__(self, p, r0= pi, scale= .9, tols= None):        self._n= p.shape[1]        self._root, self._p= _create_tree(p, r0, scale, tols)    def traverse(self, f, order= pre_order, cs= 'Cartesian'):        self.points= self._p        if cs is 'Cartesian':            self.points= from_polar(self._p)        order(self, self._root, f, 0)        return self    def simplify(self):        self._root= _simplify(self)        return self    def is_root(self, ndx):        return ndx== self._p.shape[1]- 1    def is_leaf(self, ndx):        return ndx< self._nif __name__ == '__main__':    # ToDO: add tests    from numpy import r_, round    from numpy.random import rand    from pylab import plot, show    def _l(t, n, l):        # print round(a, 3), n, l, t.is_root(n[0]), t.is_leaf(n[1])        plot(t.points[0, n], t.points[1, n])        if 0== l:            plot(t.points[0, n[0]], t.points[1, n[0]], 's')        if t.is_leaf(n[1]):            plot(t.points[0, n[1]], t.points[1, n[1]], 'o')    n= 123    p= r_[2* pi* rand(1, n)- pi, ones((1, n))]    t= tree(p).simplify().traverse(_l)    # t= tree(p).traverse(_l, cs= 'Polar')    show()    # print    # t.traverse(_l, post_order, cs= 'Polar')

radial_support.py:

"""All supporting functionality is collected here."""from numpy import r_, arctan2, cos, sinfrom numpy import atleast_2d as a2d# ToDo: create proper documentation stringsdef _a(a0, a1):    return r_[a2d(a0), a2d(a1)]def from_polar(p):    """(theta, radius) to (x, y)."""    return _a(cos(p[0])* p[1], sin(p[0])* p[1])def to_polar(c):    """(x, y) to (theta, radius)."""    return _a(arctan2(c[1], c[0]), (c** 2).sum(0)** .5)def d_to_polar(D):    """Distance matrix to (theta, radius)."""    # this functionality is to adopt for more general situations    # intended functionality:    # - embedd distance matrix to 2D    # - return that embedding in polar coordinates    passif __name__ == '__main__':    from numpy import allclose    from numpy.random import randn    c= randn(2, 5)    assert(allclose(c, from_polar(to_polar(c))))    # ToDO: implement more tests

radial_visualizer.py:

"""All visualization functionality is collected here."""from pylab import plot# ToDo: create proper documentationdef simple_link(t, ndx, level):    """Simple_link is just a minimal example to demonstrate what can be    achieved when it's called from _grouper.tree.traverse for each link.    - t, tree instance    - ndx, a pair of (from, to) indicies    - level, of from, i.e. root is in level 0    """    plot(t.points[0, ndx], t.points[1, ndx])    if 0== level:        plot(t.points[0, ndx[0]], t.points[1, ndx[0]], 's')    if t.is_leaf(ndx[1]):        plot(t.points[0, ndx[1]], t.points[1, ndx[1]], 'o')# ToDO: implement more suitable link visualizers# No doubt, this will the part to burn most of the dev. resourcesif __name__ == '__main__':    # ToDO: implement tests    pass

You can find the source code here. Please feel free to modify it anyway you like, but please keep the future modifications synced with the gist.

I believe you can do this using the networkx package in conjunction with matplotlib. Check out the following example from the networkx gallery:

http://networkx.lanl.gov/examples/drawing/circular_tree.html

In general networkx has a number of really nice graph analysis and plotting methods

I added a function fix_verts that merges the verticies at the base of each "U" in the dendrogram.

try this:

import scipyimport pylabimport scipy.cluster.hierarchy as schdef fix_verts(ax, orient=1):    for coll in ax.collections:        for pth in coll.get_paths():            vert = pth.vertices            vert[1:3,orient] = scipy.average(vert[1:3,orient]) # Generate random features and distance matrix.x = scipy.rand(40)D = scipy.zeros([40,40])for i in range(40):    for j in range(40):        D[i,j] = abs(x[i] - x[j])fig = pylab.figure(figsize=(8,8))# Compute and plot first dendrogram.ax1 = fig.add_axes([0.09,0.1,0.2,0.6])Y = sch.linkage(D, method='centroid')Z1 = sch.dendrogram(Y, orientation='right')ax1.set_xticks([])ax1.set_yticks([])# Compute and plot second dendrogram.ax2 = fig.add_axes([0.3,0.71,0.6,0.2])Y = sch.linkage(D, method='single')Z2 = sch.dendrogram(Y)ax2.set_xticks([])ax2.set_yticks([])# Plot distance matrix.axmatrix = fig.add_axes([0.3,0.1,0.6,0.6])idx1 = Z1['leaves']idx2 = Z2['leaves']D = D[idx1,:]D = D[:,idx2]im = axmatrix.matshow(D, aspect='auto', origin='lower', cmap=pylab.cm.YlGnBu)axmatrix.set_xticks([])fix_verts(ax1,1)fix_verts(ax2,0)fig.savefig('test.png')

The result is this:

I hope that is what you were after.