spearman coefficient

spearman.py

def spearman_coefficient(X, Y):
    """
    Considering the rows of X (and Y=X) as vectors, compute the
    distance matrix between each pair of vectors.

    Like  Pearson Coefficient , but compares relative ranking of preference
    values instead of preference values themselves. That is, each user's
    preferences are sorted and then assign a rank as their preference value,
    with 1 being assigned to the least preferred item.

    Parameters
    ----------
    X: array of shape (n_samples_1, n_features)

    Y: array of shape (n_samples_2, n_features)

    Returns
    -------
    distances: array of shape (n_samples_1, n_samples_2)

    Examples
    --------
    >>> from scikits.crab.metrics.pairwise  import spearman_coefficient
    >>> X = [[('a',2.5),('b', 3.5), ('c',3.0), ('d',3.5)],[ ('e', 2.5),
              ('f', 3.0),('g', 2.5), ('h', 4.0)] ]
    >>> # distance between rows of X
    >>> spearman_coefficient(X, X)
    array([[ 1.,  0.],
           [ 0.,  1.]])
    >>> spearman_coefficient(X, [[('a',2.5),('b', 3.5), ('c',3.0), ('k',3.5)]])
    array([[ 1.],
           [ 0.]])
    """
    # should not need X_norm_squared because if you could precompute that as
    # well as Y, then you should just pre-compute the output and not even
    # call this function.
    if X is Y:
        X = Y = np.asanyarray(X, dtype=[('x', 'S30'), ('y', float)])
    else:
        X = np.asanyarray(X,  dtype=[('x', 'S30'), ('y', float)])
        Y = np.asanyarray(Y,  dtype=[('x', 'S30'), ('y', float)])

    if X.shape[1] != Y.shape[1]:
        raise ValueError("Incompatible dimension for X and Y matrices")

    X.sort(order='y')
    Y.sort(order='y')

    result = []

    #TODO: Check if it is possible to optimize this function
    i = 0
    for arrayX in X:
        result.append([])
        for arrayY in Y:
            Y_keys = [key for key, value in arrayY]

            XY = [(key, value) for key, value in arrayX if key in Y_keys]

            sumDiffSq = 0.0
            for index, tup in enumerate(XY):
                sumDiffSq += pow((index + 1) - (Y_keys.index(tup[0]) + 1), 2.0)

            n = len(XY)
            if n == 0:
                result[i].append(0.0)
            else:
                result[i].append(1.0 - ((6.0 * sumDiffSq) / (n * (n * n - 1))))
        result[i] = np.asanyarray(result[i])
        i += 1

    return np.asanyarray(result)