def get_function(points, mu, sigma): # f_ik [n,k]
div = coef * tf.rsqrt(tf.batch_matrix_determinant(sigma)) # ((2pi)^p*|S_k|)^-1/2 [k]
div = tf.tile(tf.reshape(div, [1, k]), [n, 1]) # [n,k]
diff = tf.sub(tf.tile(points, [k, 1, 1]), tf.tile(mu, [n, 1, 1])) # x_i-u_k [n*k, p, 1]
sigma = tf.tile(sigma, [n, 1, 1]) # [n*k,p,p]
exp = tf.exp(
-0.5
* tf.batch_matmul(tf.transpose(diff, perm=[0, 2, 1]), tf.batch_matmul(tf.batch_matrix_inverse(sigma), diff))
) # e^(d'*S^-1*d)_ik [n*k, 1, 1]
exp = tf.reshape(exp, [n, k])
return tf.mul(div, exp)
def get_function(points, mu, sigma): # f_ik [n,k]
div = coef * tf.rsqrt(
tf.batch_matrix_determinant(sigma)) # ((2pi)^p*|S_k|)^-1/2 [k]
div = tf.tile(tf.reshape(div, [1, k]), [n, 1]) # [n,k]
diff = tf.sub(tf.tile(points, [k, 1, 1]),
tf.tile(mu, [n, 1, 1])) # x_i-u_k [n*k, p, 1]
sigma = tf.tile(sigma, [n, 1, 1]) # [n*k,p,p]
exp = tf.exp(-0.5 * tf.batch_matmul(
tf.transpose(diff, perm=[0, 2, 1]),
tf.batch_matmul(tf.batch_matrix_inverse(sigma),
diff))) # e^(d'*S^-1*d)_ik [n*k, 1, 1]
exp = tf.reshape(exp, [n, k])
return tf.mul(
div, exp
) # Multivariate normal distribution evaluated for each vector, for each cluster parameter. Hence the [n,k] shape.
def _verifyInverse(self, x):
for np_type in [np.float32, np.float64]:
y = x.astype(np_type)
with self.test_session():
# Verify that x^{-1} * x == Identity matrix.
if x.ndim == 2:
inv = tf.matrix_inverse(y)
tf_ans = tf.matmul(inv, y)
np_ans = np.identity(y.shape[-1])
else:
inv = tf.batch_matrix_inverse(y)
tf_ans = tf.batch_matmul(inv, y)
tiling = list(y.shape)
tiling[-2:] = [1, 1]
np_ans = np.tile(np.identity(y.shape[-1]), tiling)
out = tf_ans.eval()
self.assertAllClose(np_ans, out)
self.assertShapeEqual(y, tf_ans)
def _verifyInverse(self, x):
for np_type in [np.float32, np.float64]:
y = x.astype(np_type)
with self.test_session():
# Verify that x^{-1} * x == Identity matrix.
if x.ndim == 2:
inv = tf.matrix_inverse(y)
tf_ans = tf.matmul(inv, y)
np_ans = np.identity(y.shape[-1])
else:
inv = tf.batch_matrix_inverse(y)
tf_ans = tf.batch_matmul(inv, y)
tiling = list(y.shape)
tiling[-2:] = [1, 1]
np_ans = np.tile(np.identity(y.shape[-1]), tiling)
out = tf_ans.eval()
self.assertAllClose(np_ans, out)
self.assertShapeEqual(y, tf_ans)
def Test(self):
with self.test_session():
np.random.seed(1)
m = np.random.uniform(low=1.0, high=100.0, size=np.prod(shape)).reshape(
shape).astype(dtype)
a = tf.constant(m)
epsilon = np.finfo(dtype).eps
# Optimal stepsize for central difference is O(epsilon^{1/3}).
delta = epsilon ** (1.0 / 3.0)
tol = 1e-3
if len(shape) == 2:
ainv = tf.matrix_inverse(a)
else:
ainv = tf.batch_matrix_inverse(a)
theoretical, numerical = gc.ComputeGradient(a, shape, ainv, shape,
delta=delta)
self.assertAllClose(theoretical, numerical, atol=tol, rtol=tol)
def Test(self):
with self.test_session():
np.random.seed(1)
m = np.random.uniform(
low=1.0, high=100.0,
size=np.prod(shape_)).reshape(shape_).astype(dtype_)
a = tf.constant(m)
