src.model.deeplearn.layer.rbf_feat_extract_layer

Classes

RBFFeatExtractLayer(*args, **kwargs)

class src.model.deeplearn.layer.rbf_feat_extract_layer.RBFFeatExtractLayer(*args, **kwargs)
Author:

Alberto M. Esmoris Pena

A RBF feature extraction layer is governed by a matrix \(\pmb{Q}\) representing the kernel’s structure space in a \(n_x\)-dimensional Euclidean space such that:

\[\pmb{Q} \in \mathbb{R}^{K \times n_x}\]

For 3D point clouds, \(n_x=3\) and the matrix \(\pmb{Q}\) represents the coordinates of the kernel points in a 3D space centered at zero.

On top of that, a RBF feature extraction layer is also governed by a \(\pmb{\omega} \in \mathbb{R}^K\) vector that parametrizes the curvature of each radial basis function.

The output of a RBF feature extraction layer when considering a Gaussian kernel is given by the expression below:

\[\pmb{Y} \in \mathbb{R}^{m \times K} \;\text{s.t.}\; y_{ij} = \exp\biggl({ - \dfrac{ \lVert{\pmb{x_{i*}}-\pmb{q_{j*}}}\rVert^2 }{ \omega_{j}^2 }}\biggr)\]

The \(\pmb{Y}\) matrix can be understood as a feature matrix extracted from the \(m\) input points through its interaction with the kernel.

Variables:

  • structure_initialization_type (str) – The type of initialization strategy for the kernel’s structure space.

  • max_radii (np.ndarray of float) – The radius of the last ellipsoid along each axis \(\pmb{r}^* \in \mathbb{R}^{n_x}\).

  • radii_resolution (int) – How many concentric ellipsoids must be considered \(n \in \mathbb{Z}_{>0}\) (the first one is the center point, the last one is the biggest outer ellipsoid).

  • angular_resolutions (np.ndarray of int) – How many angles consider for each ellipsoid \((m_1, \ldots, m_n)\).

  • kernel_function_type (str) – The type of kernel function to be used (e.g., “Gaussian” or “Markov”).

  • kernel_function (function) – The kernel function to be used.

  • num_kernel_points (int) – The number of points representing the kernel \(K \in \mathbb{Z}_{>0}\).

  • Q (tf.Tensor) – The kernel’s structure space matrix

  • trainable_Q (bool) – Flag to control whether Q is trainable or not.

  • built_Q (bool) – Flag to control whether Q has been built or not.

  • omega (tf.Tensor) – The vector of kernel’s sizes (can be thought as a curvature).

  • trainable_omega (bool) – Flag to control whether omega is trainable or not.

  • built_omega (bool) – Flag to control whether omega has been built or not.

__init__(max_radii, radii_resolution=4, angular_resolutions=(1, 2, 4, 8), kernel_function_type='Gaussian', structure_initialization_type='concentric_ellipsoids', structure_dimensionality=3, trainable_Q=True, trainable_omega=True, built_Q=False, built_omega=False, **kwargs)

See Layer and layer.Layer.__init__().

build(dim_in)

Build the \(\pmb{Q} \in \mathbb{K \times n_x}\) matrix representing the kernel’s structure, and the \(\pmb{\omega}\) vector representing the kernel’s sizes (think about curvature).

The \(\pmb{Q}\) matrix represents the disposition of the kernel’s points while the \(\pmb{\omega}\) vector represents the size of each radial basis function. The size of a radial basis function for typical Gaussian kernels can be seen as the parameter governing the curvature of the exponential.

See Layer and layer.Layer.build().

call(inputs, training=False, mask=False)

The computation of the \(\pmb{Y} \in \mathbb{R}^{m \times K}\) matrix of output features. For example, for a Gaussian kernel this matrix would be:

\[y_{ij} = \exp\left(-\dfrac{ \lVert{\pmb{x_{i*}} - \pmb{q_{j*}}}\rVert^2 }{ \omega_j^2 }\right)\]

Where \(\pmb{x_{i*}}\) is the i-th input point and \(\pmb{q_{j*}}\) is the j-th kernel point.

Returns:

The extracted output features.

Return type:

tf.Tensor

compute_gaussian_kernel(D_squared)

Compute a Gaussian kernel function.

\[y_{ij} = \exp\left( - \dfrac{ \lVert{\pmb{x_{i*}}} - \pmb{q_{j*}}\rVert^2 }{ \omega_{j}^2 } \right)\]
Returns:

The computed Gaussian kernel function.

Return type:

tf.Tensor

compute_markov_kernel(D_squared)

Compute a Markov kernel function.

\[y_{ij} = \exp\left( - \dfrac{ \lVert{\pmb{x_{i*}}} - \pmb{q_{j*}}\rVert }{ \omega_{j}^2 } \right)\]
Returns:

The computed Markov kernel function.

Return type:

tf.Tensor

get_config()

Return necessary data to serialize the layer

classmethod from_config(config)

Use given config data to deserialize the layer

export_representation(dir_path, out_prefix=None, Qpast=None)

Export a set of files representing the state of the kernel’s structure.

Parameters:

  • dir_path (str) – The directory where the representation files will be exported.

  • out_prefix (str) – The output prefix to name the output files.

  • Qpast (np.ndarray or tf.Tensor or None) – The structure matrix of the layer in the past.

Returns:

Nothing at all, but the representation is exported as a set of files inside the given directory.