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.

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.

Attributes and methods of interest

graph -- The corresponding mdp.graph.Graph object

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)
Growing Neural Gas algorithm.

_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. (Return ([node1, node2], [dist1, dist2])

_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)

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.

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 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.

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)

Growing Neural Gas algorithm.

Parameters:

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.
eps_b - coefficient of movement of the nearest node to a new data point. Typical values are 0 < eps_b << 1 .

Default: 0.2
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
max_age - remove an edge after max_age updates. Typical values are 10 < max_age < lambda.

Default: 50
lambda_ - insert a new node after lambda_ steps. Typical values are O(100).

Default: 100
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
d - each step the error of the nodes are multiplied by 0<d<1. Typical values are close to 1.

Default: 0.995
max_nodes - maximal number of nodes in the graph.

Default: 2^31 - 1

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. (Return ([node1, node2], [dist1, dist2])

_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)

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.

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

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)

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)