epsilon = np.finfo(dtype_).eps
# Optimal stepsize for central difference is O(epsilon^{1/3}).
delta = epsilon**(1.0 / 3.0)
tol = 1e-3
if len(shape_) == 2:
ainv = tf.matrix_inverse(a)
else:
ainv = tf.batch_matrix_inverse(a)
theoretical, numerical = tf.test.compute_gradient(a,
shape_,
ainv,
shape_,
delta=delta)
self.assertAllClose(theoretical, numerical, atol=tol, rtol=tol)
def calc_snf_loss_tf(point, hyperplanes, variances, weights):
#variances = tf.maximum(variances,1e-6) # Avoid NaN errors
# Calculate the distance of the point from each hyperplane
hyperplanes = tf.reshape(hyperplanes, [k, m, m])
hp_inv = tf.batch_matrix_inverse(hyperplanes) # [k,m,m]
x = tf.ones((k, m, 1))
a = tf.batch_matmul(hp_inv, x) # [k,m,1]
point = tf.reshape(point, [m, 1])
a = tf.reshape(a, [k, m])
D = tf.matmul(a, point) - 1
D = tf.reshape(D, [k])
norm = tf.sqrt(tf.reduce_sum(tf.square(a), reduction_indices=[1])) # [k]
D /= norm #tf.maximum(norm,1e-6) # [k]
losses = tf.square(D) # [k]
losses /= -2 * variances # [k]
losses = -tf.exp(losses) # [k]
var_coeffs = 1 / tf.sqrt(2 * variances * 3.14) # [k]
losses *= var_coeffs # [k]
losses *= weights # element-wise [k]
loss = tf.reduce_mean(losses) # Average over the hyperplanes
return loss
# tf.matrix_determinant x = np.random.rand(5, 5) z_matrix_determinant = tf.matrix_determinant(x) # tf.batch_matrix_determinant batch_x = np.random.rand(10, 5, 5) z_batch_matrix_determinant = tf.batch_matrix_determinant(batch_x) # tf.matrix_inverse x = np.random.rand(10, 10) z_matrix_inverse = tf.matrix_inverse(x) # tf.batch_matrix_inverse batch_x = np.random.rand(10, 5, 5) z_batch_matrix_inverse = tf.batch_matrix_inverse(batch_x) # tf.cholesky x = np.random.rand(10, 10) z_cholesky = tf.cholesky(x) # tf.batch_cholesky batch_x = np.random.rand(10, 5, 5) z_batch_cholesky = tf.batch_cholesky(x) # tf.self_adjoint_eig x = np.random.rand(10, 8) z_self_adjoint_eig = tf.self_adjoint_eig(x) # tf.batch_self_adjoint_eig batch_x = np.random.rand(10, 8, 5)
def test_BatchMatrixInverse(self):
t = tf.batch_matrix_inverse(self.random(2, 3, 4, 3, 3))
self.check(t)
def get_function(points, mu, sigma): # f_ik [n,k]
div = coef*tf.rsqrt(tf.batch_matrix_determinant(sigma)) # ((2pi)^p*|S_k|)^-1/2 [k]
div = tf.tile(tf.reshape(div, [1,k]), [n,1]) # [n,k]
diff = tf.sub(tf.tile(points, [k,1,1]), tf.tile(mu, [n,1,1])) # x_i-u_k [n*k, p, 1]
sigma = tf.tile(sigma, [n,1,1]) # [n*k,p,p]
exp = tf.exp(-0.5*tf.batch_matmul( tf.transpose(diff,perm=[0,2,1]), tf.batch_matmul(tf.batch_matrix_inverse(sigma), diff) )) # e^(d'*S^-1*d)_ik [n*k, 1, 1]
exp = tf.reshape(exp, [n,k])
return tf.mul(div, exp) # Multivariate normal distribution evaluated for each vector, for each cluster parameter. Hence the [n,k] shape.
def get_function(points, mu, sigma): # f_ik [n,k]
div = coef*tf.rsqrt(tf.batch_matrix_determinant(sigma)) # ((2pi)^p*|S_k|)^-1/2 [k]
div = tf.tile(tf.reshape(div, [1,k]), [n,1]) # [n,k]
diff = tf.sub(tf.tile(points, [k,1,1]), tf.tile(mu, [n,1,1])) # x_i-u_k [n*k, p, 1]
sigma = tf.tile(sigma, [n,1,1]) # [n*k,p,p]
exp = tf.exp(-0.5*tf.batch_matmul( tf.transpose(diff,perm=[0,2,1]), tf.batch_matmul(tf.batch_matrix_inverse(sigma), diff) )) # e^(d'*S^-1*d)_ik [n*k, 1, 1]
exp = tf.reshape(exp, [n,k])
return tf.mul(div, exp)