Hierarchical clustering on sparse observation matrix

Question

I'm trying to perform hierarchical clustering on large sparse observation matrix. The matrix represents movie ratings for a number of users. My goal is to cluster similar users based on their movie preferences. However, I need a dendrogram, rather than single division. In order to do this, I tried to use SciPy:

R = dok_matrix((nrows, ncols), dtype=np.float32)

for user in ratings:
    for item in ratings[user]:
        R[item, user] = ratings[user][item]

Z = hierarchy.linkage(R.transpose().toarray(), method='ward')

This works fine on a small data-set:

However, I (obviously) get memory problems when scaling up. If there any way I can feed sparse matrix to the algorithm?

Answer 1

From scipy/cluster/hierarchy.py linkage processes the y argument as:

y = _convert_to_double(np.asarray(y, order='c'))

if y.ndim == 1:
    distance.is_valid_y(y, throw=True, name='y')
    [y] = _copy_arrays_if_base_present([y])
elif y.ndim == 2:
    if method in _EUCLIDEAN_METHODS and metric != 'euclidean':
        raise ValueError("Method '{0}' requires the distance metric "
                         "to be Euclidean".format(method))
    y = distance.pdist(y, metric)
else:
    raise ValueError("`y` must be 1 or 2 dimensional.")

When I apply asarray to a dok I get a 0d object array. It just wraps the dictionary in an array.

In [905]: M=sparse.dok_matrix([[1,0,0,2,3],[0,0,0,0,1]])
In [906]: M
Out[906]: 
<2x5 sparse matrix of type '<class 'numpy.int32'>'
    with 4 stored elements in Dictionary Of Keys format>
In [908]: m = np.asarray(M)
In [909]: m
Out[909]: 
array(<2x5 sparse matrix of type '<class 'numpy.int32'>'
    with 4 stored elements in Dictionary Of Keys format>, dtype=object)
In [910]: m.shape
Out[910]: ()

linkage accepts a 1d compressed style distance matrix, or the equivalent 2d one.

Looking further in linkage I deduce that ward uses nn_chain, which is in the compiled scipy/cluster/_hierarchy.cpython-35m-i386-linux-gnu.so file. That puts the working part of the method even further out of reach of the casual Python programmer.