VSB Power Line Blog - SVD Entropy

svd_entropy.py

def _embed(x, order=3, delay=1):
  N = len(x)
  # In our case, N-(order-1)*delay = 800000 - (3-1)*1 = 799998
  # Y.shape = 3x799998
  Y = np.zeros((order, N - (order - 1) * delay))
  for i in range(order):
    # Y[0] = x[0:799998], Y[1] = x[1:799999], Y[2] = x[3:800000]
    Y[i] = x[(i * delay) : (i * delay) + Y.shape[1]].T
  # Y.T[0] = [x[0],x[1],x[2]], Y.T[1] = [x[1],x[2],x[3]], ... , Y.T[799998] = [x[799998],x[799999],x[800000]]
  return Y.T

def svd_entropy(x, order=3, delay=1, normalize=False):
  x = np.array(x)
  mat = _embed(x, order=order, delay=delay)
  # W is an array containing singular values obtained after computation of SVD
  W = np.linalg.svd(mat, compute_uv=False)
  # Normalize the singular values
  W /= sum(W)
  svd_e = -np.multiply(W, np.log2(W)).sum()
  if normalize:
    svd_e /= np.log2(order)
  return svd_e