Similarity metrics for Sparse Matrices

similarity.py

def jaccard_metric(x, y):
    """
    x: scipy.sparse CSR matrix shape (1, n)
    y: scipy.sparse CSR matrix shape (1, n)
    returns: jaccard similarity
    """
    return x.minimum(y).sum()/x.maximum(y).sum()

def l2_metric(x,y):
    """
    x: scipy.sparse CSR matrix shape (1, n)
    y: scipy.sparse CSR matrix shape (1, n)
    returns: l2 similarity
    """
    from scipy.sparse import linalg
    return -linalg.norm(x-y)

def cos_metric(x, y):
    """
    x: scipy.sparse CSR matrix shape (1, n)
    y: scipy.sparse CSR matrix shape (1, n)
    returns: cosine similarity
    """
    from scipy.sparse import linalg
    return x.dot(y) / (linalg.norm(x) * linalg.norm(y))

def jaccard_pdist(X, Y):
    """
    X: scipy.sparse CSR matrix, shape (m1, n)
    Y: scipy.sparse CSR matrix, shape (m2, n)
    returns: pairwise jaccard distance between X and Y, shape (m1, m2)
    """
    m2 = Y.shape[0]
    d = []
    Y_idx = np.repeat(0, m2)
    for i in range(m2):
        num = np.asarray(X.minimum(Y[Y_idx]).sum(1))
        denom = np.asarray(X.maximum(Y[Y_idx]).sum(1))
        d.append(num/denom)
        Y_idx += 1
    return np.hstack(d)

def l2_pdist(X, Y):
    """
    help from https://stackoverflow.com/a/37903795
    X: scipy.sparse CSR matrix, shape (m1, n)
    Y: scipy.sparse CSR matrix, shape (m2, n)
    returns: pairwise l2 distance between X and Y, shape (m1, m2)
    """
    m2 = Y.shape[0]
    d = []
    Y_idx = np.repeat(0, m2)
    for i in range(m2):
        d.append(-np.sqrt(np.asarray((X-Y[Y_idx]).power(2).sum(1))))
        Y_idx += 1
    return np.hstack(d)

def cos_pdist(X, Y):
    """
    help from https://stackoverflow.com/a/43493487
    X: scipy.sparse CSR matrix, shape (m1, n)
    Y: scipy.sparse CSR matrix, shape (m2, n)
    returns: pairwise cosine distance between X and Y, shape (m1, m2)
    """
    sumyy = np.asarray((Y.power(2)).sum(1)).flatten()
    sumxx = np.asarray((X.power(2)).sum(1))
    sumxy = X.dot(Y.T).toarray()
    return (sumxy/np.sqrt(sumxx))/np.sqrt(sumyy)