稀疏观测矩阵上的分层聚类 [英] Hierarchical clustering on sparse observation matrix

问题描述

我正在尝试对大型稀疏观察矩阵执行层次聚类.该矩阵表示多个用户的电影评分.我的目标是根据他们的电影偏好对相似的用户进行聚类.但是，我需要一个树状图，而不是单一的部门.为了做到这一点，我尝试使用 SciPy:

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')

这适用于小数据集:

但是，我(显然)在扩展时遇到了内存问题.如果有什么办法可以将稀疏矩阵提供给算法?

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

推荐答案

从 scipy/cluster/hierarchy.py linkage 处理 y参数为:

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.")

当我将 asarray 应用于 dok 时，我得到一个 0d 对象数组.它只是将字典包装在一个数组中.

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 接受一维压缩样式距离矩阵，或等效的二维矩阵.

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

进一步查看 linkage 我推断 ward 使用 nn_chain，它在编译的 scipy/cluster/_hierarchy.cpython 中-35m-i386-linux-gnu.so 文件.这使得该方法的工作部分甚至超出了临时 Python 程序员的能力范围.

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.

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