SpectralMethods.py 文件源码

def getDiffusionMap(SSM, Kappa, t = -1, includeDiag = True, thresh = 5e-4, NEigs = 51):
    """
    :param SSM: Metric between all pairs of points
    :param Kappa: Number in (0, 1) indicating a fraction of nearest neighbors
                used to autotune neighborhood size
    :param t: Diffusion parameter.  If -1, do Autotuning
    :param includeDiag: If true, include recurrence to diagonal in the markov
        chain.  If false, zero out diagonal
    :param thresh: Threshold below which to zero out entries in markov chain in
        the sparse approximation
    :param NEigs: The number of eigenvectors to use in the approximation
    """
    N = SSM.shape[0]
    #Use the letters from the delaPorte paper
    K = getW(SSM, int(Kappa*N))
    if not includeDiag:
        np.fill_diagonal(K, np.zeros(N))
    RowSumSqrt = np.sqrt(np.sum(K, 1))
    DInvSqrt = sparse.diags([1/RowSumSqrt], [0])

    #Symmetric normalized Laplacian
    Pp = (K/RowSumSqrt[None, :])/RowSumSqrt[:, None]
    Pp[Pp < thresh] = 0
    Pp = sparse.csr_matrix(Pp)

    lam, X = sparse.linalg.eigsh(Pp, NEigs, which='LM')
    lam = lam/lam[-1] #In case of numerical instability

    #Check to see if autotuning
    if t > -1:
        lamt = lam**t
    else:
        #Autotuning diffusion time
        lamt = np.array(lam)
        lamt[0:-1] = lam[0:-1]/(1-lam[0:-1])

    #Do eigenvector version
    V = DInvSqrt.dot(X) #Right eigenvectors
    M = V*lamt[None, :]
    return M/RowSumSqrt[:, None] #Put back into orthogonal Euclidean coordinates