Package mdp :: Package nodes :: Class GrowingNeuralGasNode
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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.
 
_insert_new_node(self)
Insert a new node in the graph where it is more necessary (i.e.
 
_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.
 
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`.
 
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