def K(self, X, X2=None):
"""
Computes the Laplace kernel matrix between inputs X (and X2) belonging to a SPD manifold.
Parameters
----------
:param X: input points on the SPD manifold (Mandel notation)
Optional parameters
-------------------
:param X2: input points on the SPD manifold (Mandel notation)
Returns
-------
:return: kernel matrix of X or between X and X2
"""
# Transform input vector to matrices
X = vector_to_symmetric_matrix_tf(X, self.matrix_dim)
if X2 is None:
X2 = X
else:
X2 = vector_to_symmetric_matrix_tf(X2, self.matrix_dim)
# Compute beta value from beta_shifted
beta = self.beta_shifted + self.beta_min_value
# Compute the kernel
aff_inv_dist = affine_invariant_distance_tf(X, X2, full_dist_mat=True)
aff_inv_dist = tf.multiply(aff_inv_dist, beta)
return tf.multiply(self.variance, tf.exp(-aff_inv_dist))
def K(self, X, X2=None):
"""
Computes the Stein kernel matrix between inputs X (and X2) belonging to a SPD manifold.
Parameters
----------
:param X: input points on the SPD manifold (Mandel notation)
Optional parameters
-------------------
:param X2: input points on the SPD manifold (Mandel notation)
Returns
-------
:return: kernel matrix of X or between X and X2
"""
# Transform input vector to matrices
X = vector_to_symmetric_matrix_tf(X, self.matrix_dim)
if X2 is None:
X2 = X
else:
X2 = vector_to_symmetric_matrix_tf(X2, self.matrix_dim)
# Compute beta value from beta_shifted
beta = self.beta_shifted + self.continuous_param_space_limit
# Compute the kernel
X = tf.expand_dims(X, 1)
X2 = tf.expand_dims(X2, 0)
X = tf.tile(X, [1, tf.shape(X2)[1], 1, 1])
X2 = tf.tile(X2, [tf.shape(X)[0], 1, 1, 1])
mult_XX2 = tf.matmul(X, X2)
add_halfXX2 = 0.5 * tf.add(X, X2)
detmult_XX2 = tf.linalg.det(mult_XX2)
detadd_halfXX2 = tf.linalg.det(add_halfXX2)
dist = tf.divide(tf.math.pow(detmult_XX2, beta), tf.math.pow(detadd_halfXX2, beta))
return tf.multiply(self.variance, dist)
def K(self, X, X2=None):
"""
Computes the Log-Euclidean kernel matrix between inputs X (and X2) belonging to a SPD manifold.
Parameters
----------
:param X: input points on the SPD manifold (Mandel notation)
Optional parameters
-------------------
:param X2: input points on the SPD manifold (Mandel notation)
Returns
-------
:return: kernel matrix of X or between X and X2
"""
# Transform input vector to matrices
X = vector_to_symmetric_matrix_tf(X, self.matrix_dim)
if X2 is None:
X2 = X
else:
X2 = vector_to_symmetric_matrix_tf(X2, self.matrix_dim)
# Compute the kernel
X = tf.expand_dims(X, 1)
X2 = tf.expand_dims(X2, 0)
X = tf.tile(X, [1, tf.shape(X2)[1], 1, 1])
X2 = tf.tile(X2, [tf.shape(X)[0], 1, 1, 1])
diff_XX2 = tf.cast(tf.subtract(tf.linalg.logm(tf.cast(X, dtype=tf.complex64)), tf.linalg.logm(tf.cast(X2, dtype=tf.complex64))), dtype=tf.float64)
logeucl_dist = tf.norm(diff_XX2, axis=(-2, -1))
logeucl_dist2 = tf.square(logeucl_dist)
logeucl_dist2 = tf.multiply(logeucl_dist2, self.beta_param)
return tf.multiply(self.variance, tf.exp(-logeucl_dist2))