Package mdp :: Package nodes :: Class GrowingNeuralGasNode

Class GrowingNeuralGasNode

Learn the topological structure of the input data by building a corresponding graph approximation.

The algorithm expands on the original Neural Gas algorithm (see mdp.nodes NeuralGasNode) in that the algorithm adds new nodes are added to the graph as more data becomes available. Im this way, if the growth rate is appropriate, one can avoid overfitting or underfitting the data.

Reference

More information about the Growing Neural Gas algorithm can be found in B. Fritzke, A Growing Neural Gas Network Learns Topologies, in G. Tesauro, D. S. Touretzky, and T. K. Leen (editors), Advances in Neural Information Processing Systems 7, pages 625-632. MIT Press, Cambridge MA, 1995.

Instance Methods

[hide private]

__init__(self, start_poss=None, eps_b=0.2, eps_n=0.006, max_age=50, lambda_=100, alpha=0.5, d=0.995, max_nodes=2147483647, input_dim=None, dtype=None)
Initializes an object of type 'GrowingNeuralGasNode'.

_add_edge(self, from_, to_)

_add_node(self, pos)

_get_nearest_nodes(self, x)
Return the two nodes in the graph that are nearest to x and their squared distances.

_insert_new_node(self)
Insert a new node in the graph where it is more necessary (i.e. where the error is the largest).

_move_node(self, node, x, eps)
Move a node by eps in the direction x.

_remove_old_edges(self, edges)
Remove all edges older than the maximal age.

_set_input_dim(self, n)

_train(self, input)

get_nodes_position(self)

tuple

nearest_neighbor(self, input)
Assign each point in the input data to the nearest node in the graph. Return the list of the nearest node instances, and the list of distances.

train(self, input)
Update the internal structures according to the input data x.

Inherited from unreachable.newobject: __long__, __native__, __nonzero__, __unicode__, next

Inherited from object: __delattr__, __format__, __getattribute__, __hash__, __new__, __reduce__, __reduce_ex__, __setattr__, __sizeof__, __subclasshook__

Inherited from Node

__add__(self, other)

__call__(self, x, *args, **kwargs)
Calling an instance of Node is equivalent to calling its execute method.

__repr__(self)
repr(x)

__str__(self)
str(x)

_check_input(self, x)

_check_output(self, y)

_check_train_args(self, x, *args, **kwargs)

_execute(self, x)

_get_supported_dtypes(self)
Return the list of dtypes supported by this node.

_get_train_seq(self)

_if_training_stop_training(self)

_inverse(self, x)

_pre_execution_checks(self, x)
This method contains all pre-execution checks.

_pre_inversion_checks(self, y)
This method contains all pre-inversion checks.

_refcast(self, x)
Helper function to cast arrays to the internal dtype.

_set_dtype(self, t)

_set_output_dim(self, n)

_stop_training(self, *args, **kwargs)

copy(self, protocol=None)
Return a deep copy of the node.

execute(self, x, *args, **kwargs)
Process the data contained in x.

get_current_train_phase(self)
Return the index of the current training phase.

get_dtype(self)
Return dtype.

get_input_dim(self)
Return input dimensions.

get_output_dim(self)
Return output dimensions.

get_remaining_train_phase(self)
Return the number of training phases still to accomplish.

get_supported_dtypes(self)
Return dtypes supported by the node as a list of numpy.dtype objects.

has_multiple_training_phases(self)
Return True if the node has multiple training phases.

inverse(self, y, *args, **kwargs)
Invert y.

is_training(self)
Return True if the node is in the training phase, False otherwise.

save(self, filename, protocol=-1)
Save a pickled serialization of the node to filename. If filename is None, return a string.

set_dtype(self, t)
Set internal structures' dtype.

set_input_dim(self, n)
Set input dimensions.

set_output_dim(self, n)
Set output dimensions.

stop_training(self, *args, **kwargs)
Stop the training phase.

Static Methods

[hide private]

Inherited from Node

is_invertible()
Return True if the node can be inverted, False otherwise.

is_trainable()
Return True if the node can be trained, False otherwise.

Instance Variables

[hide private]

graph
The corresponding mdp.graph.Graph object.

