Get norm of numpy sparse matrix rows

问题:

I have a sparse matrix that I obtained by using Sklearn's TfidfVectorizer object:

vect = TfidfVectorizer(sublinear_tf=True, max_df=0.5, analyzer='word', vocabulary=my_vocab, stop_words='english')
tfidf = vect.fit_transform([my_docs])

The sparse matrix is (taking out the numbers for generality):

<sparse matrix of type '<type 'numpy.float64'>'
with stored elements in Compressed Sparse Row format>]

I am trying to get a numeric value for each row to tell me how high a document had the terms I am looking for. I don't really care about which words it contained, I just want to know how many it contained. So I want to get the norm of each or the row*row.T. However, I am having a very hard time working with numpy to obtain this.

My first approach was to just simply do:

tfidf[i] * numpy.transpose(tfidf[i])

However, numpy will apparently not transpose an array with less than one dimension so that will just square the vector. So I tried doing:

tfidf[i] * numpy.transpose(numpy.atleast_2d(tfidf[0]))

But numpy.transpose(numpy.atleast_2d(tfidf[0])) still would not transpose the row.

I moved on to trying to get the norm of the row (that approach is probably better anyways). My initial approach was using numpy.linalg.

numpy.linalg.norm(tfidf[0])

But that gave me a "dimension mismatch" error. So I tried to calculate the norm manually. I started by just setting a variable equal to a numpy array version of the sparse matrix and printing out the len of the first row:

my_array = numpy.array(tfidf)
print my_array
print len(my_array[0])

It prints out my_array correctly, but when I try to access the len it tells me:

IndexError: 0-d arrays can't be indexed

I just simply want to get a numeric value of each row in the sparse matrix returned by fit_transform. Getting the norm would be best. Any help here is very appreciated.

回答1:

Some simple fake data:

a = np.arange(9.).reshape(3,3)
s = sparse.csr_matrix(a)

To get the norm of each row from the sparse, you can use:

np.sqrt(s.multiply(s).sum(1))

And the renormalized s would be

s.multiply(1/np.sqrt(s.multiply(s).sum(1)))

or to keep it sparse before renormalizing:

s.multiply(sparse.csr_matrix(1/np.sqrt(s.multiply(s).sum(1))))

To get ordinary matrix or array from it, use:

m = s.todense()
a = s.toarray()

If you have enough memory for the dense version, you can get the norm of each row with:

n = np.sqrt(np.einsum('ij,ij->i',a,a))

or

n = np.apply_along_axis(np.linalg.norm, 1, a)

To normalize, you can do

an = a / n[:, None]

or, to normalize the original array in place:

a /= n[:, None]

The [:, None] thing basically transposes n to be a vertical array.

回答2:

scipy.sparse is a great package, and it keeps getting better with every release, but a lot of things are still only half cooked, and you can get big performance improvements if you implement some of the algorithms yourself. For instance, a 7x improvement over @askewchan's implementation using scipy functions:

In [18]: a = sps.rand(1000, 1000, format='csr')

In [19]: a
Out[19]: 
<1000x1000 sparse matrix of type '<type 'numpy.float64'>'
    with 10000 stored elements in Compressed Sparse Row format>

In [20]: %timeit a.multiply(a).sum(1)
1000 loops, best of 3: 288 us per loop

In [21]: %timeit np.add.reduceat(a.data * a.data, a.indptr[:-1])
10000 loops, best of 3: 36.8 us per loop

In [24]: np.allclose(a.multiply(a).sum(1).ravel(),
    ...:             np.add.reduceat(a.data * a.data, a.indptr[:-1]))
Out[24]: True

You can similarly normalize the array in place doing the following:

norm_rows = np.sqrt(np.add.reduceat(a.data * a.data, a.indptr[:-1]))
nnz_per_row = np.diff(a.indptr)
a.data /= np.repeat(norm_rows, nnz_per_row)

If you are going to be using sparse matrices often, read the wikipedia page on compressed sparse formats, and you will often find better ways than the default to do things.