Package mdp :: Package nodes :: Class FDANode
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Class FDANode


Perform a (generalized) Fisher Discriminant Analysis of its
input. It is a supervised node that implements FDA using a
generalized eigenvalue approach.

FDANode has two training phases and is supervised so make sure to
pay attention to the following points when you train it:

- call the 'train' function with *two* arguments: the input data
  and the labels (see the doc string of the train method for details)
  
- if you are training the node by hand, call the train function twice

- if you are training the node using a flow (recommended), the
  only argument to Flow.train must be a list of (data_point,
  label) tuples or an iterator returning lists of such tuples,
  *not* a generator.  The Flow.train function can be called just
  once as usual, since it takes care of "rewinding" the iterator
  to perform the second training step.

More information on Fisher Discriminant Analysis can be found for
example in C. Bishop, Neural Networks for Pattern Recognition,
Oxford Press, pp. 105-112.
              
Internal variables of interest:
self.avg -- Mean of the input data (available after training)
self.v -- Transposed of the projection matrix, so that
          output = dot(input-self.avg, self.v)
          (available after training)

Nested Classes [hide private]
    Inherited from Node
  __metaclass__
This Metaclass is meant to overwrite doc strings of methods like execute, stop_training, inverse with the ones defined in the corresponding private methods _execute, _stop_training, _inverse, etc...
Instance Methods [hide private]
 
__init__(self, input_dim=None, output_dim=None, dtype=None)
If the input dimension and the output dimension are unspecified, they will be set when the 'train' or 'execute' method is called for the first time.
 
_check_train_args(self, x, cl)
 
_execute(self, x, range=None)
Compute the output of the FDA projection.
 
_get_supported_dtypes(self)
Return the list of dtypes supported by this node.
 
_get_train_seq(self)
 
_inverse(self, y)
 
_stop_fda(self)
Solve the eigenvalue problem for the total covariance.
 
_stop_means(self)
Calculate the class means.
 
_train(self, x, cl)
Update the internal structures according to the input data 'x'.
 
_train_fda(self, x, cl)
Gather data for the overall and within-class covariance
 
_train_means(self, x, cl)
Gather data to compute the means and number of elements.
 
_update_SW(self, x, lbl)
Update the covariance matrix of the class means.
 
_update_means(self, x, lbl)
Update the internal variables that store the data for the means.
 
execute(self, x, *args, **kargs)
Compute the output of the FDA projection.
 
train(self, x, *args, **kwargs)
Update the internal structures according to the input data 'x'.

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

    Inherited from Node
 
__add__(self, other)
 
__call__(self, x, *args, **kargs)
Calling an instance of Node is equivalent to call its 'execute' method.
 
__repr__(self)
repr(x)
 
__str__(self)
str(x)
 
_check_input(self, x)
 
_check_output(self, y)
 
_if_training_stop_training(self)
 
_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_input_dim(self, n)
 
_set_output_dim(self, n)
 
_stop_training(self, *args, **kwargs)
 
copy(self, protocol=-1)
Return a deep copy of the node.
 
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.
 
inverse(self, y, *args, **kargs)
Invert 'y'.
 
is_invertible(self)
Return True if the node can be inverted, False otherwise.
 
is_trainable(self)
Return True if the node can be trained, False otherwise.
 
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.
Properties [hide private]

Inherited from object: __class__

    Inherited from Node
  _train_seq
List of tuples: [(training-phase1, stop-training-phase1), (training-phase2, stop_training-phase2), ...
  dtype
dtype
  input_dim
Input dimensions
  output_dim
Output dimensions
  supported_dtypes
Supported dtypes
Method Details [hide private]

__init__(self, input_dim=None, output_dim=None, dtype=None)
(Constructor)

 
If the input dimension and the output dimension are
unspecified, they will be set when the 'train' or 'execute'
method is called for the first time.
If dtype is unspecified, it will be inherited from the data
it receives at the first call of 'train' or 'execute'.

Every subclass must take care of up- or down-casting the internal
structures to match this argument (use _refcast private
method when possible).

Overrides: object.__init__
(inherited documentation)

_check_train_args(self, x, cl)

 
Overrides: Node._check_train_args

_execute(self, x, range=None)

 
Compute the output of the FDA projection.

if 'range' is a number, then use the first 'range' functions.
if 'range' is the interval=(i,j), then use all functions
between i and j.

Overrides: Node._execute

_get_supported_dtypes(self)

 
Return the list of dtypes supported by this node.

Overrides: Node._get_supported_dtypes

_get_train_seq(self)

 
Overrides: Node._get_train_seq

_inverse(self, y)

 
Overrides: Node._inverse

_stop_fda(self)

 
Solve the eigenvalue problem for the total covariance.

_stop_means(self)

 
Calculate the class means.

_train(self, x, cl)

 
Update the internal structures according to the input data 'x'.

x -- a matrix having different variables on different columns
     and observations on the rows.
cl -- can be a list, tuple or array of labels (one for each data point)
      or a single label, in which case all input data is assigned to
      the same class.

Overrides: Node._train

_train_fda(self, x, cl)

 
Gather data for the overall and within-class covariance

_train_means(self, x, cl)

 
Gather data to compute the means and number of elements.

_update_SW(self, x, lbl)

 
Update the covariance matrix of the class means.

x -- Data points from a single class.
lbl -- The label for that class. 

_update_means(self, x, lbl)

 
Update the internal variables that store the data for the means.

x -- Data points from a single class.
lbl -- The label for that class. 

execute(self, x, *args, **kargs)

 
Compute the output of the FDA projection.

if 'range' is a number, then use the first 'range' functions.
if 'range' is the interval=(i,j), then use all functions
between i and j.

Overrides: Node.execute

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

 
Update the internal structures according to the input data 'x'.

x -- a matrix having different variables on different columns
     and observations on the rows.
cl -- can be a list, tuple or array of labels (one for each data point)
      or a single label, in which case all input data is assigned to
      the same class.

Overrides: Node.train