nystrom.py

import numpy as np

def dr_toolbox(D,n_components=None):
    """
    Landmark isomap dimensionality reduction method
    This is the version implemented in
    http://homepage.tudelft.nl/19j49/Matlab_Toolbox_for_Dimensionality_Reduction.html
    
    Parameters
    ----------
    C : matrix of geodesic distances to the landmarks
    
    Returns
    -------
    embedded_coords : embedded coordinates of the original points
    """    
    (n, nl) = map(float, D.shape)
    subB = -0.5 * (
        D - np.array(
            [D.mean(axis=1)]*int(nl)
            ).transpose() - np.array(
            [D.mean(axis=0)]*int(n)
            ) + np.ones(D.shape)*D.sum() / (n * nl))
    subB2 = np.dot(subB.T, subB)
    beta,alpha = np.linalg.eig(subB2)
    val = map(np.sqrt, np.asarray(beta,dtype=complex))
    invVal = np.linalg.inv(np.diag(val))
    vec = np.dot( np.dot(subB,  alpha), invVal)

    # Computing final embedding
    val = np.array(map(np.real,val))
    ind = val.argsort()
    ind = ind[::-1] # we want decreasing order
    val = val.take(ind)
    vec = vec.take(ind, axis=1)
    return vec*[map(sqrt, val)]