Computing sufficient statistics for Fisher vectors

descs_to_sstats.py

def descriptors_to_sufficient_statistics(xx, gmm, **kwargs):
    # yael assumes that the data is in C-contiguous format.
    xx = np.ascontiguousarray(np.atleast_2d(xx))

    N = xx.shape[0]
    K = gmm.k
    D = gmm.d

    # Compute posterior probabilities using yael.
    Q = gmm_predict_proba(xx, gmm)  # NxK

    # Get parameters and reshape them.
    pi = yael.fvec_to_numpy(gmm.w, K)                          # 1xK
    mu = yael.fvec_to_numpy(gmm.mu, K * D).reshape(K, D)       # DxK
    sigma = yael.fvec_to_numpy(gmm.sigma, K * D).reshape(K, D) # DxK

    # Compute the sufficient statistics of descriptors.
    Q_sum = np.sum(Q, 0)[:, np.newaxis] / N  # Kx1
    Q_xx = np.dot(Q.T, xx) / N               # KxD
    Q_xx_2 = np.dot(Q.T, xx ** 2) / N        # KxD

    # Merge sufficient statistics into a vector.
    return np.hstack((Q_sum, Q_xx.flatten(), Q_xx_2.flatten()))