Properties

[hide private]

Inherited from object: __class__

Inherited from Node

_train_seq
List of tuples:

dtype
dtype

input_dim
Input dimensions

output_dim
Output dimensions

supported_dtypes
Supported dtypes

Method Details

[hide private]

init(self, start_poss=None, eps_b=0.2, eps_n=0.006, max_age=50, lambda_=100, alpha=0.5, d=0.995, max_nodes=2147483647, input_dim=None, dtype=None)
(Constructor)

Initializes an object of type 'GrowingNeuralGasNode'.

:param start_poss: Sequence of two arrays containing the position of the
    first two nodes in the GNG graph. If unspecified, the
    initial nodes are chosen with a random position generated
    from a gaussian distribution with zero mean and unit
    variance.
:type start_poss: list, tuple, numpy.ndarray

:param eps_b: Coefficient of movement of the nearest node to a new data
    point. Typical values are 0 < eps_b << 1 .

    Default: 0.2
:type eps_b: float

:param eps_n: Coefficient of movement of the neighbours of the nearest
    node to a new data point. Typical values are
    0 < eps_n << eps_b .

    Default: 0.006
:type eps_n: float

:param max_age: Remove an edge after `max_age` updates. Typical values are
    10 < max_age < lambda.

    Default: 50
:type max_age: int

:param lambda_: Insert a new node after `lambda_` steps. Typical values are O(100).

    Default: 100
:type lambda_: int

:param alpha: When a new node is inserted, multiply the error of the
    nodes from which it generated by 0<alpha<1. A typical value
    is 0.5.

    Default: 0.5
:type alpha: float

:param d: Each step the error of the nodes are multiplied by 0<d<1.
    Typical values are close to 1.

    Default: 0.995
:type d: float

:param max_nodes: Maximal number of nodes in the graph.
:type max_nodes: int

:param input_dim: The input dimensionality.
:type input_dim: int

:param dtype: The datatype.
:type dtype: numpy.dtype or str

Overrides: object.__init__

_add_edge(self, from_, to_)

_add_node(self, pos)

_get_nearest_nodes(self, x)

Return the two nodes in the graph that are nearest to x and their
squared distances.
:param x: Coordinates of point to compute distance to in order to
    specifiy nearest nodes.
:type x: numpy.ndarray

:return: The coordinates of the nearest two nodes and their
    distances to x. ([node1, node2], [dist1, dist2])
:rtype: tuple

_insert_new_node(self)

Insert a new node in the graph where it is more necessary (i.e. where the error is the largest).

_move_node(self, node, x, eps)

Move a node by eps in the direction x.

Parameters:

node () - The node to move.
x (numpy.ndarray) - The point to move in the direction of.
eps (float) - The distance to move.

_remove_old_edges(self, edges)

Remove all edges older than the maximal age.

Parameters:

edges () - Candidates that are considered to be removed.

_set_input_dim(self, n)

Overrides: Node._set_input_dim

_train(self, input)

Overrides: Node._train

get_nodes_position(self)

nearest_neighbor(self, input)

Assign each point in the input data to the nearest node in the graph. Return the list of the nearest node instances, and the list of distances.

Executing this function will close the training phase if necessary.

Parameters:

input (numpy.ndarray) - Points to find the nearest node in the graph to.

Returns: tuple

The list of the nearest node instances and the list of distances.

train(self, input)

Update the internal structures according to the input data x.

x is a matrix having different variables on different columns and observations on the rows.

By default, subclasses should overwrite _train to implement their training phase. The docstring of the _train method overwrites this docstring.

Note: a subclass supporting multiple training phases should implement the same signature for all the training phases and document the meaning of the arguments in the _train method doc-string. Having consistent signatures is a requirement to use the node in a flow.

Overrides: Node.train

Instance Variable Details

[hide private]

graph

The corresponding mdp.graph.Graph object.

Class GrowingNeuralGasNode

__init__(self, start_poss=None, eps_b=0.2, eps_n=0.006, max_age=50, lambda_=100, alpha=0.5, d=0.995, max_nodes=2147483647, input_dim=None, dtype=None) (Constructor)

_add_edge(self, from_, to_)

_add_node(self, pos)

_get_nearest_nodes(self, x)

_insert_new_node(self)

_move_node(self, node, x, eps)

_remove_old_edges(self, edges)

_set_input_dim(self, n)

_train(self, input)

get_nodes_position(self)

nearest_neighbor(self, input)

train(self, input)

graph

init(self, start_poss=None, eps_b=0.2, eps_n=0.006, max_age=50, lambda_=100, alpha=0.5, d=0.995, max_nodes=2147483647, input_dim=None, dtype=None)
(Constructor)