python - 将非常重复的矩阵添加到 numpy/scipy 中的稀疏矩阵中？

Question

我正在尝试在 NumPy/Scipy 中实现一个函数来计算 Jensen-Shannon divergence在单个(训练)向量和大量其他(观察)向量之间。观察向量存储在一个非常大的 (500,000x65536) Scipy sparse matrix 中(密集矩阵不适合内存)。

作为算法的一部分，我需要为每个观察向量 Oi 计算 T+Oi，其中 T 是训练向量。我无法使用 NumPy 的常用广播规则找到一种方法来做到这一点，因为稀疏矩阵似乎不支持那些(如果 T 保留为密集数组，Scipy 尝试首先使稀疏矩阵密集，它运行内存不足；如果我将 T 设为稀疏矩阵，则 T+Oi 会失败，因为形状不一致)。

目前我正在采取非常低效的步骤，将训练向量平铺到 500,000x65536 稀疏矩阵中:

training = sp.csr_matrix(training.astype(np.float32))
tindptr = np.arange(0, len(training.indices)*observations.shape[0]+1, len(training.indices), dtype=np.int32)
tindices = np.tile(training.indices, observations.shape[0])
tdata = np.tile(training.data, observations.shape[0])
mtraining = sp.csr_matrix((tdata, tindices, tindptr), shape=observations.shape)

但是当它只存储大约 1500 个“真实”元素时，这会占用大量内存(大约 6GB)。构建也很慢。

我试图通过使用 stride_tricks 使 CSR 矩阵的 indptr 和数据成员不使用重复数据的额外内存来变得聪明。

training = sp.csr_matrix(training)
mtraining = sp.csr_matrix(observations.shape,dtype=np.int32)
tdata = training.data
vdata = np.lib.stride_tricks.as_strided(tdata, (mtraining.shape[0], tdata.size), (0, tdata.itemsize))
indices = training.indices
vindices = np.lib.stride_tricks.as_strided(indices, (mtraining.shape[0], indices.size), (0, indices.itemsize))
mtraining.indptr = np.arange(0, len(indices)*mtraining.shape[0]+1, len(indices), dtype=np.int32)
mtraining.data = vdata
mtraining.indices = vindices

但这不起作用，因为跨步 View mtraining.data 和 mtraining.indices 是错误的形状(并且根据 this answer 没有办法使它成为正确的形状)。尝试使用 .flat 迭代器使它们看起来平坦失败，因为它看起来不够像数组(例如，它没有 dtype 成员)，并且使用 flatten() 方法最终会复制。

有什么办法可以做到这一点吗？

Answer 1

我什至没有考虑过的另一种选择是自己以稀疏格式实现总和，以便您可以充分利用数组的周期性。如果您滥用 scipy 稀疏矩阵的这种特殊行为，这很容易做到:

>>> a = sps.csr_matrix([1,2,3,4])
>>> a.data
array([1, 2, 3, 4])
>>> a.indices
array([0, 1, 2, 3])
>>> a.indptr
array([0, 4])

>>> b = sps.csr_matrix((np.array([1, 2, 3, 4, 5]),
...                     np.array([0, 1, 2, 3, 0]),
...                     np.array([0, 5])), shape=(1, 4))
>>> b
<1x4 sparse matrix of type '<type 'numpy.int32'>'
    with 5 stored elements in Compressed Sparse Row format>
>>> b.todense()
matrix([[6, 2, 3, 4]])

所以你甚至不必在你的训练向量和观察矩阵的每一行之间寻找巧合来将它们相加:只需用正确的指针填充所有数据，并且需要求和的内容将被求和当数据被访问时。

编辑

鉴于第一个代码的缓慢，您可以按如下方式用内存换取速度:

def csr_add_sparse_vec(sps_mat, sps_vec) :
    """Adds a sparse vector to every row of a sparse matrix"""
    # No checks done, but both arguments should be sparse matrices in CSR
    # format, both should have the same number of columns, and the vector
    # should be a vector and have only one row.

    rows, cols = sps_mat.shape
    nnz_vec = len(sps_vec.data)
    nnz_per_row = np.diff(sps_mat.indptr)
    longest_row = np.max(nnz_per_row)

    old_data = np.zeros((rows * longest_row,), dtype=sps_mat.data.dtype)
    old_cols = np.zeros((rows * longest_row,), dtype=sps_mat.indices.dtype)

    data_idx = np.arange(longest_row) < nnz_per_row[:, None]
    data_idx = data_idx.reshape(-1)
    old_data[data_idx] = sps_mat.data
    old_cols[data_idx] = sps_mat.indices
    old_data = old_data.reshape(rows, -1)
    old_cols = old_cols.reshape(rows, -1)

    new_data = np.zeros((rows, longest_row + nnz_vec,),
                        dtype=sps_mat.data.dtype)
    new_data[:, :longest_row] = old_data
    del old_data
    new_cols = np.zeros((rows, longest_row + nnz_vec,),
                        dtype=sps_mat.indices.dtype)
    new_cols[:, :longest_row] = old_cols
    del old_cols
    new_data[:, longest_row:] = sps_vec.data
    new_cols[:, longest_row:] = sps_vec.indices
    new_data = new_data.reshape(-1)
    new_cols = new_cols.reshape(-1)
    new_pointer = np.arange(0, (rows + 1) * (longest_row + nnz_vec),
                            longest_row + nnz_vec)

    ret = sps.csr_matrix((new_data, new_cols, new_pointer),
                         shape=sps_mat.shape)
    ret.eliminate_zeros()

    return ret

它没有以前那么快，但它可以在大约 1 秒内完成 10,000 行。:

In [2]: a
Out[2]: 
<10000x65536 sparse matrix of type '<type 'numpy.float64'>'
    with 15000000 stored elements in Compressed Sparse Row format>

In [3]: b
Out[3]: 
<1x65536 sparse matrix of type '<type 'numpy.float64'>'
    with 1500 stored elements in Compressed Sparse Row format>

In [4]: csr_add_sparse_vec(a, b)
Out[4]: 
<10000x65536 sparse matrix of type '<type 'numpy.float64'>'
    with 30000000 stored elements in Compressed Sparse Row format>

In [5]: %timeit csr_add_sparse_vec(a, b)
1 loops, best of 3: 956 ms per loop

编辑 这段代码非常非常慢

def csr_add_sparse_vec(sps_mat, sps_vec) :
    """Adds a sparse vector to every row of a sparse matrix"""
    # No checks done, but both arguments should be sparse matrices in CSR
    # format, both should have the same number of columns, and the vector
    # should be a vector and have only one row.

    rows, cols = sps_mat.shape

    new_data = sps_mat.data
    new_pointer = sps_mat.indptr.copy()
    new_cols = sps_mat.indices

    aux_idx = np.arange(rows + 1)

    for value, col in itertools.izip(sps_vec.data, sps_vec.indices) :
        new_data = np.insert(new_data, new_pointer[1:], [value] * rows)
        new_cols = np.insert(new_cols, new_pointer[1:], [col] * rows)
        new_pointer += aux_idx

    return sps.csr_matrix((new_data, new_cols, new_pointer),
                          shape=sps_mat.shape)