import tensorflow as tf
def cross_matrices(tensor_a, a_inputs, tensor_b, b_inputs):
"""Tiles two tensors in perpendicular dimensions."""
expanded_a = tf.expand_dims(tensor_a, 1)
expanded_b = tf.expand_dims(tensor_b, 0)
tiled_a = tf.tile(expanded_a, tf.constant([1, b_inputs, 1]))
tiled_b = tf.tile(expanded_b, tf.constant([a_inputs, 1, 1]))
return [tiled_a, tiled_b]
def linear_kernel(tensor_a, a_inputs, tensor_b, b_inputs):
"""Returns the linear kernel (dot product) matrix of two matrices of vectors
element-wise."""
cross = cross_matrices(tensor_a, a_inputs, tensor_b, b_inputs)
kernel = tf.reduce_sum(tf.mul(cross[0], cross[1]), reduction_indices=2)
return kernel
def gaussian_kernel(tensor_a, a_inputs, tensor_b, b_inputs, gamma):
"""Returns the Gaussian kernel matrix of two matrices of vectors
element-wise."""
cross = cross_matrices(tensor_a, a_inputs, tensor_b, b_inputs)
kernel = tf.exp(tf.mul(tf.reduce_sum(tf.square(
tf.sub(cross[0], cross[1])), reduction_indices=2),
tf.neg(tf.constant(gamma, dtype=tf.float32))))
return kernel
def cost(training, classes, inputs, kernel_type="gaussian", C=1, gamma=1):
"""Returns the kernelised cost to be minimised."""
beta = tf.Variable(tf.zeros([inputs, 1]))
offset = tf.Variable(tf.zeros([1]))
if kernel_type == "linear":
kernel = linear_kernel(training, inputs, training, inputs)
elif kernel_type == "gaussian":
kernel = gaussian_kernel(training, inputs, training, inputs, gamma)
x = tf.reshape(tf.div(tf.matmul(tf.matmul(
beta, kernel, transpose_a=True), beta), tf.constant([2.0])), [1])
y = tf.sub(tf.ones([1]), tf.mul(classes, tf.add(
tf.matmul(kernel, beta, transpose_a=True), offset)))
z = tf.mul(tf.reduce_sum(tf.reduce_max(
tf.concat(1, [y, tf.zeros_like(y)]), reduction_indices=1)),
tf.constant([C], dtype=tf.float32))
cost = tf.add(x, z)
return beta, offset, cost
def decide(training, training_instances, testing, testing_instances,
beta, offset, kernel_type="gaussian", gamma=1):
"""Tests a set of test instances."""
if kernel_type == "linear":
kernel = linear_kernel(
testing, testing_instances, training, training_instances)
elif kernel_type == "gaussian":
kernel = gaussian_kernel(
testing, testing_instances, training, training_instances, gamma)
return tf.sign(tf.add(tf.matmul(kernel, beta), offset))
