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Modular toolkit for Data Processing MDP
Package mdp :: Package nodes :: Class NeuralGasNode
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Class NeuralGasNode

Learn the topological structure of the input data by building a corresponding graph approximation (original Neural Gas algorithm).


Reference

The Neural Gas algorithm was originally published in Martinetz, T. and Schulten, K.: A "Neural-Gas" Network Learns Topologies. In Kohonen, T., Maekisara, K., Simula, O., and Kangas, J. (eds.), Artificial Neural Networks. Elsevier, North-Holland., 1991.

Instance Methods [hide private]
 
__init__(self, num_nodes=10, start_poss=None, epsilon_i=0.3, epsilon_f=0.05, lambda_i=30.0, lambda_f=0.01, max_age_i=20, max_age_f=200, max_epochs=100, n_epochs_to_train=None, input_dim=None, dtype=None)
Initializes an object of type 'NeuralGasNode'.
list
_rank_nodes_by_distance(self, x)
Return the nodes in the graph in a list ranked by their squared distance to x.
 
_remove_old_edges(self, max_age)
Remove all edges older than the maximal age.
 
_train(self, input)
 
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 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.
 
_set_input_dim(self, n)
 
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.
    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.
  max_epochs
Maximum number of epochs until which to train.
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, num_nodes=10, start_poss=None, epsilon_i=0.3, epsilon_f=0.05, lambda_i=30.0, lambda_f=0.01, max_age_i=20, max_age_f=200, max_epochs=100, n_epochs_to_train=None, input_dim=None, dtype=None)
(Constructor)

 

Initializes an object of type 'NeuralGasNode'.

Default parameters taken from the original publication.

Parameters:
  • num_nodes (int) - Number of nodes to use. Ignored if start_poss is given. Default is 10.
  • start_poss (list, tuple or numpy.ndarray) - Sequence of two arrays containing the position of the first two nodes in the GNG graph. In unspecified, the initial nodes are chosen with a random position generated from a gaussian distribution with zero mean and unit variance. Default is None.
  • epsilon_i (float) - Initial value of epsilon. Fraction of the distance between the closest node and the presented data point by which the node moves towards the data point in an adaptation step. Epsilon decays during training by e(t) = e_i(e_f/e_i)^(t/t_max) with t being the epoch. Default is 0.3.
  • epsilon_f (float) - Final value of epsilon. Fraction of the distance between the closest node and the presented data point by which the node moves towards the data point in an adaptation step. Epsilon decays during training by e(t) = e_i(e_f/e_i)^(t/t_max) with t being the epoch. Default is 0.05.
  • lambda_i (float) - Initial value of lambda. Lambda influences how the weight change of nodes in the ranking decreases with lower rank. It is sometimes called the "neighborhood factor". Lambda decays during training in the same manner as epsilon does. Default is 30. .
  • lambda_f (float) - Final value of lambda. Lambda influences how the weight change of nodes in the ranking decreases with lower rank. It is sometimes called the "neighborhood factor". Lambda decays during training in the same manner as epsilon does. Default is 0.01.
  • max_age_i (int) - Initial lifetime, after which an edge will be removed. Lifetime is measured in terms of adaptation steps, i.e., presentations of data points. It decays during training like epsilon does. Default is 20.
  • max_age_f (int) - Final lifetime, after which an edge will be removed. Lifetime is measured in terms of adaptation steps, i.e., presentations of data points. It decays during training like epsilon does. Default is 200.
  • max_epochs (int) - Number of epochs to train. One epoch has passed when all data points from the input have been presented once. The default in the original publication was 40000, but since this has proven to be impractically high too high for many real-world data sets, we adopted a default value of 100.
  • n_epochs_to_train (int) - Number of epochs to train on each call. Useful for batch learning and for visualization of the training process. Default is to train once until max_epochs is reached.
  • input_dim (int) - The input dimensionality.
  • dtype (numpy.dtype or str) - The datatype.
Overrides: object.__init__

_rank_nodes_by_distance(self, x)

 
Return the nodes in the graph in a list ranked by their squared distance to x.
Parameters:
  • x (numpy.ndarray) - Point to compute distance to.
Returns: list
List of nodes ordered by the distance of the node to x.

_remove_old_edges(self, max_age)

 
Remove all edges older than the maximal age.
Parameters:
  • edges () - Candidates that are considered to be removed.
Overrides: GrowingNeuralGasNode._remove_old_edges

_train(self, input)

 
Overrides: Node._train

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.

max_epochs

Maximum number of epochs until which to train.

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Modular toolkit for Data Processing MDP
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