机器学习概念 —— 样本距离矩阵

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• 样本（$X_{N\cdot d}$）之间的距离矩阵

  N, d = X.shape
  X_square = np.sum(X*X, axis=1).reshape(N, 1)
  dist_mat = 2*X_square - 2*X.dot(X.T)

  $$p_{j|i}=\frac{\exp\left(-\|x_i-x_j\|^2\big/2\sigma_i^2\right)}{\sum\limits_{k\neq i}\exp\left(-\|x_i-x_k\|^2\big/2\sigma_i^2\right)}$$

  def _joint_distribution_matrix(D, sigma):
      P = np.exp(-D*D/2/sigma**2)
      P /= np.sum(P, axis=1)
      return P